PROTOTYPE AND
CONTEXTUALIZED
DAILY LESSON
PLANS IN
GRADE 6
MATHEMATICS
QUARTER 3
i
ii
ACKNOWLEDGMENT
With deep appreciation and gratitude for the expertise and collaborative
efforts of various individuals on the writing, editing, validating, and printing of the
Contextualized Prototype Daily Lesson Plans in Mathematics 6 ( Third Quarter).
WRITERS
Jean P. Guiriba
Eugene C. Cervantes
Benelyn D. Bueta
Linda S. Dela Rosa
Rey H. Robeso
Liza Marie A. Abelita
Efren A. Alita. Jr.
Lowelyn P. Alteza
Moralyn D. Olayvar
Christy D. Isidera
Ruby S. Gutierrez
DEMONSTRATION TEACHERS
Ruby S. Gutierrez
Jean P. Guiriba
Eugene C. Cervantes
Rey H. Robeso
Moralyn D. Olayvar
Lowelyn P. Alteza
Efren A. Alita, Jr.
Christy D. Isidera
LAYOUT ARTISTS
Joevylyn C. Ruiz
Ronaldo Z. Ongotan
John Cedric A. Jacobo
EDITORS / VALIDATORS
Vivian D. Caballero
Ruchel C. Taumatorgo
Nathan A. Campo
Mary Joy M. Romero
Janet Z. Dumangas
EPS, Mathematics
Judy M. Quinanola
Emie D. Rapsing
Dinnah A. Banares
EPS, LRMDS
Noel D. Logronio
Chief, Curriculum Implementation Division
Lauro B. Millano
OIC, Assistant Schools Division Superintendent
Norma B. Samantela, CESO VI
Schools Division Superintendent
iii
TABLE OF CONTENTS
THIRD QUARTER
Week/Day
Lesson/Topic
Page
Visualizing and Describing the Different Solid Figures:
Cube, Prism, Pyramid, Cylinder, Cone and Sphere
Visualizing and Describing the Different Solid Figures:
Cube, Prism and Pyramid
Visualizing and Describing the Different Solid Figures:
Cylinder, Cone and Sphere
Differentiating Solid Figures from Plane Figures
Differentiating Solid Figures from Plane Figures
1- 5
WEEK 1
Day 1
Day 2
Day 3
Day 4
Day 5
6 - 11
12- 17
18 - 23
24 -29
WEEK 2
Day 1
Day 2
Day 3
Day 4
Day 5
Illustrating the Different Solid Figures Using Various
Concrete and Pictorial Models
Illustrating the Different Solid Figures Using Various
Concrete and Pictorial Models
Identifying the Faces of a Solid Figure
Identifying the Faces of a Solid Figure
Identifying the Faces of a Solid Figure
30 - 34
Visualizing and Describing the Different Solid Figures:
Cube, Prism, Pyramid, Cylinder, Cone and Sphere
Visualizing and Describing the Different Solid Figures:
Cube, Prism, Pyramid, Cylinder, Cone and Sphere
Visualizing and Describing the Different Solid Figures:
Cube, Prism, Pyramid, Cylinder, Cone and Sphere
Identifying the Nets of the Following Space Figures:
Cube, Prism, Pyramid, Cylinder, Cone and Sphere
Using Plane Figures
Identifying the Nets of the Following Space Figures:
Cube, Prism, Pyramid, Cylinder, cone and Sphere
Using Plane Figures
57 - 69
35 - 40
41 - 45
46 - 50
51 - 56
WEEK 3
Day 1
Day 2
Day 3
Day 4
Day 5
70 - 76
77 - 88
89 - 97
98 - 104
WEEK 4
Day 1
Day 2
Day 3
Day 4
Day 5
Formulating the Rule in Finding the nth Term Using
Different Strategies
Formulating the Rule in Finding the nth Term Using
Different Strategies
Formulating the Rule in Finding the nth Term Using
Different Strategies
Differentiating Expression from Equation
105 - 108
Differentiating Expression from Equation
122 - 125
Giving the Translation of Real-life Verbal Expressions
and Equations into Letters or Symbols and Vice versa
126 - 131
109 - 112
113 - 116
117 - 121
WEEK 5
Day 1
iv
Day 2
Day 3
Day 4
Day 5
Giving the Translation of Real-life Verbal Expressions
and Equations into Letters or Symbols and Vice Versa
Defining a Variable in an Algebraic Expression and
Equation
Defining a Variable in an Algebraic Expression and
Equation
Representing Quantities in Real-Life Situations Using
Algebraic Expressions and Equations
132 - 136
Solving Routine and Non-Routine Problems Involving
Different Types of Numerical Expressions and
Equations
Solving Routine and Non-Routine Problems Involving
Different Types of Numerical Expressions and
Equations
Solving Routine and Non-Routine Problems Involving
Different Types of Numerical Expressions and
Equations
Creating Routine and Non- Routine Problems
Involving Numerical Expressions and Equations
Creating Routine and Non-Routine Problems Involving
Numerical Expressions and Equations
151 - 155
Calculating Speed
Calculating Distance
Calculating Time
Solving Problems Involving Average Rate and Speed
Solving Problems Involving Average Rate and Speed
170 - 174
171 - 182
183 - 189
190 - 198
199 - 208
Finding the Area of Composite Figures Formed by
Two or More of the Following; Triangle, Square,
Rectangle, Circle and Semi-Circle
Finding the Area of Composite Figures Formed by
Two or More of the Following: Triangle, Square,
Rectangle, Circle and Semi-Circle
Finding the Area of Composite Figures Formed by
Two or More of the Following: Triangle, Square,
Rectangle, Circle and Semi- Circle
Solves Routine and Non-Routine Problems Involving
Area of Composite Figures Formed by Any Two or
More of the Following: Triangle, Square, Rectangle,
Circle and Semi-Circle
Solves Routine and Non-Routine Problems Involving
Area of Composite Figures Formed by any Two or
More of the Following: Triangle, Square, Rectangle,
Circle and Semi-Circle
209 - 213
Visualizing and Describing Surface Area and Naming
the Unit of Measure Used for Measuring the Surface
Area of Solid/Space Figures
235 - 239
137 - 141
142- 145
146 - 150
WEEK 6
Day 1
Day 2
Day 3
Day 4
Day 5
156 - 156
157 - 159
160 - 163
164 - 169
WEEK 7
Day 1
Day 2
Day 3
Day 4
Day 5
WEEK 8
Day 1
Day 2
Day 3
Day 4
Day 5
214 - 217
218 - 222
223 - 229
230 - 234
WEEK 9
Day 1
v
Day 2
Day 3
Day 4
Day 5
Deriving a Formula for Finding the Surface Area of
Cubes, Prisms, Pyramids, Cylinders, Cones and
Spheres
Deriving a Formula for Finding the Surface Area of
Cubes, Prisms, Pyramids, Cylinders, Cones and
Spheres
Finding the Surface Area of Cubes, Prisms, Pyramids,
Cylinders, Cones and Spheres
Finding the Surface Area of Cubes, Prisms,
Pyramids,
Cylinders, Cones and Spheres
240 - 243
Solving Word Problems Involving Measurement of
Surface Area of Prism
Solving Word Problems Involving Measurement of
Surface Area of Pyramid
Solving Word Problems Involving Measurement of
Surface Area of Cone
Solving Word Problems Involving Measurement of
Surface Area of Cylinder
Solving Word Problems Involving Measurement of
Surface Area of Sphere
257 - 261
244 - 248
249 - 252
253 - 256
WEEK 10
Day 1
Day 2
Day 3
Day 4
Day 5
Table of Specification Pre-Test
Pre-Test
Table of Specification Post-Test
Post-Test
262 - 266
267 - 270
271 - 274
275 - 278
279 - 280
281 - 284
285 - 286
287 - 290
vi
School:
Teacher:
Dates and Day:
Week 1- Day 1
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of solid
figures.
The leaner able to construct and describe the
different solid figures.
The learner visualizes and describes the different
solid figures: cube, prism, pyramid, cylinder, cone and
sphere.
Code: M6GE-IIIa-27
II.CONTENT
Visualizing and Describing the Different Solid
Figures: Cube, Prism, Pyramid, Cylinder, Cone and
Sphere.
Subject Integration: MAPEH (Arts)
III. LEARNING RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials Pages
3.Textbook Pages
4. Additional Materials from
Learning Resources (LR)
Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide, 2016. Grade 5
page 160
Mathletes 6, pages 156 - 199
Marker, pictures (ice cream cone, tire, balloon, etc.)
Manila paper Power Point Presentation Colored
papers real objects (blocks, ball, etc.), pictures from
www.shutterstock.com, www.goggle.com
IV. PROCEDURES
A. Review Previous
Lessons


Recalling the common shapes
Describing each shape
1
Guessing Game
What are the common shapes you know?
Name of the Shape
B. Establishing purpose for
the Lesson
C. Presenting Examples /
instances of the new lesson
Figure
Description

Circle
- round

Square
- the sides have
the same length

Triangle
- 3 sides

Rectangle
- have 2 long
(parallel) and 2 short
sides (vertical)
Look around and outside our classroom. Cite
examples of objects/things with three dimensions.
Ask: What/Which space figure it represents?
Advance Learners
Average Learners
I. Connect the
figure/s to its name:
I. Connect the figures to
its common object:
sphere
cube
prism
pyramid
cone
cylinder
1. The pupils will paste the figures and pictures
on a manila paper/cartolina.
2. After 5 minutes they will present their output.
3. The teacher will check their answer.
2
D. Discussing new
concepts and practicing
new skills # 1
Using Direct Instruction:
Show the pupils pictures of solid figures in a table
presentation.
Picture of SL
Name
Picture
Pyramid
cone
sphere
cube
cylinder
rectangular prism
What are the solid figures shown in the chart?
How many solid figures are there in all?
E. Discussing New
Concepts and Practicing
New Skills # 2
F. Developing Mastery
Aside from the picture-examples given in each solid
figure, can you give more objects which look like the
solid figures above? Cite at least 3 examples of
each solid figure.
What is a solid figure?
Group Activity
(Differentiated Instruction)
Direction: Do the following:
 Group 1
 Draw a common object for each solid
figure and name it.
3
Picture of
Solid Figure
Drawing
Name of the
Drawing
Group 2
 Encircle the picture that looks like the solid
figures below: (printed in a bondpaper)
Solid Figure
4
G. Practical Application
What are the solid figures that we commonly use
in building a house?
H. Making Generalizations
I. Evaluation
a. What is a solid figure?
A solid figure has three dimensions:
length, width and height.
b. What are the solid figures that we learned
today?
Advance Learners
Average Learners
Direction: Write the name
Direction: Write the name
of the solid figures:
of the solid figures
1.
1.
2.
2.
3.
3.
J. Additional Activities
4.
4.
5.
5.
Write at least 5 equipment / appliances inside your
home that look like the solid figures discussed.
V. REMARKS
VI. REFLECTIONS
5
School:
Teacher:
Dates and Day:
Week 1- Day 2
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of solid
figures.
The learner able to construct and describe the
different solid figures.
The learner visualizes and describes the different
solid figures: cube, prism, pyramid, cylinder, cone and
sphere.
Code: M6GE-IIIa-27
II.CONTENT
Visualizing and Describing the Different Solid
Figures: Cube, Prism, Pyramid, Cylinder, Cone and
Sphere.
UNPACKED LEARNING COMPETENCY:
Describing the Different Solid Figures: Cube,
Prism, and Pyramid.
Subject Integration: English
III. LEARNING RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials Pages
3.Textbook Pages
4. Additional Materials from
Learning Resources (LR)
Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6,
pp. 160
Mathletes 6, pages 156 - 199
Marker, blocks of different solid figures, real objects
like: ball, drinking glass, shoe box, soda container,
pictures of: food pyramid, party hat, mountain and
table
IV. PROCEDURES
A. Review Previous
Lessons
 Show the models of different solid figures and
let the pupils give the name of each, like:
6
Solid Figure
Name of the Solid
Figure
Pyramid
Rectangular Prism
Rectangular Pyramid
Triangular Prism
Triangular Pyramid
Pentagonal Prism
 Have them give at least 2 examples of objects
that resembles the shapes.
Game – “Describe Me”
 Group the class into 5. Each group will choose
their place in any corner of the classroom.
 Each group will have a flaglet to raise to
describe the solid figure shown by the teacher.
 The teacher will show the picture of a solid
figure and any member of the group can
describe it.
7
 The group who will raise their flaglet “first” will
describe the shown solid figure as such:
Solid Figure
Name
Description
Rectangular
Prism
(Pupils answers
may vary)
Cube
(Pupils answers
may vary)
pyramid
(Pupils answers
may vary)
 The group who have describe the solid figure
most, will have plus points in “Performance
Tasks”.
B. Establishing purpose for
the Lesson
C. Presenting Examples /
instances of the new lesson
Advance Learners
Average Learners
Direction: Connect the
statement that describes
the solid figure:
Direction: Encircle the
word/s that best describe
the solid figure.
A
B
1. have 5 faces a. prism
and 8 edges
1.
2. a solid figure b. cube
which has 12
edges an 8
corners
2.
( 8 edges, 6 edges)
( 5 faces, 4 faces)
3.
3. have 8
c. pyramid
corners and
6 equal faces
8
(8 corners, 10 corners)
 The teacher may
assists the pupils in
answering the activity
through reading
1. The activity had been written on a manila
paper/cartolina;
2. Pupils will present their output after 5
minutes;
3. The teacher will assess the answers of the
pupils.
D. Discussing new
concepts and practicing
new skills # 1
 Maybe
presented
on
presentation.
 Show the table below:
a
powerpoint
Show the pupils pictures of solid figures in a table
presentation.
Solid Figure
Name
pyramid
cube
Description
1 square base, and 4
triangular
sides,
have 8 edges
5 equal faces, 1
square base, 12
edges and 8 corners
6 faces, have 12
Rectangular edges and have 8
prism
corners
What are the three solid figures shown in the table?
Do these solid figures have height, width and length?
E. Discussing New
Concepts and Practicing
New Skills # 2
If these, solid figures have height, width and length,
describe each solid figure.
What is a solid figure?

While showing the solid figures, show and
count the faces, edges and corners of each.
F. Developing Mastery
Group Activity
Direction: Do the following:
 Group 1
9
 Draw 3 solid figures and describe each.
Solid Figure
1.
2.
3.
Description
Group 2
 Encircle the solid figure described by the
statements below:
1. A ( pyramid, prism, cube ) is a solid figure
that have 8 edges and 6 equal faces).
2. The solid figure that have 12 edges and 8
corners is ( pyramid, cube, prism ).
3. The ( pyramid, prism, cube ) have 5 faces
and 8 edges.
 Group 3
 Choose the correct answer inside the box.
pyramid
prism
cube
1. A solid figure that have 5 faces and 8 edges.
2. The
have 8 edges and 6 equal faces.
3. This the solid figure that have 6 faces, have
12 edges and have 8 corners.
 Group 4
 Using the manipulative objects/blocks
(prism, cube, pyramid) fill in the needed
information about the solid figure.
Solid Figures
1. Prism
2. Cube
3. Pyramid
10
How Many…?
Faces Edges Corners Faces Edges Corners Faces Edges Corners -
 The pupils will present their output after 10
minutes;
 The teacher will check the answers of the
pupils;
 Asks: (Valuing)
a.
How did you find the activity?
b.
Are all group members participated in
the activities?
c.
What did you do to describe the given
solid figures?
G. Practical Applications
H. Making Generalizations
I. Evaluation
Describe the shape of a cabinet, camp tent, rubik
cube, hollow block.
a. Identify the solid figures you learned today.
b. How will you describe each figure?
Advance Learners
Average Learners
Direction: Describe each Direction: Encircle the
solid figure.
solid figure that being
described:
1. Rectangular Prism
1. Faces: 5
–
Edges: 8
Corners: 5
2. Cube –
2. Faces: 6
Edges: 12
Corners: 8
3. Pyramid –
 Use your
rubrics
J. Additional Activities
3. Equal Faces: 6
Edges: 12
own
Corners: 8
Describe the following:
1. a pencil box
2. a rectangular chocolate bar
3. a diamond
V. REMARKS
VI. REFLECTIONS
11
School:
Teacher:
Dates and Day:
Week 1- Day 3
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of solid
figures.
The learner able to construct and describe the
different solid figures.
The learner visualizes and describes the different
solid figures: cube, prism, pyramid, cylinder, cone and
sphere.
Code: M6GE-IIIa-27
II.CONTENT
Visualizing and Describing the Different Solid
Figures: Cube, Prism, Pyramid, Cylinder, Cone and
Sphere.
UNPACKED LEARNING COMPETENCY:
Describing the Different Solid Figures: Sphere,
Cone and Cylinder
Subject Integration: English (Reading)
III. LEARNING RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials Pages
3.Textbook Pages
4. Additional Materials from
Learning Resources (LR)
Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6,
page 160
Mathletes 6, pages 156 - 199
Marker, blocks of different solid figures, real objects
like: drinking glass, soda container, ball, balloon,
plate, ice cream cone, road signs, pictures from:
www.shutterstock.com and www.google.com
IV. PROCEDURES
A. Review Previous
Lessons
 Recall the three (3) solid figures discussed
yesterday.
 Flash the picture of cube, prism and pyramid
one at a time.
12
 Have pupils describe each solid figure.
B. Establishing purpose for
the Lesson
Did you win any contest? What contest was it? What did
you feel? How did you win the contest? What made you
win the said activity?
Elicit the importance of teamwork/cooperation in
participating contest/doing an activity.
C. Presenting Examples /
instances of the new lesson Group Activity
 Group the class into 3.
 Each group will be given a solid figure like:
cylinder (for Group 1); cone (for Group 2) and
sphere (for Group 3).
 Each member of the group will give an
example of object that looks like the solid figure
assigned to them.
 The group will give two words to describe the
solid figure.
 The group who had described the solid figure
will have plus points in “Performance Tasks”.
D. Discussing new
concepts and practicing
new skills # 1
Advance Learners
Average Learners
Direction: Write one or
two words that describe/s
the solid figure.
Direction: Connect the
solid figures to the
word/s that best
describe them:
1.
A
B
1.
a. 1 base
1 vertex
2.
b. 1 surface
0 corners
3.
c. 2 faces
0 corners
2.
3.
13
 The activity had been written on a Manila
paper/cartolina;
 Pupils will present their output after 5 minutes;
 The teacher will assess the answers of the
pupils.
E. Discussing New
Concepts and Practicing
New Skills # 2
 Maybe
presented
presentation.
 Show the table below:
in
a
powerpoint
Show the pictures of solid figures in a table
presentation.
Solid Figure
Name
Description
cone
have 1 circular base
have 1 vertex and
no edges
sphere
1 curved surface
and no edges and
corners
cylinder
have 2 circular
bases and no
corners and edges
LOTS:
a. Name the 3 solid figures shown in the table.
b. Cite an example on each solid figure.
c. How many vertices does the cone have?
d. How many bases does the cylinder have?
e. How many surface does the sphere have?
HOTS:
a. Are these solid figures useful? Why and/or why
not?
b. Describe each solid figure.

While showing the solid figures, show its
bases, faces, edges, corners and/or vertices.
14
F. Developing Mastery
Differentiated Instruction:
Group 1
Direction: Encircle the solid figure that is best
described by the statement.
1. This solid figure have 1 vertex and 1 circular
base. ( cone, sphere, cylinder)
2. A (cone, sphere, cylinder) has 1 curved
surface and no edges.
3. It is the (cone, sphere, cylinder) that has 2
circular bases and no corners.
*(the teacher will assists the pupils in reading the
sentences).
Group 2
Direction: Color the solid figure that being
described on the first column.
Description
Solid Figure
1. Bases: 2
Corners: 0
Edges: 0
Vertex: 0
2. Faces: 1
Corners: 0
Edges: 0
Vertex: 0
3. Faces: 1
Corners: 0
Edges: 0
Vertex: 1
Group 3
Direction: Connect the solid figure to the
informations that describe it:
1.
a. 1 curved surface
0 edges
0 vertex
15
2.
b. 2 circular bases
No edges
No corners
3.
c. 1 circular base
1 vertex
no corners
Group 4
Direction: Fill in the needed information.
(Group members will use the manipulative devices)
1.
This solid figure has ____ circular
bases, ____ edges and corners.
2.
The cone has ______ vertex,
____ base and _____ corners.
3.
The sphere has __ corners and _______
circular base the sphere have.
 The pupils will present their output after 10
minutes;
 The teacher will check the answers of the
pupils;
 Asks: (Valuing)
a. How did you find the activity?
b. Are all group members participated in
the activities?
c. What did you do to describe the given
solid figures?
16
G. Practical Application
Describe the following objects:
1.
2.
3.
4.
5.
Christmas ball
Ice cream cone
Can of sardines
Party hat
Basketball
H. Making Generalizations
a. What are the solid figures you have learned
today?
b. Describe each figure.
I. Evaluation
Advance Learners
Average Learners
Direction: Describe each Direction: Describe each
solid figures.
solid figure.
1. Cylinder–
1.
2. Cone –
2.
3. Sphere –
3.
J. Additional Activities
Direction:
Describe the following:
1. Shape of a cylindrical water container?
2. Shape of wheel of a car?
3. Shape of a circular chair?
V. REMARKS
VI. REFLECTIONS
17
School:
Teacher:
Dates and Day:
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
Week 1- Day 4
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
The learner demonstrate understanding of solid
figures.
The learner is able to construct and describe the
different solid figures.
The learner differentiates solid figure from plane
figures.
Code: M6GE-IIIa-28
II.CONTENT
Differentiating Solid Figures from Plane Figures
Subject Integration: English (Reading)
III. LEARNING RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials Pages
3.Textbook Pages
4. Additional Materials from
Learning Resources (LR)
Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6
page 160
Mathletes 6, pages 156 - 199
Marker, pictures or real objects of different solid
figures and plane figures like: drinking glass, soda
container, ball, balloon, plate, ice cream cone, road
signs,
IV. PROCEDURES
A. Review Previous
Lessons
 Show solid figures like cone, cylinder and
sphere.
 Have pupils describe each solid figure.
18
B. Establishing purpose for
the Lesson
Ask the importantance of cooperation/teamwork in
accomplishing a task or an activity.
How will you do it in your group?
C. Presenting Examples /
Game: “WHAT are WE?”
instances of the new lesson
 Divide the class into 4 (2 groups for the boys
and 2 groups for the girls)
 Each group will be given pictures of solid
figures and plane figures.
 Each group will paste the pictures on the board
and classify them if it is a solid figure or a plane
figure.
 After classifying, each group will differentiate
solid figures from plane figures and/or vice
versa.
 Group members will take note what are the
difference of solid figures from plane figures.
RUBRICS
Points
5
Indicator
Show eagerness an cooperation
to do the task, participation
actively, do great help to the
group
4
Shows
eagerness
and
cooperation to do the task, good
followers only
3
2
1
19
Participated
but
late
teacher’s supervision
with
Activity was done but does not
show eagerness to participate or
cooperate
No interest in participating the
activities
D. Discussing new
concepts and practicing
new skills # 1
Advance Learners
Average Learners
Direction: Encircle the
letter/s of the statement
that differentiate the solid
figure from a plane figure:
Direction:
Differentiate
the given solid and plane
figures by encircling the
words
inside
the
sentences:
a. A plane figure is a three
dimensional figure while
solid figure is a two
dimensional figure.
b. A plane figure is a two
dimensional figure while
solid figure is a three a. The solid figure is a
dimensional figure.
( three dimensional, two
dimensional) figure, while
c. The difference between the plane figure is a
plane and solid figure is in (three dimensional, two
their dimension.
dimensional) figure.
d. The difference between b.
The
difference
plane and solid figure is in between plane and solid
their texture and height.
figure
is
in
their
(dimension, texture).
a. Pupils will present their output after 5
minutes;
b. The teacher will assess the answers of the
pupils.
E. Discussing New
Concepts and Practicing
New Skills # 2
 Show pictures or objects that like plane or solid
figure.
 Have pupils describe each figure.
 Discuss the difference between plane figures
and solid figures, like:
Plane Figures
a. figures
dimensions
with
Solid Figures
two a. figures with three
dimensions
b. made up of an infinite b. they are figures
number of planes
with space
20
c. includes sides, which c. objects with length,
are straight lines that width and height
make up the shape and
corners,
which
are
where two sides come
together
d. bounded
segments
by
line d. Do not limit to one
plane and have depth
e. a closed-flat figure
e. the flat surface are
its faces or sides as
they
commonly
called.
* While presenting the difference of the figures show
the plane or solid figures before the class.
F. Developing Mastery
Advance Learners
Average Learners
Direction: What is the
difference
of
solid
figures
from
plane
figures? Choose your
answer inside the box.
Direction: What is the
difference
of
solid
figures
from
plane
figures? Encircle your
answer.
a. bounded by line
segments
1. A three dimensional
figure ( solid figure ,
plane figure )
b. the flat surface
are its faces or sides
as they commonly
called.
2. A figure which is
made up of infinite
number of planes ( solid
figure, plane figure )
c. figures with two
dimensions
3. A plane figure is a
closed-flat figure while
solid figure is ( have
depth, have sizes )
d. figures with three
dimensions
4. They are figures with
space (plane figures,
solid figures )
21
Plane Figures
a.
b.
Solid Figures
a.
b.
G. Practical Applications
Direction: Differentiate the following.
1. A piece of bond paper from a book.
2. A photograph from a photo frame.
3. A circular cloth table from a basketball.
H. Making Generalizations
What are the difference between plane figures
and solid figures? Give at least 3.
I. Evaluation
Advance Learners
Average Learners
Direction: Write the Direction: Differentiate
differences
of
solid solid figures and plane
figures
from
plane figures. Write true or
figures.
false after the statement:
1.
1. Solid figures are
three-dimensional
figures
while
plane
figures
are
twodimensional figures.
2.
3.
4.
2. Plane figures are
bounded
by
line
segments while solid
figures are do not limit to
one plane and have
depth.
5.
3. The difference of solid
figures
from
plane
figures is their sizes.
22
J. Additional Activities
Direction: Differentiate the following.
1. A poster from a book.
2. A round table from a thin piece of biscuit.
3. A curtain from a chalkboard.
V. REMARKS
VI. REFLECTIONS
23
School:
Teacher:
Dates and Day:
Week 1- Day 5
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of solid
figures.
The learner able to construct and describe the
different solid figures.
The learner differentiates solid figures from plane
figures.
Code: M6GE-IIIa-28
II.CONTENT
Differentiating Solid Figures from Plane Figures
Subject Integration: English (Reading)
III. LEARNING RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials Pages
3.Textbook Pages
4. Additional Materials from
Learning Resources (LR)
Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6
page 160
Mathletes 6, pages 156 - 199
Marker, pictures or real objects of different solid
figures, like: drinking glass, soda container, ball,
balloon, plate, ice cream cone, road signs
IV. PROCEDURES
A. Review Previous
Lessons
Ask the following questions:
a. What is a solid figure?
b. What is a plane figure?
c. Give a difference between plane figure
and a solid figure?
Game: “Flashing In!”
 Divide the class into 4 groups.
 The teacher flashes a picture either solid figure
or plane figure.
24
 Each member of the group will write a word
about the picture. They will write their answers
on the board.
 After all the pictures were flashed, the teacher
will check the answers of the pupils.
 The group who got the highest number of
correct answers will have plus points in the
Performance Task.
RUBRICS
Points
5
Indicator
Show eagerness an cooperation
to do the task, participation
actively, do great help to the
group
4
Shows
eagerness
and
cooperation to do the task, good
followers only
3
2
1
B. Establishing purpose for
the Lesson
Participated
but
late
teacher’s supervision
with
Activity was done but does not
show eagerness to participate or
cooperate
No interest in participating the
activities
What made your group won the contest?
What will you do in the coming activities so that your
group will win? Is it important that all members of
the group should share his/her ideas? Why?
Why not?
25
C. Presenting
Examples/Instances of the
new lesson
Advance Learners
Average Learners
 Divide
the
Advance Learners
into 2 teams.
 There will be a
drawlots to whom
which the team will
give
first
a
statement
about
the solid figure.
 The next group will
answer
the
difference of the
figure
that
mentioned by the
first group.
 Do the same steps
until
all
the
differences of solid
figures from plane
figures were given.
 The team who
gave the difference
of solid figures
from plane figures
immediately, will
“win”.
 Divide
the
Average Learners
into 2 groups.
 From a manila
paper, each group
will choose the
differences
of
solid figures from
plane figures.
a. Plane figures are
bounded by line
segments while
solid figures are
three dimensional
figures.
b. the flat surface
are its faces or sides
as they commonly
called.
c. figures with two
dimensions
d. figures with three
dimensions
e.
A
three
dimensional figure is
called solid figure
while plane figure is
a two-dimensional
figure.
.
f. A figure which is
made up of infinite
number of planes is
plane figure while a
solid figure is a
closed-flat figure.
 They will write
their answers on a
manila paper.
26
a. Pupils will present their output after 10
minutes;
b. The teacher will check the answers of the
pupils.
D. Discussing new
concepts and practicing
new skill #1
 Discuss further the difference between plane
figures and solid figures, like:
Plane Figures
a. figures
dimensions
with
Solid Figures
two a. figures with three
dimensions
b. made up of an infinite b. they are figures
number of planes
with space
c. includes sides, which c. objects with length,
are straight lines that width and height
make up the shape and
corners,
which
are
where two sides come
together
d. bounded
segments
by
line d. Do not limit to one
plane and have depth
e. a closed-flat figure
E. Discussing New
Concepts and Practicing
New Skills #2
e. the flat surface are
its faces or sides as
they
commonly
called.
* While presenting the difference of the figures show
the plane or solid figures before the class.
How did you differentiate plane figure from solid
figures?
27
F. Developing Mastery
Advance Learners
Average Learners
Direction: What is the
difference between solid
figures
and
plane
figures?
Direction: What is the
difference between solid
figures
and
plane
figures? Encircle your
answer.
Solid
Figure
1.
2.
3.
28
Plane
Figure
Plane
Figures
Solid
Figures
a. figures
with
no
dimensio
ns
a. figures
with three
dimensio
ns
b. made
up of an
infinite
number of
planes
b.
they
are
figures
with
space
c.
includes
sides,
which are
straight
lines that
make up
the shape
and
corners,
which are
where two
sides
come
together
c. objects
with
length,
width and
height
d.
bounded
by
line
segments
and
points.
d. Do not
limit
to
one plane
and have
depth
e.
a e. the flat
closedsurface
flat figure are
its
faces or
sides as
they
commonl
y called.
G. Practical Applications
H. Making Generalizations
I. Evaluation
Direction: Differentiate the following.
1. A notebook from a manila paper.
2. A sharpener from a round drinking glass
cover.
3. A rectangular table from a long brown
envelope.
What are the differences between plane figures
and solid figures?
Advance Learners
Average Learners
Direction: Write the
difference
between
plane figures and solid
figures.
Direction: Write the
difference
between
plane figures and solid
figures.
1.
1.
2.
2.
3.
3.
4.
5.
J. Additional Activities
Direction: Differentiate the following.
1. A poster from a lunch box.
2. Bookshelves from a long coupon bond.
3. A book from a piece of paper.
V. REMARKS
VI. REFLECTIONS
29
School:
Teacher:
Time and Date:
Grade Level:
Learning Area:
Quarter
Week 2 – Day 1
I. OBJECTIVES
A. Content
Standard
B. Performance
Standard
C. Learning
Competencies/
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages
2. Learner’s Material
pages
3. Textbook pages
4. Additional Materials
from Learning Resource
LR portal
IV. PROCEDURE
A. Reviewing previous
lesson or
presenting new
lesson
6
Mathematics
Third
The learner demonstrates understanding of solid figures.
The learner is able to construct and describe the different solid
figures: cube, prism, pyramid, cylinder, cone, and sphere.
The learner illustrates the different solid figures using various
concrete and pictorial models.
(M6GE-IIIb-29)
Illustrating the Different Solid Figures Using Various Concrete
and Pictorial Models.
K to 12 Curriculum Guide 2016. Grade 6, page 196
21st Century MATHletes 6 pages 72-76
21st Century MATHletes 6 pages 187-199
21st Century MATHletes 6 pages 187-199
Mathletes 6 textbook, video clip, power point presentation
Advance Learners
Solving for Perimeter/Area of
Plane Figures
Average Learners
1. Solve for the perimeter of
the given plane figure.
Ex.:
Rectangle with 6 cm length
and 4 cm width
10 cm
16 cm
P=?
A=?
9m
2.Review: Identifying Spatial
Figures
What are the different spatial
figures?
Give examples of real objects
that are models of spatial
figures.
30
Triangle with 3cm, 5cm and
8cm sides.
2.Review: Identifying Spatial
Figures
What are the different spatial
figures?
Give examples of real objects
that are models of spatial
figures.
Sort the figure into 2D or 3D
figure
2D
3D
B. Establishing a
purpose for the
lesson
Illustrate the ff. figures.
Plane Figure
Illustration
1.Circle
2.Rectangle
3.Square
4.Triangle
Solid Figure
Illustration
1.Sphere
2.Rectangular
Prism
3.Cube
4.Triangular
pyramid
Illustrate the following figures
Plane Figure
Illustration
1.Circle
2.Rectangle
3.Square
4.Triangle
Solid Figure
Illustration
1.Sphere
2.Rectangular
Prism
3.Cube
4.Triangular
pyramid
Guide Questions:
Guide questions:
1.Is it possible to combine
plane figures to form solid
figures?
1. What can you say about
your drawings?
2. What is the corresponding
solid figure if circles &
rectangles will be combined?
Circle triangle? Square &
triangles? Rectangle and
triangle? What else can you
think of?
3. Can all plane figures be
combined to one another to
form different kinds of solid
figures? Give example &
explain.
31
2. Can we combine plane
figure with solid figure?
3. Can we create another form
from combining plane figure
and solid figure?
C. Presenting
1) Introduce to pupils the different spatial figures.
examples/instances Let them describe the characteristics of each figure.
of the new lesson
2) What is common among all the spatial figures?
3) Identify the spatial figures represented by each part by
completing the chart below.
D. Discussing new
concepts and
practicing new
skills #1
Parts of the Robot
Space Figures Represented
Head
Body
Arms
Legs
Feet
Hands
Mouth
Nose
Eyes
Ears
Ex.: sphere
Rectangular prism
Activity 2 – Real Situation Problem
1) Let the pupils go outside of the classroom.
2) Let them observe and identify different objects and list down
different spatial figures they saw.
3) Go back to the classroom.
4) Discuss the importance of being aware of different spatial
figures as seen and experienced through the environment.
Ex.
Object
Space Figure Represented
Basketball
Water jug
Sphere
Cylinder
32
E. Discussing new
concepts and
practicing new
skills #2
Matching Game
Identification
1) Blindfold a pupil.
Using solid figure (real and
concrete objects) let the pupils
identify what kind of solid
figure it is.
2) Let him/her go in front of
the class and hold a spatial
figure. (Can use concrete
objects)
3) Let him/her name it, identify
and describe what it is.
1. ball
2. ice cream cone
3. book
4. soda can
5. dice
F. Developing
Mastery
Identify the following pictures as cube, rectangular prism,
sphere, cone, cylinder, or a pyramid.
G. Finding practical
application of
concepts and skills
in daily living
Match Column A with column
B
1) The base is a polygon and
its faces are triangles.
2) A space figure with a
polygonal base whose edges
meet at a common vertex.
3) A space figure having a
circular base and one vertex.
4) A space figure with 2
parallel congruent faces called
bases and the other faces are
parallelograms.
5) A space figure with 2
circular bases, no edge, and
no vertex.
a. rectangular prism
b. cone
c. pyramid
d. cylinder
e. triangular prism
33
Name each of these 3D
shapes below
H. Making
generalization and
abstraction about
the lesson
What is a prism? What are the kinds of prisms? Describe each.
What is a pyramid? What are the kinds of pyramids? Describe
each.
I.
Illustrate the following solid figures
Evaluating learning
1. Cube
2. Rectangular prism
3. Square pyramid
4. Cylinder
5. Cone
J. Additional activities
for application or
remediation
Encircle the solid figures.
V. REMARKS
VI. REFLECTION
34
School:
Teacher:
Time and Date:
Grade Level:
Learning Area:
Quarter
Week 2 – Day 2
I. OBJECTIVES
A. Content
Standard
B. Performance
Standard
C. Learning
Competencies/
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
6
Mathematics
Third
The learner demonstrates understanding of solid figures.
The learner is able to construct and describe the different solid
figures: cube, prism, pyramid, cylinder, cone, and sphere.
The learner illustrates the different solid figures using various
concrete and pictorial models.
(M6GE-IIIb-29)
Illustrating the Different Solid Figures Using Various Concrete and
Pictorial Models.
K to 12 Math Curriculum Guide 2016. Grade 6, page 196
21st Century MATHletes 6 pages 72-76
2. Learner’s
Material pages
21st Century MATHletes 6 pages 187-199
3. Textbook
pages
21st Century MATHletes 6 pages 187-199
4. Additional
Materials from
Learning
Resource
LR portal
Mathletes 6 textbook, video clip, power point presentation
IV. PROCEDURE
A. Reviewing previous
lesson or
presenting new
lesson
Advance Learners
Shade in the 2D shapes
yellow and the 3D shapes
green.
35
Average Learners
Choose the correct 2D shape that
makes up each 3D shape
1.
a.
b.
2.
a.
b.
3.
a.
b.
Ask:
1. What are the difference
between solid and plane
figure?
Ask:
1. What is solid figure?
2. What is plane figure?
3. Give examples
2. Why is it called solid
figure? Plane figure?
3. Give examples
B. Establishing a
purpose for the
lesson
Illustrate the following
Give the name of the following
figures.
C. Presenting
examples/instances
of the new lesson
1) Introduce to pupils the different space figures.
Let them describe the characteristics of each figure.
1. Sphere
2. Cone
3. Cube
4. Rectangular Prism
5. Cylinder
2) What is common among all the space figures?
3) Identify the space figures represented by each part by
completing the chart below.
36
Parts of the Robot
Head
Body
Arms
Legs
Feet
Hands
Mouth
Nose
Eyes
Ears
D. Discussing new
concepts and
practicing new
skills #1
Space Figures Represented
Ex.: sphere
Rectangular prism
Let the pupils identify the figure in terms of a riddle.
1. I have 2 circular faces.
I have 1 curved face.
What am I? _______________
2. I have the same number of faces, edges and corners as a cube
What am I? _______________
3. I have 2 triangular faces.
I have 3 rectangular faces.
I have 9 edges and 6 corners.
What am I? _______________
4. I look like a closed box.
All my faces are squares.
What am I? _______________
5. I just have 1 curved face.
I am round in shape
What am I? _______________
37
E. Discussing new
concepts and
practicing new
skills #2
Activity 2 – Real Situation Problem
1) Let the pupils go outside of the classroom.
2) Let them observe and identify different objects and list down
different space figures they saw.
3) Go back to the classroom.
4) Discuss the importance of being aware of different space figures
as seen and experienced through the environment.
Ex.
Object
Space Figure Represented
Basketball Sphere
Water jug Cylinder
F. Developing
Mastery
Draw examples of the
following figures that can be
seen or use in our daily life.
Identify the space figure
represented by the following:
a. Sphere
b. Cube
c. Rectangular Prism
d. Cylinder
e. Cone
G. Finding practical
application of
concepts and skills
in daily living
Find the correct description of the following figures
a. 2 faces, 1 vertex, 1 edge
b. 3 faces, 0 vertex, 2 edges
c. 6 faces, 8 vertices, 12 edges
d. 6 faces, 8 vertices, 12 edges
e. 8 faces, 12 vertices, 18 edges
38
H. Making
generalization and
abstraction about
the lesson
What is a prism? What are the kinds of prisms? Describe each.
What is a pyramid? What are the kinds of pyramids? Describe
each.
What is a cone? Describe
What is a cylinder? Describe
What is a sphere? Describe
Expected answer:
Prism – has 2 bases, and a lateral face made of rectangles
Pyramid – has at least 3 lateral faces which are triangles, and only
1 base
Cone – has 1 circular base, and 1 vertex
Cylinder – has 1 circular base, and no vertices
Sphere – has no faces, bases, edges, or vertices. A solid figure
that has the same distance to any pint from the center.
I.
Evaluating learning
Draw the following solid
figure and give examples
that can be seen in real life.
Complete the table by putting the
right illustrations.
Sphere Cube Cone Cylinder
1. Sphere
2. Cone
3. Cube
4. Cylinder
5. Rectangular prism.
J. Additional activities
for application or
remediation
Who am I?
Write the name of each 3D
shapes.
1. I have 4 sides and they
are all equal in length. Who
am I?
__________
2. I have 1 flat face and 0
edges. Who am I?
__________
39
1.
_____
2.
_____
3. I have 6 faces and 6
corners. Who am I?
__________
3.
_____
4. I have 3 straight sides and
3 corners. Who am I?
__________
4.
_____
5. I have 0 faces, 0 sides,
and 0 edges. Who am I?
__________
5
_____.
V. REMARKS
VI. REFLECTION
40
School:
Teacher:
Time and Date:
I. OBJECTIVES
A. Content
Standard
Grade Level:
Learning Area:
Quarter
Week 2 – Day 3
6
Mathematics
Third
The learner demonstrates understanding of solid figures.
B. Performance
Standard
C. Learning
Competencies/
Objectives
The learner is able to construct and describe the different solid figures:
cube, prism, pyramid, cylinder, cone, and sphere.
The learner identifies the faces of a solid figure.
( M6NS-IIIb-30 )
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
Identifying the Faces of a Solid Figure
2. Learner’s
Material pages
21st Century MATHletes 6 pages 187-199
3. Textbook
pages
21st Century MATHletes 6 pages 187-199
K to 12 Math Curriculum Guide 2016. Grade 6, page 196
21st Century MATHletes 6 pages 72-76
4. Additional
Materials from
Learning
Resource
LR portal
IV.PROCEDURE
A. Reviewing
previous
lesson or
presenting new
lesson
Advance Learners
Match column A with column B
A
B
Cube
Cylinder
Sphere
41
Average Learners
Review:
A
B
Pyramid
Rectangular
prism
Cone
B. Establishing a
purpose for the
lesson
C. Presenting
examples/instan
ces of the new
lesson
Cut out pictures from magazine or newspapers that are models of
space figures. Describe the pictures and ask them the usage of each.
Present the ff. figures.
Guide questions: use the figures above.
 How many parallel faces are there in figure 1? Name them.
 Are all faces of figure 1 congruent? Explain.
 How many vertex/vertices can you count in figure 1?
 Give at least 2 edges of figure 1
 What kind of polygon are the faces of the second figure?
How many faces do we have in second figure?
D. Discussing new
concepts and
practicing new
skills #1
Group activity
Complete the table
Solid
figure
1.
Cube
Illustra
tion
Descri
ption
No. of
faces
No. of
edges
No. of
vertice
s
Each
side is
a
squar
e face
6
12
8
2.
Recta
ngular
Prism
42
Real
life
repres
entati
on of
object
A dice
Numb
er of
sides
on
each
face
4
3.
Spher
e
4.
Cone
5.
Cylind
er
6.
Squar
e
Pyram
id
E. Discussing new
concepts and
practicing new
skills #2
F. Developing
Mastery
Let the reporter of every group present and discuss their output.
Allow other group and give them time to say/suggest something
on the output presented.
Tony bought a robot for his little
Let the pupils identify the following
brother. He customized every
shapes.
part of the robot by putting a
This 3D shape
design on each part and the robot
is a _________
appears as shown below.
It has
Vertices ____
Edges ____
Faces ____
This 3D shape
is a _________
It has
Vertices ____
Edges ____
Faces ____
He wants to challenge his little
brother by asking him to identify
the different solid figures in each
of the corresponding parts of the
robot. What are the different solid
figures that make up the robot?
Let the pupils answer the
problem.
(Discuss the answer on page
193-194 of Textbook)
43
This 3D shape
is a _________
It has
Vertices ____
Edges ____
Faces ____
This 3D shape
is a _________
It has
Vertices ____
Edges ____
Faces ____
This 3D shape
is a _________
It has
Vertices ____
Edges ____
Faces ____
Cube, Cylinder, Sphere, Cone,
Prism
G. Finding practical Tell what 3D shape the object look like?
application of
concepts and
skills in daily
living
H. Making
generalization
and abstraction
about the
lesson
I. Evaluating
learning
How do you identify the faces of solid figures?
A face is one of the flat surfaces on a solid figure. A plane figure is a
flat, two-dimensional figure. A prism is a three-dimensional object with
two congruent parallel bases that are polygons. A pyramid is a threedimensional object with a base that is a polygon and
triangular faces that meet at one vertex.
Complete the table:
Solid Figure
Draw the
figure
1.Rectangul
ar
prism
2.square
pyramid
3.cylinder
4.cone
5.sphere
44
No. of
Vertices
No. of
faces
No. of
edges
J. Additional
activities for
application or
remediation
Complete the table.
Space Figure
1. Cube
2. Rectangular
Prism
3. Sphere
4. Cylinder
5. Triangular
Pyramid
6. Rectangular
Pyramid
7. Cone
No. of Faces
V. REMARKS
VI. REFLECTION
45
No. of Edges
No. of Vertices
School:
Teacher:
Time and Date:
I. OBJECTIVES
A. Content
Standard
Grade Level:
Learning Area:
Quarter
Week 2 – Day 4
6
Mathematics
Third
The learner demonstrates understanding of solid figures.
B. Performance
Standard
C. Learning
Competencies/
Objectives
The learner is able to construct and describe the different solid figures:
cube, prism, pyramid, cylinder, cone, and sphere.
The learner identifies the faces of a solid figure.
( M6NS-IIIb-30 )
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
Identifying the Faces of a Solid Figure
2. Learner’s
Material pages
21st Century MATHletes 6 pages 187-199
3. Textbook
pages
21st Century MATHletes 6 pages 187-199
K to 12 Math Curriculum Guide 2016. Grade 6, page 196
21st Century MATHletes 6 pages 72-76
4. Additional
Materials from
Learning
Resource
LR portal
IV.PROCEDURE
A. Reviewing
previous
lesson or
presenting new
lesson
Advance Learners
Match column A with column B:
Average Learners
A
1. Has 2 bases, and lateral faces made of rectangles
2. Has at least 3 lateral faces, which are triangles and only 1 base
3. Has 2 circular bases and no vertices
4. Has 1 circular base and 1 vertex.
5. Has no faces, bases, edges or vertices. A solid figure that has the
same distance to any point from the center
B
a. Sphere
b. Cone
c. Pyramid
d. Cylinder
e. Prism
46
B. Establishing a
purpose for the
lesson
1. Group the pupils into Learning Team.
2. Provide each group nets of solid figures.
3. Let them identify what solid figure is formed by the nets.
4. Form solid figures out of the given nets.
5. Describe it.
C. Presenting
examples/instan
ces of the new
lesson
Present the lesson through this activity:
a. Call each group to present their output
b. Let them show their finished products to the class.
c. Have them describe each and identify its parts.
d. Have them identify its faces.
D. Discussing new
concepts and
practicing new
skills #1
E. Discussing new
concepts and
practicing new
skills #2
e. Call the other group.
Let the pupils identify the following shapes.
1.
2.
5.
6.
3.
4.
7.
8.
Group Activity: Find the correct shape from the 3 possibilities.
Faces: 6
Edges: 12
Vertices: 8
Faces: 5
Edges: 9
Vertices: 6
Faces: 5
Edges: 8
Vertices: 5
Faces: 4
Edges: 6
Vertices: 4
47
Faces: 7
Edges: 15
Vertices: 10
F. Developing
Mastery
Group Activity:
Complete the table on the activity
sheet given by the teacher.
Shapes
Name
Work in pair.
Identify the faces, edges, and
vertices.
Number
of faces
6
Cube
Rectang
ular
Prism
Cube
Cone
Sphere
Faces:
Edges:
Vertices:
Faces:
Edges:
Vertices:
Faces:
Edges:
Vertices:
Cylinder
Pyramid
Faces:
Edges:
Vertices:
Faces:
Edges:
Vertices:
Rectang
ular
Prism
Triangul
ar Prism
Faces:
Edges:
Vertices:
G. Finding practical identify solid figure and tell the number of faces, edges, and vertices.
application of
(Use real object)
concepts and
skills in daily
Object
Faces
Edges
Vertices
living
48
H. Making
generalization
and abstraction
about the
lesson
How do you identify the faces of solid figures?
I. Evaluating
learning
Complete the table:
A face is one of the flat surfaces on a solid figure. A plane figure is a
flat, two-dimensional figure. A prism is a three-dimensional object with
two congruent parallel bases that are polygons. A pyramid is a threedimensional object with a base that is a polygon and
triangular faces that meet at one vertex.
Shape
Name
Faces
49
Edges
Vertices
J. Additional
activities for
application or
remediation
Complete the table
Na
me
Illus
trati
on
Fac
es
Complete the table
Edg
es
Tria
ngul
ar
Pyr
ami
d
Tria
ngul
ar
Pris
m
Pen
tago
nal
Pris
m
Hex
ago
nal
Pris
m
Oct
ago
nal
Pris
m
V. REMARKS
VI. REFLECTION
50
Vert
ices
Sha
pe
Nam
e
Fac
es
Edg
es
Verti
ces
School:
Teacher:
Time and Date:
I. OBJECTIVES
A. Content
Standard
Grade Level:
Learning Area:
Quarter
Week 2 – Day 5
6
Mathematics
Third
The learner demonstrates understanding of solid figures.
B. Performance
Standard
C. Learning
Competencies/
Objectives
The learner is able to construct and describe the different solid figures:
cube, prism, pyramid, cylinder, cone, and sphere.
The learner identifies the faces of a solid figure.
( M6NS-IIIb-30 )
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
Identifying the Faces of a Solid Figure
2. Learner’s
Material pages
21st Century MATHletes 6 pages 187-199
3. Textbook pages
4. Additional
Materials from
Learning
Resource
LR portal
21st Century MATHletes 6 pages 187-199
IV.PROCEDURE
A. Reviewing
previous
lesson or
presenting
new lesson
Advance Learners
Average Learners
Sort out the figure in their corresponding column
K to 12 Math Curriculum Guide, 2016. Grade 6, page 196
21st Century MATHletes 6 pages 72-76
2-dimensional object
51
3-dimensional object
B. Establishing a
purpose for the
lesson
Group activity
Let each group give examples of the figure assigned to them.
(Real and non-real objects)
Group 1
Sphere
Group 2
Cube
Group 3
Cone
Group 4
Cylinder
How did your group accomplish the assigned activity? Elicit the
value of unity/teamwork/cooperation?
C. Discussing new
concepts and
practicing new
skills #1
Group Activity.
Let the pupils identify the names, faces, edges and vertices.
Name:
Faces:
Edges:
Vertices:
Name:
Faces:
Edges:
Vertices:
Name:
Faces:
Edges:
Vertices:
Name:
Faces:
Edges:
Vertices:
52
Name:
Faces:
Edges:
Vertices:
D. Discussing new
concepts and
practicing new
skills #2
E. Developing
Mastery
Name:
Faces:
Edges:
Vertices:
Discuss with the pupils the properties of 3D shapes
Cone – 2 faces, 1 edge, 1 vertex
Sphere – 1 face, 1 edge, 0 vertices
Triangular Prism – 6 faces, 12, edges, 8 vertices
Cylinder – 3 faces, 2 edges, 0 vertices
Cube – 6 faces, 12 edges, 8 vertices
Triangular Prism – 5 faces, 9 edges, 6 vertices
Let them enumerate example of objects with 3D shapes.
Group Activity
Group Activity
Write the name of each shape.
Also find the number of faces,
edges, and vertices
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
53
Complete the table:
Figu
re
Fac
es
Edg
es
Verti
ces
Wha
t am
I?
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
F. Finding practical Fill in the name, and number of faces, edges and vertices for each
application of
shape.
concepts and
skills in daily
living
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
54
Faces:
Vertices:
Edges:
Name:
Faces:
Vertices:
Edges:
Name:
G. Making
generalization
and abstraction
about the
lesson
What is the face of a 3-D object? The vertex? The edge?
H. Evaluating
learning
Complete the table:
Write the name of the figure and identify the faces, edges and vertices
Faces – the individual surfaces of a 3-D object.
Vertex – the point where two or more straight lines meet.
Edge – the line where two surfaces meet.
Figure
Name
55
Faces
Edges
Vertices
I. Additional
activities for
application or
remediation
Complete the table
Figure
Name
V. REMARKS
VI. REFLECTION
56
Number of
sides
Number of
edges
Number of
vertices
School
Teacher
Time and
Date
Grade Level 6
Learning Mathematics
Area:
Quarter: Third
Week 3- Day 1
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of solid figures.
B. Performance
Standards
The learner is able to construct and describe the different
solid figures: cube, prism, pyramid, cylinder, cone, and
sphere.
C. Learning
Competencies/
Objectives
The learner visualizes and describes the different solid
figures: cube, prism, pyramid, cylinder, cone, and
sphere.
M6GE-IIIc-31
II. CONTENT
Visualizing and describing the different solid figures:
cube, prism, pyramid, cylinder, cone, and sphere.
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
K to 12 Math Curriculum Guide, 2016. Grade 6, page197
Lesson Guide in Elementary Math Gr. 6 p. 77-83
2. Learner’s
Material pages
3. Textbook
pages
21st Century MATHletes pp. 200-209
21st Century MATHletes pp. 200-209
4. Additional
DLP 6 Module 54
Materials from
Learning
Resource
LR
portal
B. Other Learning https://www.supertacherworksheets.com/solid-shapes.html
Resources
57
IV. PROCEDURE
A. Reviewing
previous lesson or
presenting new
lesson.
ADVANCE LEARNERS
DRILL
Sort out the figures into their corresponding column.
Individual:
Given Figure
Twodimensional
Figure
ThreeDimensional
Figure
AVERAGE LEARNERS
By Pair:
Given Figure
58
Twodimensional
Figure
Threedimensional
Figure
B. Establishing a
purpose for the
lesson
ADVANCE LEARNERS
MOTIVATION
Circle the 3d shapes below.
AVERAGE LEARNERS
Circle the 3d shapes below.
59
C. Presenting
examples/
instances of the
new lesson.
Present the following examples of real- life solid figures.
Wherever we look, we see three-dimensional shapes. Buildings,
furniture, plants, even people themselves: all are solid objects.
Whenever we look at the world around us, we see it in three
dimensions: length, width and height.
D. Discussing new
concepts
and
practicing
new
skills #1
Show a video of visualizing solid figures.
https://www.youtube.com/watch?v=7uAbGoGYLcc
60
E. Discussing new
concepts
and
practicing
new
skills #2
Group Activity:
ADVANCE LEARNERS
AVERAGE LEARNERS
61
Fill in the name, and number of faces, edges and vertices for
F. Developing Mastery each shape.
ADVANCE LEARNERS
AVERAGE LEARNERS
62
G. Finding
practical
application
of concepts
and skills in
daily living.
ADVANCE LEARNERS
Pair-Share
AVERAGE LEARNERS
https://www.supertacherworksheets.com/solid-shapes.html
67
H.
Making
generalizations and
abstractions bout
the lesson
I. Evaluating
Learning
What is a solid figure?
How can you describe a solid figure?
-A solid or space figure is three – dimensional. It has length,
width and height.
-Face – is the flat surface.
- Edge – is the intersection of any two faces.
-Vertex – is the intersection of three or more faces.
ADVANCE LEARNERS
Choose a word from the box to correctly answer each
question.
1. A star apple is shaped like which solid?
2. A box of cereal is shaped like which solid?
3. A die is shaped like which solid?
4. A volcano is shaped like which solid?
5. A can of sardines is shaped like which solid?
6. What is the name of the place on a solid
where two faces meet?
7. What are the flat surfaces on a pyramid,
cube, or rectangular prism called?
8. What is the name of a corner on a solid
where three or more edges meet?
9. How many edges does a rectangular prism
have?
10. How many faces does a cube have?
AVERAGE LEARNERS
Choose a word from the box to correctly answer each
question.
1. A box of cereal is shaped like which solid?
68
2. A die is shaped like which solid?
3. A volcano is shaped like which solid?
4. What are the flat surfaces on a pyramid, cube, or
rectangular prism called?
5. What is the name of a corner on a solid where three or
more edges meet?
J. Additional
Answer Math Challenge on page 208-209
activities
for
application or
remediation
69
School
Teacher
Time and
Date
Grade Level 6
Learning Mathematics
Area:
Quarter: Third
Week 3- Day 2
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives
II. CONTENT
IV. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
The learner demonstrates understanding of solid
figures.
The learner is able to construct and describe the
different solid figures: cube, prism, pyramid,
cylinder, cone, and sphere.
The learner visualizes and describes the different
solid figures: cube, prism, pyramid, cylinder,
cone, and sphere.
M6GE-IIIc-31
Visualizing and describing the different solid
figures: cube, prism, pyramid, cylinder, cone,
and sphere.
K to 12 Math Curriculum Guide, 2016. Grade 6,
page 196
Lesson Guide in Elementary Math Gr. 6 p. 77-83
21st Century MATHletes pp. 200-209
2. Learner’s
Material pages
3. Textbook
21st Century MATHletes pp. 200-209
pages
4. Additional
DLP 6 Module 54
Materials from
Learning
Resource LR
portal
B. Other Learning https://www.supertacherworksheets.com/solid-shapes.html
Resources
IV. PROCEDURE
A. Reviewing previous
lesson or presenting
new lesson.
Drill: BRING ME!
The pupils will bring an object representing the
spatial figure that the teacher will say. The one that
can bring the most correct object wins the game.
Ex: Rectangular Prism, Cube etc.
70
B. Establishing a purpose
for the lesson
MOTIVATION:
ADVANCE LEARNERS
By Pair
WORD HUNT
Answer this activity. Practice speed and accuracy. Search
and ring the defined words in the grid that corresponds to
the word hints given below.
1.
2.
3.
4.
Flat parts of the solid figure.
The line where two faces meet.
The point where three edges meet.
A solid figure with curved surface of points that are all
the same distance from the center.
5. A polyhedron with five equal sides and angles.
AVERAGE LEARNERS
By Pair
WORD HUNT
Answer this activity. Practice speed and accuracy. Search
and ring the defined words in the grid that corresponds to
the word hints given below.
71
1. Flat parts of the solid figure.
2. The line where two faces meet.
3. The point where three edges meet.
C. Presenting examples/
instances of the new
lesson.
Present the following real life examples of solid figures.
https://www.supertacherworksheets.com/solid-shapes.html
D.
Discussing
new
concepts
and Show a video on visualizing solid figures.
practicing new skills
https://www.youtube.com/watch?v=nKwfkW_DkcM
#1
72
E.
ADVANCE LEARNERS
Discussing
new
concepts
and Group Activity:
practicing new skills Find the correct shape from the three possibilities.
Faces: 6
#2
Edges: 12
Vertices: 8
Faces: 5
Edges: 9
Vertices: 6
Faces: 5
Edges: 8
Vertices: 5
Faces: 4
Edges: 6
Vertices: 4
Faces: 7
Edges: 15
Vertices: 10
AVERAGE LEARNERS
Group Activity:
Find the correct shape from the three possibilities.
Faces: 6
Edges: 12
Vertices: 8
Faces: 5
Edges: 9
Vertices: 6
Faces: 5
Edges: 8
Vertices: 5
Faces: 4
Edges: 6
Vertices: 4
73
F. Developing mastery
ADVANCE LEARNERS
Find the correct shape from the three possibilities.
By Pair:
Faces: 8
Edges: 18
Vertices: 12
Faces: 5
Edges: 8
Vertices: 5
Faces: 6
Edges: 8
Vertices: 12
Faces: 7
Edges: 15
Vertices: 10
Faces: 7
Edges: 12
Vertices: 7
AVERAGE LEARNERS
Find the correct shape from the three possibilities.
By Triad:
Faces: 8
Edges: 18
Vertices: 12
Faces: 5
Edges: 8
Vertices: 5
Faces: 6
Edges: 8
Vertices: 12
Faces: 7
Edges: 15
Vertices: 10
74
G. Finding practical
application of
concepts and skills in
daily living.
ADVANCE LEARNERS
AVERAGE LEARNERS
https://www.supertacherworksheets.com/solid-shapes.html
75
H. Making
generalizations
and abstraction
about the lesson
What is a solid figure?
How can you describe a solid figure?
-A solid or space figure is three – dimensional. It has
length, width and height.
-Face – is the flat surface.
- Edge – is the intersection of any two faces.
-Vertex – is the intersection of three or more faces.
ADVANCE LEARNERS
I. Evaluating learning
Write true if the statement is correct. Write false if it is
incorrect.
1.
2.
3.
4.
5.
6.
7.
A rectangular prism has 8 vertices.
A sphere has no faces and vertices.
A square pyramid has 5 faces
A cube has 10 edges.
A cone is a polyhedron.
A pyramid is a polyhedron.
There are two congruent circular bases in a
cylinder.
8. A pyramid has triangular faces.
9. A cylinder has no vertices.
10. A sphere is a solid figure.
AVERAGE LEARNERS
Write true if the statement is correct. Write false if it is
incorrect.
1.
2.
3.
4.
5.
J. Additional
activities for
application or
remediation
V. REMARKS
VI. REFLECTION
A rectangular prism has 8 vertices.
A sphere has no faces and vertices.
A square pyramid has 5 faces
A cube has 10 edges.
A cone is a polyhedron.
Answer Math Challenge on page 208-209
76
School
Teacher
Time and
Date
Grade Level 6
Learning Mathematics
Area:
Quarter: Third
Week 3- Day 3
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives
II. CONTENT
The learner demonstrates understanding of
solid figures.
The learner is able to construct and describe
the different solid figures: cube, prism,
pyramid, cylinder, cone, and sphere.
The learner visualizes and describes the
different solid figures: cube, prism, pyramid,
cylinder, cone, and sphere.
M6GE-IIIc-31
Visualizing and describing the different
solid figures: cube, prism, pyramid,
cylinder, cone, and sphere.
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
2. Learner’s Material
pages
3. Textbook
pages
4. Additional Materials
from Learning
Resource LR
portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide, 2016. Grade
6, page 196
Lesson Guide in Elementary Math Gr. 6 p. 7783
21st Century MATHletes pp. 200-209
21st Century MATHletes pp. 200-209
DLP 6 Module 54
https://www.supertacherworksheets.com/solidshapes.html
77
IV. PROCEDURE
A. Reviewing
previous lesson or
presenting new
lesson.
Advance Learners
Drill: Guess who am I? My name is given in the box
below. Oops! Spelling of my name is jumbled up.
Try to identify it from the clues given below and
write it in the blank space.
(1) I am a solid whose base is a polygon and
whose faces are triangles. ________
(2) I am a prism whose all faces are square.
________
(3) Looks like marbles but have no vertex.
________
(4) I am a flat figure that can be folded and can
form a closed, three-dimensional object.
RAYPDIM
EBCU
SERPEH
NET
Average Learners
Drill: Guess who am I? My name is given in the box
below. Oops! Spelling of my name is jumbled up.
Try to identify it from the clues given below and
write it in the blank space.
(1) I am a prism whose all faces are square.
________ (2) Looks like marbles but have no
vertex. ________
(3) I am a solid whose base is a polygon and whose
faces are triangles. _______
RAYPDIM
SERPEH
EBCU
78
B. Establishing a
purpose for the
lesson
Advance Learners
MOTIVATION:
Ask the pupils to illustrate the figures.
By Pair
Guide Questions:
1. Is it possible to combine plane figures to form
solid figures?
2. What is the corresponding solid figure if circles
and rectangle will be combined? Circle and
triangle? Square and triangles? Rectangle and
triangle? What else can you think of?
3. Can all plane figures be combined to one another
to form different kinds of solid figures? Give
example and explain.
Plane
Figures
Illustration
Solid
Figures
Circle
Sphere
Rectangle
Rectangular
Prism
Square
Cube
Triangle
Triangular
Pyramid
Illustration
Average Learners
Ask the pupils to illustrate the figures.
By Triad
Guide Questions:
1. Is it possible to combine plane figures to form
solid figures.
2. What is the corresponding solid figure if circles
and rectangle will be combined? Circle and
triangle? Square and triangles? Rectangle and
triangle? What else can you think of?
3. Can all plane figures be combined to one another
to form different kinds of solid figures? Give
example and explain.
79
Plane
Figures
Illustration
Solid
Figures
Illustration
Circle
Sphere
Rectangle
Rectangular
Prism
Square
Cube
Triangle
Triangular
Pyramid
AVERAGE LEARNERS
C. Presenting examples/
instances of the new
lesson.
Group Activity:
Distribute an activity sheet to each group.
Complete the table below by putting tick mark across
the respective property found in mentioned.
Properties
Cone
1. The figure is a
polyhedron.
2. The figure
has
diagonals.
3. The shape
has curved
edges.
4. The base of
figure is a
polygon
5. The bases
are
congruent.
80
Cylinder
Prism
Pyramid
Answer:
Properties
1. The figure is a
polyhedron.
2. The figure
has
diagonals.
3. The shape
has curved
edges.
4. The base of
figure is a
polygon
5. The bases
are
congruent.
Cone Cylinder
X
X
Prism
/
Pyramid
/
X
X
X
/
/
/
X
X
X
X
/
X
/
/
/
X
AVERAGE LEARNERS
Complete the table below by putting tick mark across the
respective property found in mentioned.
Properties
1. The figure is
a polyhedron.
2. The figure has
diagonals.
3. The shape
has curved
edges.
.
Cone Cylinder
Answer:
Properties
Cone Cylinder
1. The figure is
X
X
a polyhedrn.
X
X
2. The figure
has
diagonals.
/
/
3. The shape
has curved
edges.
84
Prism
Pyramid
Prism
/
Pyramid
/
X
/
X
X
D.
Discussing
new
concepts
and
practicing new skills
#1
Given:
1. Cube
Use the figure above to answer the following questions.
1.
2.
3.
4.
5.
E.
Discussing
new
concepts
and
practicing new skills
#2
How many parallel faces are there in figure 1? Name them.
Are all faces of figure 1 congruent? Explain.
How many vertex/vertices can you count name in figure 1?
Give at least 2 edges of figure 1.
What kind of polygon are the faces of the second figure?
How many faces do we have in second figure?
Show a video of visualizing solid figures.
https://www.youtube.com/watch?v=7uAbGoGYLcc
85
F.
Developing
Mastery
ADVANCE LEARNERS
Put your answer on the box.
AVERAGE LEARNERS
Put your answer on the box.
86
G. Finding
practical application of
concepts and skills in
daily living
Mr. Delos Santos wants to buy a water container. He
is thinking on which is best to buy- the rectangular or
a cylindrical solid figures.
1. Imagine that the 2 containers have the same height
and width/diameter, does the solid figure have
something to do with quantity of water that the
container hold?
2. Which of the 2 containers will you suggest to Mr.
Delos Santos is best to buy? Explain your answer.
H. Making
generalizations
and What is a solid figure?
abstraction about the
- Solid figures have three dimensions the length,
lesson
width and the height. Solids are boundaries that
enclose a part of space. There are two kinds, the
prism and pyramid.
What is a prism? A pyramid?
- A prism is a solid figure whose two bases are
congruent polygon in parallel planes, and the other
faces called lateral faces, are parallelograms.
- A pyramid is a space figure in which one face is
called the base, and the other faces, called lateral
faces, are triangles having a common vertex called
the apex.
I. Evaluating
There are solid figures that are bounded by curve
surfaces.
- A cylinder is a prism with bases bounded by simple
closed curves usually circles.
- A cone is a pyramid with circular base and all line
segments from a circle meet at a point called apex.
A sphere is a solid all points of which are equidistant
from some given point.
ADVANCE LEARNERS
Read each clue. Write the name of the solid figure it
describes.
1.
2.
3.
4.
5.
6.
7.
8.
I have one flat face. I come to a point.________
I have one square and four triangles._________
I have no faces.___________
I have six squares.___________
I have two flat faces. I can roll.__________
I have four triangles but no rectangles.________
I have two triangles and three rectangles._______
I have six rectangles._________
87
AVERAGE LEARNERS
Read each clue. Write the name of the solid figure it
describes.
1.
2.
3.
4.
5.
J. Additional activities
for application or
remediation
V. REMARKS
VI. REFLECTION
I have one flat face. I come to a point. ________
I have one square and four triangles. _________
I have no faces. ___________
I have six squares. ___________
I have two flat faces. I can roll. __________
Answer Math Challenge on page 208-209
88
School
Teacher
Time and
Date
Grade Level 6
Learning Mathematics
Area:
Quarter: Third
Week 3- Day 4
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives
II. CONTENT
The learner demonstrates understanding of
solid figures.
The learner is able to construct and describe the
different solid figures: cube, prism, pyramid,
cylinder, cone, and sphere.
The learner identifies the nets of the following
space figures: cube, prism, pyramid, cylinder,
cone, and sphere using plane figures.
M6GE-IIIc-32
Identifying the nets of the following space
figures: cube, prism, pyramid, cylinder, cone,
and sphere using plane figures.
V. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
K to 12 Math Curriculum, 2016. Grade 6, page 197
Lesson Guide in Elementary Math Gr. 6 p. 77-83
2. Learner’s
Material pages
3. Textbook
pages
21st Century MATHletes pp. 200-209
21st Century MATHletes pp. 200-209
4. Additional
DLP 6 Module 54
Materials from
Learning
Resource LR
portal
B. Other Learning https://www.math-salamanders.com/geometry-nets.html
Resources
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
89
IV. PROCEDURE
A. Reviewing
previous lesson or
presenting new
lesson.
ADVANCE LEARNERS
Drill (Flascards)
Name the solid figure that each object represents.
1. Fluorescent Light
2. Party Hat
3. Funnel
4. Globe
5. Drum
AVERAGE LEARNERS
Drill (Flashcards)
Name the solid figure that each object represents.
1. Book
2. Volcano
3. Ball
B. Establishing a MOTIVATION:
purpose for the Every morning, we take our breakfast to jumpstart our
day. Breakfast is the first and most important meal of
lesson
the day. People have different preferences for
breakfast. Some prefer to have a light breakfast, while
others want it heavy. One good example of a healthy
breakfast is a bowl of cereals. All cereals are available
in a similar box. What kind of solid figure is it? Have
you tried unfolding cereal box?
Present the lesson on page 200.
Let us unfold a cereal box.
Based on the illustration (see the illustration on page
200), if we unfold the cereal box we will come up
with a closed plane figure.
This two-dimensional figure is called a net.
90
C. Presenting
examples/ instances
of the new lesson.
ADVANCE LEARNERS
Group Activity:
Identify the solids that can be formed by the given
figures.
Given Nets
Transformed
Figures
Observations
AVERAGE LEARNERS
Identify the solids that can be formed by the given
Figures.
Given Nets
91
Transformed
Figures
Observations
D.
E.
Discussing
new
concepts and practicing
new skills #1
Show a video of identifying the nets of a solid figures.
Discussing
new
concepts and practicing
new skills #2
NETS INFORMATION SHEET
https://www.youtube.com/watch?v=jVlFsmpZe6o
Cube
Cuboid
Triangular Prism
Faces: 6
Edges: 12
Vertices: 8
Faces: 6
Edges: 12
Vertices: 8
Faces: 5
Edges: 9
Vertices: 6
Square-based
pyramid
Tetrahedron
Hexagonal-based
pyramid
Faces: 5
Edges:8
Vertices: 5
Faces: 4
Edges: 6
Vertices: 4
Faces: 7
Edges: 12
Vertices: 7
Octahedron
Dodecahedron Icosahedron
Faces: 8
Edges: 12
Vertices: 16
Faces: 12
Edges: 30
Vertices: 20
Faces: 20
Edges: 30
Vertices: 12
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
92
F. Developing
mastery
ADVANCE LEARNERS
For each 3d shape, shade the correct net.
AVERAGE LEARNERS
For each 3d shape, shade the correct net.
93
G. Finding
Draw a line to match these 3D shapes with the nets
practical
below.
application of
concepts and Pair-Share
skills in daily
living
H. Making
What is a net?
generalizations
- A net is a flat figure that can be folded to form a
and abstraction
closed, three-dimensional object. Such an
about
the
object is called a solid.
lesson
Differentiate the nets of pyramids, prisms, cones and
cylinders from each other
- Prisms and pyramids are solid geometric
shapes that have flat sides, flat bases and
angles. However, the bases and side faces
on prisms and pyramids differ. Prisms have
two bases -- pyramids only have one. A
cylinder is similar to a prism, but its two bases
are circles, not polygons. Also, the sides of a
cylinder are curved, not flat. A cone has one
circular base and a vertex that is not on the
base. The sphere is a space figure having all
its points an equal distance from the center
point.
94
I. Evaluating
learning
ADVANCE LEARNERS
Choose the correct nets for each solid shapes.
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
95
AVERAGE LEARNERS
Choose the correct nets for each solid shapes.
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
J. Additional
activities for
application or
remediation
Answer remediation on TG page 81
96
What solid shape does each nets make?
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
V. REMARKS
VI. REFLECTION
97
School
Teacher
Time and
Date
Grade Level 6
Learning Mathematics
Area:
Quarter: Third
Week 3- Day 5
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of
solid figures.
B. Performance Standards The learner is able to construct and
describe the different solid figures: cube,
prism, pyramid, cylinder, cone, and
sphere.
C. Learning
The learner identifies the nets of the
Competencies/
following space figures: cube, prism,
Objectives
pyramid, cylinder, cone, and sphere using
plane figures.
M6GE-IIIc-32
Identifying the nets of the following
II. CONTENT
space figures: cube, prism, pyramid,
cylinder, cone, and sphere using plane
figures.
III. LEARNING
RESOURCES
A. References
K to 12 Math Curriculum Guide, 2016.
1. Teacher’s Guide
Grade 6, page 197
pages
Lesson Guide in Elementary Math Gr. 6
p. 77-83
21st Century MATHletes pp. 200-209
2. Learner’s Material
pages
3. Textbook pages
21st Century MATHletes pp. 200-209
4. Additional Materials
from Learning
Resource LR
portal
B. Other Learning
Resources
LP 6 Module 54
https://www.math-salamanders.com/geometrynets.html
https://www.tes.com/teaching-resource/y4-b3worksheet-visualising-3d-shapes-make-nets6088210
98
IV. PROCEDURE
A. Reviewing
previous lesson or
presenting new
lesson.
Advance Learners
A.Drill: Identify what spatial figure is being shown.
1.
2.
4.
3.
5.
6.
Average Learners
1.
2.
4.
3.
5.
https://www.tes.com/teaching-resource/y4-b3-worksheetvisualising-3d-shapes-make-nets-6088210
99
B. Establishing a
purpose for the
lesson
By Pair
Advance Learners
Average Learners
By Triad
100
C. Presenting
examples/ instances
of the new lesson.
D.
Discussing
concepts
practicing new
#1
E. Discussing
concepts
practicing new
#2
new Show a video of “Learning Solid Figures and Nets
and (cone, cylinder, prism, pyramid, cube.
skills
https://www.youtube.com/watch?v=TFshYzrrlZI
new
and
skills
https://www.youtube.com/watch?v=TFshYzrrlZI
101
F. Developing
mastery
ADVANCE LEARNERS
Group Activity.
Each group will make 1 different net for the following.
Group1: hexagonal prism
Group 2: square pyramid
Group 3: Triangular Prism
Group 4: cylinder
Group 5: rectangular prism
.
AVERAGE LEARNERS
Group Activity.
Each group will make 1 different net for the following.
Group 1: Square pyramid
Group 2: Triangular prism
Group 3: Cylinder
Group 4: Rectangular prism
.
G. Finding
Think Pair-Share
practical
application of
Choose a partner with whom you like to discuss
concepts and
these processing questions. Respect each
skills in daily
other’s insights by listening to each other’s ideas.
living
Guide Questions:
1. How do we easily know the solid figure out from
the given net?
2. How can a net help you find the space or solid
figure composed of polygons?
3. Describe a three-dimensional object that would
be difficult or impossible to unwrap into a net?
4. In what job might people find it useful to draw
nets of solid object?
How can you apply this lesson in real life?
H. Making
What is a net?
generalizations
- A net is a flat figure that can be folded to form a
and abstraction
closed, three-dimensional object. Such an
about
the
object is called a solid.
lesson
102
Differentiate the nets of pyramids, prisms, cones and
cylinders from each other
- Prisms and pyramids are solid geometric
shapes that have flat sides, flat bases and
angles. However, the bases and side faces
on prisms and pyramids differ. Prisms have
two bases -- pyramids only have one. A
cylinder is similar to a prism, but its two bases
are circles, not polygons. Also, the sides of a
cylinder are curved, not flat. A cone has one
circular base and a vertex that is not on the
base. The sphere is a space figure having all
its points an equal distance from the center
point.
I. Evaluating
learning
Identify the solid figure that can be formed by each
net.
103
J. Additional
activities for
application or
remediation
Answer Enrichment Activity on TG page 82
V. REMARKS
VI. REFLECTION
104
School
Teacher
Time and
Date
Grade level 6
Learning Area: Mathematics
Quarter Third
Week 4- Day 1
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Objectives write
the LC code for
each
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teachers Guide
Pages
2. Learner’s Material
pages
3. Textbook pages
4. Additional
Materials From
Learning
Resources (LR)
Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge or sequence
expression, and equations, mathematical problems
and real-life situations.
The learner formulates the rule in finding the nth
term using different strategies(looking for a pattern,
guessing and checking, working backwards)
M6AL – IIId – 7
Formulating the Rule in Finding the nth Term Using
Different Strategies
K to 12 Math Curriculum, 2016. Grade 6 page, 197
TG mathematics 6 pp
21st Century Mathletes 6 pp 85- 87
21st Century Mathletes 6 pp 213 - 221
Manila paper, Pictures, real objects
Drill:
Skip counting by 5, by 8, by 10, and by 12.
Advance Group
Present the following
sequence. Give the 7th
term in each.
Average Group
Present the following
sequence. Give the 6th
term in each.
1. 3, 6, 9, 12 ……….
2. 0.6, 0.12, 0.18 …….
3. 7, 14, 21, 28
1. 2, 4, 6, 8 ….
2. 0.5, 0.10, 0.15, 0.20…
3. 3, 6, 9, 12
105
B. Establishing a
purpose for the
lesson
Teacher will show letters, and pupils will guess the
next letter in the sequence below.
O. T, T. F, F, S, S, E

C. Presenting
examples/
instances of the
new lesson
Ask the pupils what are seen in the flash
cards
 What will be the next letter after letter E.
Present the Pascal’s triangle and show the sum of
the numbers horizontally.
Pascal Triangle
1
1 1
1 2 1
1 3 3
1
1 4 6 4 1
Tell the pupils to list horizontal sums in order, and let
them guess the next three. The pupils must share
what he or she thinks the existing pattern is.
D. Discussing new
concepts and
practicing new
skills # 1.
Therefore, in the pattern the next three terms in the
sequence are 12, 14, and 16.
Activity 1
Activity 1
1. Give the pupils number
figures. objects or
symbols arranged in a
definite order or
sequence that is often
encountered in
Mathematics
2. Tell them that number
figures and letters are
arranged in a definite
order, using the given
sequences.
3. Tell the pupils that
sequences usually
follow a rule that can
be applied to the
counting numbers to
find the nth term in a
sequence.
4. Give the first two
examples that follow
and show how the
rules are formulated to
find the nth term, then
106
Here are more
sequences, let the pupil
guess the next number
letter or figure.
Group 1
a. What is the
next number
2, 4, 6
Group 2
b. What is the
next figure?
Group 3
c. What is the
next letter?
E. Discussing new
concepts and
Practicing new
skills # 2
have the pupils
A, D, G, J…..
formulate the rule for
the remaining items.
Give the next three terms and give the rule that
applies to the sequence.
1.
2.
3.
4.
3, 6, 9, 12 ……….
1, 4, 9, 16 ……….
11, 12, 13, 14 …….
3, 1, -1, -3 ……….
Find the next three terms
1.
2.
3.
4.
F. Developing
Mastery
y1, y21, y31, y4……..
a1, 2b, 3c, 4d ……
a, a+b, b at2b..
7a, 5a, 3a
Possible answers
Answer y5, y6, y7
Answer 5e, 6f, 7g
Answer at3b, at4b at5b
Answer a,-a,-3a
Formulate the rule for the following items.
1. 2, 3, 4, 5 ……..
2. 2, 4, 6, 8 ……..
3. 2, 5, 8, 11……
4.
5.
G. Finding Practical
application of
concepts and skills
in daily living
1 3 5 7
, , ,
5 5 5 5
1
…….
1 3 4
, , , …….
12 3 4 3
Every year, Mang
Ramon’s kinalabaw
mango tree produces 2
more kilos of mango
that the previous year.
If 25 kilograms were
harvested in year 2012.
How many kilos will it
produce in 2017? What
is the total no. of kilos
of mangoes that the
tree produced from
2012 to 2017?

What is asked in
the problem?
107
Erica saves twice as much
as what she saved the day
before. If she starts saving
₱2.00 on March 1, how
much will she save on
March 10?
How much money will she
have in all after March?
What rule can be used to
find the amount she can
save on a specific day if
she will continue saving in
the future?

What is asked in
the problem?



H. Making
generalization and
abstraction about
the lesson
I. Evaluating learning
What are the
given facts?
What strategy
can we use to
solve the
problem?
How can you
check if your
answer is right?



What are the given
facts?
What strategy can
we use to solve the
problem?
How can you check
if your answer is
right?
How do we find the nth
term of a sequence?
Find the next three terms in each sequence. Then
write the rule for finding the nth term.
1. 10, 15, 20, 25 _____, _____, _____
Rule __________________________
2. 3, 5, 7, 9, _____, _____, _____
Rule __________________________
3.
1 1 1 1
, , , ,
2 3 4 5
____, ____, ____
Rule _________________________
4. 20, 16, 12, 8, _____, _____, _____
Rule _________________________
5. 2, 5, 8, 11, _____, _____, _____
Rule ___________________________
J. Additional activities
for application or
remediation
Solve each problem
1. Complete the pattern: 7, 12, 22, ____, 57, 82,
_____.
2. Carmi gets a starting salary of ₱ 13, 000.00 a
month and an increase of ₱ 500.00 annually.
What will be her salary during the fifth year?
V. REMARKS
VI. REFLECTION
108
School
Teacher
Time and
Date
Grade level 6
Learning Area: Mathematics
Quarter Third
Week 4 – Day 2
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies
Objectives
write the LC
code for each
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teachers
Guide Pages
2. Learner’s
Material pages
3. Textbook
pages
4. Additional
Materials From
Learning
Resources
(LR) Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous lesson
or presenting
the new lesson
The learner demonstrates understanding of sequence in
forming rules, expressions and equations.
The learner is able to apply knowledge or sequence
expression, and equations n mathematical problems and
real -life situations.
The learner formulates the rule in finding the - nth term
using different strategies(looking for a pattern guessing
and checking working backwards ).
M6AL – IIId – 7
Formulating the Rule in Finding the nth Term using
Different Strategies
K to 12 Math Curriculum Guide 2016. Grade 6, page 197
TG mathematics 6 pp
21st Century Mathletes 6 pp 85- 87
21st Century Mathletes 6 pp 213 - 221
211st century mathletes 5 pp 250 - 253
Manila paper, Pictures, real objects
Drill:
Skip counting by 2, 4, 6, 8, 10
Advance Group
Find the nth term rule for
each of the ff.
1. 2, 5, 8, 11, 14...6th term
2. 6, 7, 8, 9, 10 … 7th term
3. 14, 19,24,29,34,8th term
Show answers
109
Average Group
⬜ 1. 15,20,25,30,35,… 6th term
⬜ 2. 8,9,10,11,12,…. 7th term
⬜ 3. 3,-9,-8,-7,-6,-5…. 8th term
Check Answer
B. Establishing a
purpose for the
lesson
Teacher will show the following sequence and let the
pupils give the 7th term in each
1.
2.
3.
4.
3, 6, 9, 12 ……………
7, 14, 21, 28 …………
0.6, 0.12, 0.18 ……….
-3, -2, -1, 0, 1………...
Ask the pupils what are the next numbers for the said
term.
C. Presenting
examples/
instances of
the new lesson
D. Discussing new
concepts and
practicing new
skills # 1.
Below are Fibonacci numbers in Pascal’s triangle. Write
the next three numbers in the pattern. Give the rule in
finding the pattern.
1,1, 2, 3, 5, 8
Activity 1
Give the next two terms
Give the rule for finding the nth (6th/7th)
A. 5, 8, 11, 14, 17 ….
Give the next two terms
Give the rule for the nth term
B. 5, 9, 13, 17, 21….
Give the next two terms
Give the rule for the nth terms
C. 4, 9, 14, 19, 24….
110
E. Discussing
new concepts
and Practicing
new skills # 2
F. Developing
Mastery
Solve each problem
1. Miguel saves part or his
allowance in his piggy bank
every day, on the first day,
he saved ₱ 1.00. On the
second day, he saved ₱
2.00. On the third day, he
saved ₱5.00. On the fourth
day, he save ₱ 14.00. If this
pattern will continuous, how
much will Miguel save on the
sixth day?
a. What is asked?
How much coins will
Miguel save on the
sixth day?
b. What are the given
facts?
c. What is asked?
How much coins will
Miguel save on the
sixth day?
d. What are the given
facts?
₱ 1.00 save on first
day, ₱ 2.00 save on
second day ₱ 5.00
save on the third day
and ₱ 14.00 save on
fourth day.
₱ 3.00 save on first
day, ₱ 6.00 save on
second day ₱ 9.00
save on the third day
and ₱ 12.00 save on
fourth day.
Give the next three terms of the sequence and the rule to
find the nth term.
1.
2.
3.
4.
5.
G. Finding
Practical
application of
concepts and
skills in daily
living
1. Ben saves part or his
allowance in his piggy bank
every day, on the first day,
he saved ₱ 3.00. On the
second day, he saved ₱
6.00. On the third day, he
saved ₱9.00. On the fourth
day, he save ₱ 12.00. If this
pattern will continuous, how
much will Miguel save on the
sixth day?
2, 3, 4, 5 ____, ____, ____
2, 4, 8, 16 ____, ____, ____
7, 14, 21, 28 ____, ____, ____
1, 10, 100, 1000 ____, ____, ____
3, 4, 6, 10, ____, ____, ____
Solve each problem
1. Syd loves to draw stairs
in his notebook. He draws
6 stars on the first stage,
10 stars on the second
111
page, 14 stars on the third
page, and 18 stars on the
fourth page. If this pattern
continuous, how many
stars will be drawn on the
fifth page of his notebook?
H. Making
generalization
and abstraction
about the lesson
II. Evaluating
learning
a. What is asked in the
problem/
b. What are the given
facts?
How do we find the nth
term of a sequence?
Find the next three terms of the sequence and state the
rule in finding the nth term.
1.
2.
3.
4.
5.
J. Additional
activities for
application or
remediation
6, 11, 16, 21, ____, ____, ____,
2, 7, 22, 67, ____, ____, ____,
5, 15, 45, 135, ____, ____, ____,
1, 5, 25, 125, ____, ____, ____,
2, 4, 8, 16, ____, ____, ____,
Solve each problem
An auditorium has 12 rows of seats. It has 30 seats
in the first row, 35 seats in the second row, and 40
seats in the 3rd row. If this pattern continues, how
many seats will be there on the 7th and 8th rows?
Formulate the rule in finding pattern.
V. REMARKS
VI. REFLECTION
112
School
Teacher
Time and
Date
Grade level 6
Learning Area: Mathematics
Quarter Third
Week 4 – Day 3
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Objectives write the
LC code for each
II. Content
III. LEARNING
RESOURCES
A. References
1. Teachers Guide
Pages
2. Learner’s Material
pages
3. Textbook pages
4. Additional Materials
From Learning
Resources (LR)
Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrates understanding of sequence
in forming rules, expressions and equations.
The learner is able to apply knowledge or sequence
expression, and equations n mathematical problems
and real life situations.
The learner formulates the rule in finding the -nth
term using different strategies (looking for a pattern,
guessing and checking, working backwards)
M6AL – IIId – 7
Formulating the Rule in Finding the nth Term Using
Different Strategies
K to 12 Math Curriculum Guide 2016. Grade 6,
page 197
TG mathematics 6 pp
Financial literacy integration
21st Century Mathletes 6 pp 85- 87
21st Century Mathletes 6 pp 213 - 221
Manila paper, Pictures, real objects
Drill:
Advance Group
Supply the next three
terms
1. Z, X, V …….
2. 10, 15, 20 …….
3. a+b, 2c+2d, 3e+3f….
Average Group
Supply the next three
terms
1 1 1
1. , , …..
5 10 15
2.
113
1 2 3
, , ,
4 5 6
….
B. Establishing a
purpose for the
lesson
C. Presenting
examples/ instances
of the new lesson
Teacher will give a set of domino pieces and pupils will
construct different patterns
Present a set of domino pieces, and pupils will
construct different patterns in many ways.
Ask: what are the different pattern you constructed
Write your answer on the board
D. Discussing new
concepts and
practicing new skills
# 1.
Activity 1
Solve the given problem
below.
Problem: the amount or
your savings increases
each day. April 1 you
have an initial amount
of ₱6. How much is
your saving for the
month
Guide Questions:
1. How much money did
you have at the start
of the month?
2. How much saving will
you have an April 2?
on April 3? on April
10?
3. How many ₱2 were
added to your initial
saving on April 2? on
April 3? on April10?
4. What is the amount
on your saving for the
month?
114
5. How did you the find
the amount of your
saving for the month?
6. What will happen to
the amount of savings
if you continue setting
aside of your money
for a longer period of
time?
7. What is the advantage
of saving money?
8. it’s a student, can you
suggest other ways of
saving money?
E. Discussing new
concepts and
Practicing new
skills # 2
Activity 2 WANNA BE
PAG- IBIG II MEMBER
Read and analyze to
solve the given problem
below.
Activity 2 WANNA BE PAGIBIG II MEMBER
Read and analyze to solve
the given problem below.
Problem:
Problem:
Mrs. Lopez started
saving ₱1,500 monthly
in a modified Pag-ibig II
Saving Program.
If there was an initial
amount of ₱ 10 400
before she started
saving, what is the
amount of her saving, in
5 years? 10 years?
Mrs. Lopez started saving ₱
500 monthly in a modified
Pag-ibig II Saving Program.
If there was an initial
amount of ₱ 1,400 before
she started saving, what is
the amount of her saving, in
5 years? 10 years?
1. How did you find the
amount of saving in 5
years? 10 years?
2. What is the amount of
savings in her account
3 years after she
started saving?
3. What is the pattern
generated given by
the situation.
1. How did you find the
amount of saving in 5
years? 10 years?
2. What is the amount of
savings in her account 3
years after she started
saving?
3. What is the pattern
generated given by the
situation.
The above activity illustrates sequence where the
difference between any two consecutive terms is
constant. This constant is called the common
difference and the said sequence called an arithmetic
115
sequence is a sequence where every term after the
first is obtained by adding a constant number called
the common difference.
F. Developing
Mastery
Find the 7th term of the
Arithmetic sequence.
1. 36, 32, 38, 24, 20
2. 5, 6, 8, 11, 15
Find the 5th term of the
Arithmetic sequence.
1. 3, 7, 11, 15, 19….
2. 80, 75, 70, 65, 60
G. Finding Practical
application of
concepts and skills
in daily living
Solve each Problem
H. Making
generalization and
abstraction about the
lesson
How do we find the nth
term of a sequence?
III. Evaluating learning
What is the nth term for each arithmetic sequence and
the rule in finding nth term?
1. Carla earned
₱ 240 in the first
week ₱ 350 in the
second week and
₱ 460 in the third
week and so on.
Is the pattern
continuous? How
much did she
earn in the first
five weeks?
6. 3, 5, 7, 9, (7th term)
7. 3, 6, 9, 12, 15, ….(10th term)
8. 6, 8, 10, 12, 14, (9th term)
9. 5, 6, 7, 8, 9…. (8th term)
10. 1, 4, 9, 16, 25… (20th term)
J. Additional activities
for application or
remediation
Solve the problem
3. The second term of an arithmetic sequence is -8
and the seventh term is 17. What is the sum of
the first 10 terms?
V. REMARKS
VI. REFLECTION
116
School
Teacher
Time and
Date
Grade level 6
Learning Area: Mathematics
Quarter Third
Week 4 – Day 4
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Objectives write the
LC code for each
II. Content
III. LEARNING
RESOURCES
A. References
1. Teachers Guide
Pages
2. Learner’s Material
pages
3. Textbook pages
4. Additional Materials
From Learning
Resources (LR)
Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrate understanding of
differentiate of expressions and equations.
The learner is able to apply knowledge of
expressions and equations in mathematical
problems and real life situations.
The learner differentiates expression from
equation
M6AL – IIId – 15
Differentiating Expressions From Equations
K to 12 Math Curriculum Guide 2016. Grade 6,
page, 197
Math Textbook 6 pp 1-3 BEC PELC A. 11.1
Chart, Stopwatch, pictures of Philippine
Presidents
Lesson Guide in Mathematics 6 pages 1-3
Drill:
Giving terms or Phrases that refer to
addition, Subtraction, Multiplication or Division
(Game)
a. Divide the class into 2 groups
b. Teacher gives an operation, Say
“addition”
c. Each member of the groups
simultaneously goes to the board and
writes a term or phrase that refers to the
given operation. Ex: more than, increased
by, Plus, Added to etc.
d. Within 2 minutes, each group has to write
as many terms or phrases as they can.
After wards, the teacher checks and
counts the correct answers.
117
B. Establishing a
purpose for the
lesson
e. Repeat the same process with
subtraction, multiplication and division.
f. The group with the most number of
correct answers wins.
a. Let the pupils name the different
Presidents of the Philippines from
President Emilio Aguinaldo to President
Gloria Macapagal – Arroyo.
Show
them the pictures of the different
president and let them identify each.
b. Ask: What expressions describes
President Emilio Aguinaldo?
(The first president of the Philippines
Republic)
What expressions describes President
Manuel L. Quezon
(President of the Philippines Commonwealth)
Ask the same questions on the other president?
c. Why should we remember our past
president, Cite their good deed.
d. If we use expressions in mathematics to
describe relationships between numbers
and the operations being used.
C. Presenting
examples/ instances
of the new lesson
Teacher will present the lesson using the activity
cards
Activity 1 – Use of Chart
Word Phrases
Four times ten divide by
five
Twelve diminished by
two
Six times three added to
seven
Eight added to the three
product of five and three
Twenty – five added to
two
Three times twenty – five
less twenty
The quotient of 36 and 6
118
Numerical Expression
(4x10) ÷ 5
12 – 2
(6x3) + 7
8+ (5x3)
2+25
(3x25) - 20
36 ÷6
The sum of three and
thirty – nine divided by
seven
D. Discussing new
concepts and
practicing new skills
# 1.
(3+39) ÷ 7
Ask: what are the Mathematics terms used in
the phrases?
What terms denote addition? Subtraction?
Multiplication? Division?
Activity 2
Create your own (By
Pairs)
Each pupils thinks of 3
mathematical expressions
involving at least 2
operations
(Use only whole numbers)
Ex: 25 more than the
product of 6 and 4
The product of the sum
and difference of 8 and 5
Then he / she exchanges
with a partner and
translate the mathematical
phrases into expressions.
Check the answers.
E. Discussing new
concepts and
Practicing new
skills # 2
Write an expression
the following:
for
a. Your age less three
b. Your age plus nine
c. Your age plus twice
your age
d. Thrice your age
e. Your age plus your
seatmate’s age
f. Your age 5 years
ago
g. Your age 6 years
from now
119
F. Developing
Mastery
G. Finding Practical
application of
concepts and skills
in daily living
H. Making
generalization and
abstraction about the
lesson
IV. Evaluating learning
Write the expression for the following
1. Seventy – five decreased by five.
2. Fourteen divided by the sum of three and
four.
3. Triple the sum of elven and six.
4. One more than the product of six and
eight.
5. Twenty plus five less than eighty.
6. Take away 10 from 50.
7. Four more than twice three.
8. Difference of 17 and 8.
Solve each problem:
1. In a film showing sponsored by the
dramatic club, a ticket cost ₱ 50 for
members. What will be the expression for
non – members if the ticket cost ₱ 5 more
than the members?
2. The boat fare for an adult in going to the
province is ₱ 1,700. Write the expression
for the boat fare of children if the cost is
half the price for adults and there are 20
children.
3. The cost of one salted egg is ₱ 6.50.
What is the expression if one buys a
dozen and each egg costs 50¢?
What is an expression?
How do you translate word
phrases into expressions?
A. Which expression is correct?
Choose between A or B.
1. The sum of eleven and nineteen.
a. 11x19 b. 11+19
2. Eight decrease by five
a. 8-5
b. 8x5
3. Twelve plus thirty – six
a. 12 + 36 b. 12x36
4. Five less than seven
a. 5x7
b. 7-5
5. Four times the sum of two and five
a. 4x(2+5) b. 4x(5-2)
120
J. Additional activities
for application or
remediation
Write five examples of equation.
V. REMARKS
VI. REFLECTION
121
School
Teacher
Time and
Date
Grade level 6
Learning Area: Mathematics
Quarter Third
Week 4 – Day 5
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Objectives write the
LC code for each
II. Content
III. LEARNING
RESOURCES
A. References
1. Teachers Guide
Pages
2. Learner’s Material
pages
3. Textbook pages
4. Additional Materials
From Learning
Resources (LR)
Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrate understanding of differentiate
of expressions and equations.
The learner is able to apply knowledge of expressions
and equations in mathematical problems and real life
situations.
The learner differentiate expression from equation.
M6AL – IIId – 15
Differentiating Expressions From Equations
K to 12 Math Curriculum Guide 2016. Grade 6,
page 197
Lesson Guide in Elementary Mathematics 6
Pictures, map of the Philippines and charts
Math textbook Math 5
Math Textbook math pp 3-5 BEC PELC A. 1.1
Drill:



Recall what is an expression and equation
Identify which example of an expressions
and equations.
1.) 5(x + 2)
2.) 14y- 5(3-2y)
3.) 10x-3 ( 2x + 8) 4.) 10- 8 = p
--9
5.) 8*5= 4+ b
122
B. Establishing a
purpose for the
lesson
Teacher will show the map of the Philippines and give
5 names of active Volcanoes.
Pupils will paste the name of volcano where it is
located in the map.
Ex: Province
Batangas
Albay
Negros Oriental/occidental
Camiguin
Sorsogon
C. Presenting
examples/ instances
of the new lesson
Volcano
Taal
Mayon
Kanla – on
Hibok – hibok
Bulusan
You have associated the volcano to the province where
it is located
Ask: Where is Mt. Mayon located?
Show a picture of Mt. Mayon and let the pupils describe
it.
Say: The Phil. Is an archipelago of more than 7100
islands. Most of these Islands are of Volcanic Origin.
There are 37 Volcanoes and 18 are still active. What is
the number of Volcanoes that are inactive? Write an
equation to solve the problem.
37 – 18 = 19
D. Discussing new
concepts and
practicing new skills
# 1.
Activity 2
Use of illustration
Refer to the figure
4
6
Write an equation to find the number of small squares
in the figure.
Check the equation that you’ve made by counting the
number of squares in the figure.
Ask: Is your equation true? Are the two quantities
equal?
123
E. Discussing new
concepts and
Practicing new
skills # 2
F. Developing
Mastery
Complete the equations
a. 18 - 𚻶 = 5 + 6
b. 𚻶3 = 8𚻶
c. 2 + 2 + 8
d. (2x10) (13+7) = 20𚻶
e. 3(4 + 4 + 4) = 𚻶2
Solve each problem
1. Four friends share a boy
or pens. Each receive 3
pens write and solve the
equations to find the
number of pens in the
boy.
G. Finding Practical
application of
concepts and skills
in daily living
1. There are 56 pupils in
a class. Thirty – six of
them joined the fieldtrip.
Write an equation to find
the number of pupils who
did not join the fieldtrip
Show the table at the right
the pupils
Ask: a) Which two items
that can be purchased with
₱ 100 without change?
Write the equations
b. what is the total cost of 2
soaps and a tooth paste?
Items
Price
Bath Soap
₱ 35.50
Tooth Paste
₱ 55.50
Shampoo
₱ 64.50
Tooth brush
₱ 79.50
Write the equation
H. Making
generalization and
abstraction about the
lesson
What is an equation? What is an expression? How do
they differ?
I. Evaluating learning
Find the Value of N that will make the statement TRUE.
An equation is mathematical sentence formed by
placing an equal (=) between two expressions.
1. 2N + 5 =45
2. N = 10 (7+11)
3. N + 15 = 35 – N
4. N = 20
5
5. 2 (N + 6) = 22
124
J. Additional activities
for application or
remediation
Solve the problem
1. A car travels at an average span of 36 km per
hour. Write and solve an equation to predict now
many hours it will take to travel 432 km if it
continues at this speed.
V. REMARKS
VI. REFLECTION
125
School
Teacher
Time and Dates
Grade Level
Learning Area
Quarter
Week 5- Day 1
I. OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
a. References
b. Teacher’s Guide pages
c. Learner’s material pages
d. Textbook pages
e. Additional Materials from
Learning Resource (LR)
portal
f. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting the
new lesson
6
Mathematics
Third
The learner demonstrates understanding of sequence
in forming rules, expressions and equations.
The learner is able to apply knowledge of sequence,
expressions, and equations in mathematical problems
and real-life situations.
The learner gives the translation of real-life verbal
expressions and equations into letters or symbols and
vice versa.
M6AL-IIIe-16
Giving the Translation of Real-life Verbal Expressions
and Equations into Letters or Symbols and Vice Versa
K to 12 Math Curriculum Guide 2016. Grade 6,
page 197
21ST Century Mathletes, p.88-93
21st Century Mathletes 6,
21st Century Mathletes 6 ,224-231
Mathletes 6 textbook, video clip, power point
presentation
Advanced Learners
Supply the next 3 terms.
1.)Z, X, V,…..
2.)a + b, 2c + 2d, 3e + 3f
3.)¼, 2/5, 3/6, …..
4.)10, 15, 20, …….
5.)1/5, 1/10, 1/15
126
Average Learners
Drill: Given the ff.
scenarios, ask the pupils
which of the four basic
operations is involved.
1. Jose Miguel had typed
12 pages of her research
paper during the first day.
On the second day she
typed 14 pages. How
many pages did she type
in all?
2. John Rae was given
Php200 by his mom. His
younger brother Drake
borrowed Php20 from him.
How much money did he
have left?
3. Zia is 9years old. Her
older brother Ed is twice as
old as she is. How old is
Ed?
4. Mrs. Cruz brought home
a 2000 ml bottle of orange
juice. She divided this
equally among her five
children. How much did
each child receive
B. Establishing a purpose
for the lesson
Ask if they can give other road signs aside from the
road signs presented.
C. Presenting
examples/instances of the
new lesson
Ask the pupils the ff. questions:
The jeepney fare for the first 4km is ₱8.00 and an
additional ₱1.00 for every km. Richie will go to Cubao
from Antipolo. The distance from Antipolo to Cubao is
about 28 km. how much does she need to pay?
Study the illustration below:
If the first 4 km is ₱8.00, we need to find the amount of
fare for the remaining distance to get the amount which
Richie needs to pay. The remaining distance is 24 km.
Let y= the fixed amount of ₱1.00 for every km. to find
the total amount fare, we will use the expression 24y +
8.
Evaluate:
24y +8
24(1)+8=32
Therefore, Richie needs to pay ₱32.00
127
D. Discussing new concepts
and practicing new skills #1
Consider this problem:
Glen is a newly hired messenger in a multinational
company in Makati. As a trainee, he needs to wear a
polo-shirts every day. He was given a clothing
allowance of ₱6,000.00. How many polo-shirts can he
buy using this amount?
Study the table of prices for typical brands of clothes
BRAND Price per
Numerical
Number
shirt
Expression
of shirts
Brand A Ᵽ500.00
6000 ÷ 500
12
Brand B Ᵽ 400.00
6000 ÷ 400
15
Brand C Ᵽ 250.00
6000 ÷ 250
24
Brand D Ᵽ 300.00
6000 ÷ 300
20
Brand E Ᵽ 600.00
6000 ÷ 600
10
E. Discussing new concepts
and practicing new skills #2
F. Developing mastery (
Leads to formative
Assessment 3)
Discuss the following:
 A numerical expression is an expression that
combines numbers and one or more operation
symbols
 A variable is any letter or symbol that represents a
number
 A constant has a fixed value that does not change.
 An algebraic expression is a mathematical phrase
that uses variables, numerals and operation
symbols.
To translate word phrases into algebraic expressions,
familiarity with words and phrases associated with
symbols or operations are important. The table (on
page 226) lists some keywords that are used to
describe common mathematical operations. Discuss the
table below.
Symbol
Key words/ phrases
+
Addition, plus, the sum of, more than,
added to, increased by, the total of
Subtraction, minus, the difference of,
less than, decreased by, diminished by,
subtracted from, less
x, (), •
Multiplication, times, the product of,
twice, multiplied by, of
÷, /,
Division, divided by, the quotient of, the
ratio of
=
Is equal to, equals, is, is the same as
Advance Learners
Pair-share:
Write an expression for
each of the following:
1.the product of three
tenths and six
128
Average Learners
Pair-share:
Write an expression for
each of the following:
1.add four and eight, then
multiply by three
G. Finding practical
applications of concepts
and skills in daily living
2.trice the difference of
two hundred sixty five and
one hundred seven
3.subtract seven from
twenty four, then divide by
six
4.twice seven plus
eighteen
5.twenty diminished by
thrice six
2.subtract nine from
fourteen, then multiply by
two
3.the product of six and
twelve
4.the quotient of a number
and sixteen
5.the product of nine and
twice a number
The class will be divided
into three. The teacher
will solicit some norms to
be used in group activity.
Each group will be given
an activity card, manila
paper and a pentil pen.
Teacher will present and
explain the rubrics for
group presentation.
The class will be divided
into three. The teacher will
solicit some norms to be
used in group activity.
Each group will be given
an activity card, manila
paper and a pentil pen.
Teacher will present and
explain the rubrics for
group presentation.
Group Activity:
Group #1
Group Activity:
Group #1
Translate into algebraic
symbols. Let x be the
number.
Translate in algebraic
symbols. Let x be the
number.
1. The difference of trice a
number and six divided by
three.
2.thirteen less than half a
number
3. the ratio of a number
and seven
4. thirteen less than twice
four
5. twice a number
diminished by nineteen is
eleven
1. twice a number added to
ten
2. A number decreased by
five
3. a number and multiplied
by seven
4. the sum of seventy nine
and twenty- eight
5. twice the sum of a
number and twenty two.
Group #2
Translate algebraic
symbols into
mathematical statement.
1. x / y - 2z
2. 4( 7+5)
3. 3x + 5
4. (23 -11) ÷ 3
5. ¾ x + 34
Translate algebraic
symbols into
mathematical statement.
1. 2x + y
2. x - 3y
3. x/4
4. 4( 5+4)
5. 3r- 5
Group #2
Group #3
Translate into algebraic
symbols. Let x be the
number.
Group #3
129
Translate into algebraic
symbols. Let x be the
number.
1. six multiplied to the
sum of thirty and nine
2. twice the difference
between twenty four and y
3. the product of twenty
and five divided by two
Translate algebraic
symbols into
mathematical statement.
4.( 90 -57) ÷ 3
5. 2/c + ten
1. r multiplied by ten
2. Five times the sum of
nine and two
3. thrice y added to eight
Translate algebraic
symbols into
mathematical statement.
4. r/ 4 + 2y
5. 2w
H. Making generalizations
and abstractions about the
lesson
I. Evaluating Learning
What is an algebraic expression?
How do you translate real-life verbal expressions and
equations into letters or symbols and vice versa
Advance Learners
Average Learners
Direction. Translate into
Direction. Translate into
algebraic symbols. Let x
algebraic symbols. Let x
be the number.
be the number.
1. five more than x
1. the sum of the trice v
2. eight added to z
and ninety
3. seven subtracted from k
2. the quotient of twice w
4. m increased by ten
and twenty seven
5. twice y added to thirty
3. the difference of fortythree
nine and ten increased to
five
II. Translate algebraic
4. the product of ten and
symbols into mathematical
trice b
statement.
5. twice the sum of ten
and sixty seven
1. 5a • y
2. 2x + 3y
II. Translate algebraic
3. ¾ - 4
symbols into
4. 2k (3+6)
mathematical statement.
5. 6r- 5
1. 8 / 7 - 2z
2. 3(17- 15)
3. 3x• 5
4. (23 -11) ÷ 3
5. ¾ x + 34
J. Additional activities for
application and remediation
Advance Learners
The average of 3
numbers is 6m. Assume
that two of those numbers
are 5m and 4m. What is
the value of the third
number?
130
Average Learners
Samantha is 6 years old
now.
a. Represent her age eight
years from now.
b. represent her age three
years ago
V. REMARKS
VI. REFLECTION
a. No. of learners who
earned 80% in the evaluation
b. No. of learners who
require additional activities
for remediation who scored
below 80%
c. Did the remedial lessons
work? No. of learners who
have caught up with the
lesson
d. No. of learners who
continue to require
remediation
e. Which of my teaching
strategies worked well? Why
did these work?
f. What difficulties did I
encounter which my
principal or supervisor can
help me solve?
___ of Learners who earned 80% above
___ of Learners who require additional activities for
remediation
___Yes ___No
____ of Learners who caught up the lesson
___ of Learners who continue to require remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Power Point Presentation
___ Answering preliminary
activities/exercises
___ Discussion
___ Case Method
___ Think-Pair-Share (TPS)
___ Rereading of Paragraphs/
Poems/Stories
___ Differentiated Instruction
___ Role Playing/Drama
___ Discovery Method
___ Lecture Method Why?
___ Complete IMs
___ Availability of Materials
___ Pupils’ eagerness to learn
___ Group member’s Cooperation in doing their tasks
__ Bullying among pupils
__ Pupils’ behavior/attitude
__ Colorful IMs
__ Unavailable Technology
Equipment (AVR/LCD)
__ Science/ Computer/
Internet Lab
__ Additional Clerical works
__Reading Readiness
__Lack of Interest of pupils
131
School
Teacher
Time and Dates
Week 5- Day 2
I. OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
a. References
b. Teacher’s Guide pages
c. Learner’s material pages
d. Textbook pages
e. Additional Materials from
Learning Resource (LR) portal
f. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
B. Establishing a purpose for the
lesson
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of sequence,
expressions, and equations in mathematical
problems and real-life situations.
The learner gives the translation of real-life verbal
expressions and equations into letters or symbols
and vice versa.
M6AL-IIIe-16
Giving the Translation of Real-life Verbal
Expressions and Equations into Letters or Symbols
and Vice Versa
K to 12 Math Curriculum Guide 2016. Grade 6,
page 197
21ST Century Mathletes, p.88-93
21st Century Mathletes 6,
21st Century Mathletes 6 ,224-231
Mathletes 6 textbook, video clip, power point
presentation
Advanced Learners
Present the problem to
the class.
The cafeteria bought
lots of frozen pizzas to
serve. If you know the
total amount of money
they spent and how
many pizzas they
bought, how could you
figure out the cost of 1
pizza? Why do you
believe that? What is
the action of this
operation?
Average Learners
Present the problem to
the class.
Bob and Tyler do not
have enough money to
buy a box of donuts,
but they have the
exact amount needed
if they combine their
money. How would
you find the cost of a
box of donuts? What is
the action of this
operation?
Show a picture of the president Duterte.
132
Ask: What expression describes President Rodrigo
Duterte?
If we use expressions to describe our President, we
also use expressions in Mathematics, to describe
relationships between numbers and the operations
being used.
C. Presenting
examples/instances of the new
lesson
D. Discussing new concepts and
practicing new skills #1
Define an expression for students, "A math phrase
without an equal or inequality sign." Tell students
that expressions are solved. This lesson is to
translate written words to numbers, operational
symbols, and variables.
Remind students that a variable is a placeholder for
one or more numbers. "Some number" is a phrase
that indicates a variable is needed.
Show pupils how to break down a verbal expression,
beginning with simple expressions.
a. Example: Given "some number increased by 5",
ask students, "What action is happening in this
phrase?" (Answer: We are making larger, joining to,
adding to). Then ask, "What operation indicates this
action?" (Answer: Addition) x + 5
b. Example: Given "51 less than some number." Ask
students, "What action is happening in this phrase?"
(Answer: We are decreasing, going down,
subtracting). Then ask, "What operation indicates
this action?" (Answer: Subtraction) x - 51; taking
away from the x.
Discuss the role and plays in this written sentence.
Example: Sum of 12 and e. (12 + e)
Tell students that they have to read very carefully using
context clues to determine what action is required. They
will need to reread some problems in order to focus on
the needed information.
Advance Learners
Average Learners
Translate each phrase
Translate each phrase or
or sentence into a
sentence into a
mathematical
mathematical expression
expression or equation. or equation.
1. Two ninths of a
number is eleven.
2. Three more than
seven times a number
is nine more than five
times the number.
3. Twice a number less
eight is equal to one
more than three times
the number.
133
1. Twelve more than a
number.
2. Eight minus a number.
3. An unknown quantity
less fourteen.
E. Discussing new concepts and
practicing new skills #2
Present the problem.
A kite is flying at an
altitude of m meters
F. Developing mastery ( Leads to
formative Assessment 3)
Present the problem.
Express the number of
weeks in terms of y
days
a.
express
algebraically its new
altitude after rising for
25 meters
b.
express
algebraically its new
altitude after falling 10
meters. (Not Related
to a)
c. represent
algebraically its new
altitude after tripling
its altitude
Translate into algebraic symbols.
1.)twice a number a divided by three
2.)five times a number x minus four
3.)Thrice the sum of a number x and six
4.) A number x is divided by two added to seven
Translate algebraic symbols into mathematical
statement.
5.)5x + 2y
the product of five X added to the product of two
and y
the sum of five times x and two times y
five times x increased by twice y
twice and more than five times x
G. Finding practical applications
of concepts and skills in daily
living
Advance Learners
Pair-share:
1. Translate into
verbal phrases.
a.) 3/4x +24
b.) (7n + 18) - 8
c.) 2 / x + y
d.) 2 (b/6)
e.)2x + 3
Average Learners
Pair-share:
1. Translate into verbal
phrases.
a.)38b - 4
b.)n + 8
c.)8-6k
d.)5y - 2
e.)3/4 + 2y
2. Translate in
algebraic symbols.
a. thirteen multiplied to
the sum of nine and
eighty
b. ninety taken from
twenty times g
c. seven times to the
sum of twelve and
fourteen
2. Translate in algebraic
symbols.
a. eight times a
number x increased by
three.
b. Five times a
number n added to six.
C. fifteen added to the
quotient of a number y and
two.
134
H. Making generalizations and
abstractions about the lesson
I. Evaluating Learning
J. Additional activities for
application and remediation
V. REMARKS
VI. REFLECTION
a. No. of learners who earned
80% in the evaluation
b. No. of learners who require
additional activities for
remediation who scored below
80%
c. Did the remedial lessons
work? No. of learners who have
caught up with the lesson
d. No. of learners who continue
to require remediation
d .three added to the
D. twenty four multiplied by
the sum of x and y.
quotient of ten and
five.
E. the sum of the
e. six diminished to the number n and seven
quotient of twenty five
multiplied by two.
and five
What is an algebraic expression? How do you
translate real-life verbal expressions and equations
into letters or symbols and vice versa
You need to read very carefully using context clues
to determine what action is required. They will need
to reread some problems in order to focus on the
needed information.
Advanced Learners
Average Learners
Solve each problem.
Translate each algebraic
1. Rocky weighed t
expression into word
kilograms. Express
phrases.
algebraically his weight 1. 6- 5t
after he gained 4.7
2. w+ 3
kilograms
3. 4( w- 7)\
2. Express
4. 7g•6
algebraically the
5. ¼ ( 8+ y)
number of feet in w
inches.
3. Rovie is thrice as old
as Miguel. If Miguel is
k years old, Al is eight
years older than Rovie.
a. If Miguel is k years
old, how old is Rovie
algebraically
b. Express Al’s age
algebraically.
c. Write an expression
for the sum of Rovie
and Miguel ages.
Gandara is twice as old as Nika. Ten years ago, she
was four times as old as Dora. Write the algebraic
equation for their ages ten years ago.
___ of Learners who earned 80% above
___ of Learners who require additional activities for
remediation
___Yes ___No
____ of Learners who caught up the lesson
___ of Learners who continue to require remediation
135
e. Which of my teaching
strategies worked well? Why did
these work?
f. What difficulties did I
encounter which my principal or
supervisor can help me solve?
Strategies used that work well:
___ Group collaboration
___ Games
___ Power Point Presentation
___ Answering preliminary
activities/exercises
___ Discussion
___ Case Method
___ Think-Pair-Share (TPS)
___ Rereading of Paragraphs/
Poems/Stories
___ Differentiated Instruction
___ Role Playing/Drama
___ Discovery Method
___ Lecture Method Why?
___ Complete IMs
___ Availability of Materials
___ Pupils’ eagerness to learn
___ Group member’s Cooperation in doing their
tasks
__ Bullying among pupils
__ Pupils’ behavior/attitude
__ Colorful IMs
__ Unavailable Technology
Equipment (AVR/LCD)
__ Science/ Computer/
Internet Lab
__ Additional Clerical works
__Reading Readiness
__Lack of Interest of pupils
136
School
Teacher
Time and Dates
Week 5- Day 3
I. OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
a. References
b. Teacher’s Guide pages
c. Learner’s material pages
d. Textbook pages
e. Additional Materials from
Learning Resource (LR) portal
f. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
B. Establishing a purpose for the
lesson
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions, and equations in
mathematical problems and real-life
situations.
Defines a variable in an algebraic expression
and equation.
M6AL-IIIe-17
Defining a Variable in an Algebraic
Expression and Equation.
K to 12 Math Curriculum Guide 2016. Grade
6, page 197
21ST Century Mathletes, p.88-93
21st Century Mathletes 6,
21st Century Mathletes 6 ,224-231
Mathletes 6 textbook
video clip, power point presentation
Advance Learners
Average Learners
Translate the ff. word
Drill:
phrases to algebraic
Identify the number
expressions
that should be in
1.Five times the sum
place of the question
of a and b
mark to make the
2.Twelve decreased
mathematical
by twice x
statement correct.
3.the ratio of 11 and
1? + 5 =22
thrice p
2. 72/? =8
Translate the ff.
3. 19 =? – 12
algebraic expressions 4. 7 + 2 = 3 +?
to word phrases
5. 21 x? =63
4.)51 –(x+5)
5. x+3
2
Allow the pupils to find a partner. One
member of the pair is to make his or her own
word phrase and the other member is to
translate it into algebraic expression. Then,
the two members exchange roles. Ask some
volunteer pairs to share their word phrases
and algebraic expressions to the class. Write
these on the board.
137
C. Presenting
examples/instances of the new
lesson
Present the ff. situation to the class:
Maricel buys 5 star apples for ₱5.00 each
and 3 guyabanos for ₱32.50 each. She gives
the cashier a ₱200.00 bill. Write an
expression for the total cost of the fruits she
buys and an equation for the amount of
change the cashier should give her.
D. Discussing new concepts and
practicing new skills #1
Deepening:
Define the ff. term:
Equation a mathematical sentence with an
equal sign (=) which shows that two
expressions or both sides are equal.
Give the ff. equation and explain which the
left member is and which the right member is.
3x + 5 = 20
Common words Translated as =
equal or equals
is/are
is equal to
result is
yields
E. Discussing new concepts and
practicing new skills #2
Tell the pupils that this time, they will be
translating sentences instead of phrases. The
technique is very much the same as the
previous lesson except that this time, it
already involves the equal sign and on either
side of the equal sign is a phrase that is
represented by an algebraic expression.
Advance Learners
Average Learners
Translate into
Translate into
algebraic
algebraic
expression. Let b
expression. Let b
the number.
the number.
The product of
thirteen less than
trice a number, and
five will result to
forty five
The sum of a
number and five is
twelve
Twice the sum of a
number and two is
twenty two
Twice a number
decreased by six is
equal to sixteen
If nine is added to
the difference of a
number and
nineteen, the sum
is ninety
The product of
six and nine less
the difference of
forty and twelve
138
F. Developing mastery ( Leads to
formative Assessment 3)
Group Activity:
Give the ff.
scenarios and ask
pupils to do what is
asked in the
problem.
1. Mr. and Mrs.
Hermosa own a
laundry shop. They
had 134 customers
this week, 18 fewer
than last week. Write
an algebraic equation
for the number of
customers they had
last week.
2. Aling Martha, when
asked about her age,
replies “I am six
years older than
twice the age of my
youngest child.”
Express her age in
algebraic equation if
her age now is 66.
3. Grade 6 basketball
team scored three
less than thrice as
many points as their
opponent. Their total
score at the end of
the game was 108.
Write an algebraic
equation for the
number of points they
scored.
G. Finding practical applications
of concepts and skills in daily
living
Group Activity:
Translate the ff. into
an algebraic
equation.
1. The sum of a
number and five is
twelve.
2. Twice a number
decreased by six is
equal to sixteen.
3. If nine is added to
the difference of a
number and
nineteen, the sum is
ninety.
4. Twice the sum of a
number and two is
twenty-two
5. The product of
thirteen less than
thrice a number and
five will result to fortyfive.
Translate each
phrase or sentence
to a mathematical
expression or
equation.
Translate each
phrase or sentence
to a mathematical
expression or
equation.
1. Ten times a
quantity increased by
a number is nine.
2. When fourteen is
added to two times a
number the result is
six.
3 .Four times a
number minus
twenty-nine is eleven.
1. A number minus
the opposite of
negative one.
2. A number minus
the opposite of
negative twelve.
3. Eleven added to
three times a
number.
4. Six plus five times
an unknown number.
139
4. Three fifths of a
number plus eight is
fifty.
5. When four thirds of
a number is
increased by twelve,
the result is five.
5. Twice a number
minus seven equals
four.
H. Making generalizations and
abstractions about the lesson
What is an algebraic expression? How do you
translate real-life verbal expressions and
equations into letters or symbols and vice
versa
You need to read very carefully using context
clues to determine what action is required.
They will need to reread some problems in
order to focus on the needed information.
I. Evaluating Learning
Advance Learners
Translate each
sentence into
algebraic equation.
1. The difference
between six and a
number decreased by
four.
2. Three times a
number increased by
six is fifteen.
3. Eight less than
twice a number is
sixteen.
4. Thirty is equal to
twice a number
decreased by four.
5. If four times a
number is added to
nine, the result is
forty-nine.
Direction: Write the
expression or
equation in algebraic
form.
. 1. seven less than
the product of twelve
and a number
2. the quotient of a
number and seven is
fifty
J. Additional activities for
application and remediation
140
Average Learners
Translate each
sentence into
algebraic equation.
1. A number
increased by four is
twelve.
2. A number
decreased by nine is
equal to eleven.
3.Five times a
number is fifty
4. The quotient of a
number and seven is
eight.
5. The sum of a
number and ten is
twenty.
Direction: Write the
expression or
equation in algebraic
form.
1. two times a
number plus nine
2. x minus twenty
divided by two times
x
3. Three times the
number plus eleven
V. REMARKS
VI. REFLECTION
a. No. of learners who earned
80% in the evaluation
b. No. of learners who require
additional activities for
remediation who scored below
80%
c. Did the remedial lessons
work? No. of learners who have
caught up with the lesson
d. No. of learners who continue
to require remediation
e. Which of my teaching
strategies worked well? Why did
these work?
f. What difficulties did I
encounter which my principal or
supervisor can help me solve?
___ of Learners who earned 80% above
___ of Learners who require additional
activities for remediation
___Yes ___No
____ of Learners who caught up the lesson
___ of Learners who continue to require
remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Power Point Presentation
___ Answering preliminary
activities/exercises
___ Discussion
___ Case Method
___ Think-Pair-Share (TPS)
___ Rereading of Paragraphs/
Poems/Stories
___ Differentiated Instruction
___ Role Playing/Drama
___ Discovery Method
___ Lecture Method Why?
___ Complete IMs
___ Availability of Materials
___ Pupils’ eagerness to learn
___ Group member’s Cooperation in doing
their tasks
__ Bullying among pupils
__ Pupils’ behavior/attitude
__ Colorful IMs
__ Unavailable Technology
Equipment (AVR/LCD)
__ Science/ Computer/
Internet Lab
__ Additional Clerical works
__Reading Readiness
__Lack of Interest of pupils
141
School
Teacher
Time and Dates
Week 5- Day 4
I. OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
a. References
b. Teacher’s Guide pages
c. Learner’s material pages
d. Textbook pages
e. Additional Materials from
Learning Resource (LR) portal
f. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
Grade Level
Learning Area
Quarter
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions, and equations in
mathematical problems and real-life
situations.
Defines a variable in an algebraic expression
and equation.
M6AL-IIIe-17
Defining a Variable in an Algebraic
Expression and Equation.
K to 12 Math Curriculum Guide 2016. Grade
6, page 197
21ST Century Mathletes, p.88-93
21st Century Mathletes 6,
21st Century Mathletes 6 ,224-231
Mathletes 6 textbook
video clip, power point presentation
Advance Learners
Translate the following
word phrases into
algebraic expression.
1. m increased by eight
2.three two less than
twenty nine
3.thrice four
4. the ration of sixth and
seventh
5. the product of three
and thirty
B. Establishing a purpose for the
lesson
6
Mathematics
Third
Translate
the
ff.
sentences to algebraic
equations
142
Average
Learners
Give the
fundamental
operation
associated in
each following
key words or
phrases.
1. The total of
2. twice
3. the ratio of
4. the quotient of
5.diminished by
Translate the ff.
sentences
to
algebraic
equations
1. If three times a number
is decreased by two, the
answer is seven.
2.Half of the sum of a
number and three is six
3. The difference of
seven and a number is
equal to six times the
number.
1. Twice a number
is equal to six.
2. The ratio of a
number and ten is
two.
C. Presenting
examples/instances of the new
lesson
Aling Rosa, when asked
about her age, replies, “I
am six years older than
twice the age of my
youngest child”. Express
her age in algebraic
expression if her age
now is 66.
The product of
twenty nine plus
eight, and two will
result to seventy
four.
D. Discussing new concepts and
practicing new skills #1
Translate each
algebraic expression
into words.
Translate each
algebraic
expression into
words.
1. 3k+ 7 = 33
2. 5y – 9 = 13
1. ½x + 3= 18
2. 67/w – 2 = 3
E. Discussing new concepts and
practicing new skills #2
Deepening:
Define the ff. term:
Equation a mathematical sentence with an
equal sign (=) which shows that two
expressions or both sides are equal.
Give the ff. equation and explain which the
left member is and which the right member is.
3x + 5 = 20
Common words Translated as =
equal or equals
is/are
is equal to
result is
yields
Tell the pupils that this time, they will be
translating sentences instead of phrases. The
technique is very much the same as the
previous lesson except that this time, it
already involves the equal sign and on either
side of the equal sign is a phrase that is
represented by an algebraic expression.
143
F. Developing mastery ( Leads to
formative Assessment 3)
Advance learners
Translate into algebraic
expression.
Let a be the number
1. Thrice the product of a
number and ten is thirty.
2. Twice a number
diminished by ten yields
to sixteen
G. Finding practical applications
of concepts and skills in daily
living
H. Making generalizations and
abstractions about the lesson
I. Evaluating Learning
Pair-share:
Translate the following
into algebraic
expression. Let c be
the number:
Average
Learners
Translate into
algebraic
expression.
Let x be the
number
1. the sum of a
number and
eighteen the
result is thirty four
2. nineteen fewer
than the number
is twelve
Pair-share:
Translate each
algebraic
expression into
words.
1.the product of three
tenths and a number
1. 5( v+ 28) = 150
2. trice the difference of
2. 1/8 ( 4v-1)= 5
two hundred sixty five
3. 2v- 13=9
and a number
3.subtract seven from a
number, then divide by
six
What is an algebraic expression? How do you
translate real-life verbal expressions and
equations into letters or symbols and vice
versa
You need to read very carefully using context
clues to determine what action is required.
They will need to reread some problems in
order to focus on the needed information.
Advance learners
Translate each sentence
into an algebraic
equation. Let r be the
number
1. three times a number
increased by six is fifteen
2. Thirty is equal to twice
a number decreased by
four
3. eight less than trice a
number is sixteen
144
Average
Learners
Translate each
sentence into an
algebraic
equation. Let s be
the number
1. A number is
increased by four
is twelve
2. A number
decreased by
nine is equal to
eleven
Translate each algebraic
equation into words.
4. 2/3 (m+3)= 6
5. 2/3a + 2= 9
J. Additional activities for
application and remediation
V. REMARKS
VI. REFLECTION
a. No. of learners who earned
80% in the evaluation
b. No. of learners who require
additional activities for
remediation who scored below
80%
c. Did the remedial lessons
work? No. of learners who have
caught up with the lesson
d. No. of learners who continue
to require remediation
e. Which of my teaching
strategies worked well? Why did
these work?
f. What difficulties did I
encounter which my principal or
supervisor can help me solve?
3. five times a
number is fifty
Translate each
algebraic
equation into
words.
4. 3r + 45 = 67
5. ( t- 12) = 43
Write an algebraic equation for the cost of 21
liters of gasoline, if x pesos per liter is
Ᵽ2,092.00
___ of Learners who earned 80% above
___ of Learners who require additional
activities for remediation
___Yes ___No
____ of Learners who caught up the lesson
___ of Learners who continue to require
remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Power Point Presentation
___ Answering preliminary
activities/exercises
___ Discussion
___ Case Method
___ Think-Pair-Share (TPS)
___ Rereading of Paragraphs/
Poems/Stories
___ Differentiated Instruction
___ Role Playing/Drama
___ Discovery Method
___ Lecture Method Why?
___ Complete IMs
___ Availability of Materials
___ Pupils’ eagerness to learn
___ Group member’s Cooperation in doing
their tasks
__ Bullying among pupils
__ Pupils’ behavior/attitude
__ Colorful IMs
__ Unavailable Technology
Equipment (AVR/LCD)
__ Science/ Computer/
Internet Lab
__ Additional Clerical works
__Reading Readiness
__Lack of Interest of pupils
145
chool
Teacher
Time and Dates
Grade Level
Learning Area
Quarter
Week 5- Day 5
I. OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
a. References
6
Mathematics
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions, and equations in
mathematical problems and real-life situations.
The learner represents quantities in real-life
situations using algebraic expressions and
equations.
M6AL-IIIe-18
Representing Quantities in Real-life Situations
Using Algebraic Expressions and Equations.
b. Teacher’s Guide pages
c. Learner’s material pages
K to 12 Math Curriculum Guide 2016. Grade 6,
page 197
21ST Century Mathletes, p.91-93
21st Century Mathletes 6,
d. Textbook pages
21st Century Mathletes 6,
e. Additional Materials from
Learning Resource (LR) portal
f. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
Mathletes 6 textbook, video clip, power point
presentation
Advance learners
Write the expression for
the following:
1. Seventy-five decreased
by five
2.Fourteen divided by the
sum of three and four
3.Triple the sum of eleven
and six
4.One more than the
product of six and eight
5.Twenty plus five less
than eighty
6.Take away 10 from 50
7.Four more than twice
three
8.Difference of 17 and 8
9. fifteen more than the
quotient of seventy-two
and nine
146
Average Learners
Give the
expressions of the
following verbal
phrases.
1. the sum of six
and a number
2. eight more than
a number
3. A number plus
five
4. A number
increased by seven
5. Seven divided by
a number
10. one hundred twenty
increased by nineteen
B. Establishing a purpose for the
lesson
C. Presenting
examples/instances of the new
lesson
D. Discussing new concepts and
practicing new skills #1
Advance learners
Show a video of
“Translating Verbal
Expressions into
Algebraic
Equations”
Write a variable
expression to
represent each of
the following:
1.A number times six
plus the same number
times two
2.A number squared
plus seven take a way
four
3.A number divided by
three plus twelve
4.A number times five
and another number
times six
5.Sixteen less than a
number times
negative four
6.A number times
eight divided by two
7.A number divided by
six and another
number times
negative five
8.A number divided by
four plus another
number divided by
sixteen
E. Discussing new concepts and
practicing new skills #2
Average Learners
Show a video of
“Translating Verbal
Expressions into
Algebraic Equations”
Write a variable
expression to
represent each of the
following:
1.The sum of a number
and twelve.
2.The difference
between a number and
eight.
3.Three times a
number
4.A number squared
plus five
5.A number divided by
two plus seven
6.Four times the
quantity of a number
plus six
7.A number times two
divided by four
Discuss examples 5-8
on how to translate
verbal phrases or
sentences to algebraic
equations.
Discuss examples 5-8
on how to translate
verbal phrases or
sentences to algebraic
equations.
Translate the ff. into
an algebraic
equation.
Translate the ff. into
an algebraic
equation.
147
F. Developing mastery ( Leads to
formative Assessment 3)
1. Twelve times a
number is sixty
2. The quotient of a
number and nine is
one hundred thirtyfive.
3. The sum of a
number and forty-six
is one hundred
twenty-five.
1. A number decreased
by seven is fifteen.
2. A number increased
by fifty-five is equal to
eighty-eight.
3. Twelve times a
number is sixty
Translate each
algebraic equation
into words.
1. 56/w – 2 = 3
2. 4 ( 32 – 3x ) =2
3. 2/3 ( m+ 3 ) =6
Translate each
algebraic equation
into words.
1. a + 5= 12
2. 2d – 7 = 33
3. 2 + 6b = 22
Write a variable
expression to
represent each of
the following:
1. Thirteen less than
thrice a number
2. The ratio of 2 and
five yields to forty.
3. The quotient of
sixteen and a number
will result to four.
G. Finding practical applications
of concepts and skills in daily
living
Translate each
phrase or sentence
to a mathematical
expression or
equation.
1. If four times a
number is added to
nine, the result is forty
nine.
2. Three times a
number increased by
six is fifteen.
3. Thrice the
difference of a number
and eight is seventy
five.
4. The product of
nineteen more than
twice a number, and
148
Write a variable
expression to
represent each of the
following:
1. Four times ten
divided by five
2. Twelve diminished
by two
3. Six times three
added to seven
4. Eight added to the
product of five and
three
5. Twenty-five added to
two
Translate each
phrase or sentence to
a mathematical
expression or
equation.
1. A quantity less
twelve.
2. Six more than an
unknown number.
3. A number minus
four.
4. A number plus
seven.
5. A number increased
by one.
6. A number decreased
by ten.
five yields to sixty
four.
5. Twice a number
diminished by ten is
twenty seven.
7. Negative seven
added to some
number.
8. Negative nine added
to a number.
9. A number plus the
opposite of six.
10. A number minus
the opposite of five.
H. Making generalizations and
abstractions about the lesson
What is an algebraic
expression? How do
you translate real-life
verbal expressions
and equations into
letters or symbols and
vice versa?
What is an algebraic
expression? How do
you translate real-life
verbal expressions and
equations into letters or
symbols and vice
versa?
I. Evaluating Learning
Solve each problem.
1. Write an algebraic
equation for the cost
of 21 liters of gasoline,
if x pesos per liter is
Ᵽ2 092.00.
2. Samantha is y
years old now. Write
an algebraic equation
for Samantha’s age if
her age 5 years from
now is 17.
3. In three years, the
price of new model of
an S6 –mobile phone
will be six more than
twice its current price.
If the projected price
of the new S6 phone
is
Ᵽ40 000, what is the
algebraic equation to
express its current
price?
Translate each
algebraic equation into
words.
1. ½x + 3 =18
2. 3k + 7 =34
3. 5 (b+ 28) =34
4. ¾ (5n—1) =5
5. 5y-9 =13
J. Additional activities for
application and remediation
Vincent’s weight is 6
kilograms more than
Ezekiel’s weight.
Daniel’s weight is 3
kilograms less than
Ezekiel’s weight. Write
an algebraic equation
for the weight of the
three boys having an
Art is twice as old as
Karen. Four years ago,
he has three times as
old as Karen. Write the
algebraic equation for
their ages four years
ago.
149
average weight of 63
kilograms.
V. REMARKS
VI. REFLECTION
a. No. of learners who earned
80% in the evaluation
b. No. of learners who require
additional activities for
remediation who scored below
80%
c. Did the remedial lessons
work? No. of learners who have
caught up with the lesson
d. No. of learners who continue
to require remediation
e. Which of my teaching
strategies worked well? Why did
these work?
f. What difficulties did I
encounter which my principal or
supervisor can help me solve?
___ of Learners who earned 80% above
___ of Learners who require additional activities
for remediation
___Yes ___No
____ of Learners who caught up the lesson
___ of Learners who continue to require
remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Power Point Presentation
___ Answering preliminary
activities/exercises
___ Discussion
___ Case Method
___ Think-Pair-Share (TPS)
___ Rereading of Paragraphs/
Poems/Stories
___ Differentiated Instruction
___ Role Playing/Drama
___ Discovery Method
___ Lecture Method Why?
___ Complete IMs
___ Availability of Materials
___ Pupils’ eagerness to learn
___ Group member’s Cooperation in doing
their tasks
__ Bullying among pupils
__ Pupils’ behavior/attitude
__ Colorful IMs
__ Unavailable Technology
Equipment (AVR/LCD)
__ Science/ Computer/
Internet Lab
__ Additional Clerical works
__Reading Readiness
__Lack of Interest of pupils
150
School
Teacher
Time
Week 6 - Day 1
and Date
I.
OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competency
II. CONTENT
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions and equations in
mathematical problems and real life situations.
The learner solves routine and non-routine
problems involving different types of numerical
expressions and equations such as 7+9 =___ +
6.
M6AL-IIIf-19
Solving Routine and Non-routine Problems
Involving Different Types of Numerical
Expressions and Equations.
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
 K to 12 Mathematics Curriculum Guide
page
August 2016, page 198
2. Learner’s Materials
 21st Century Mathletes pp.239-246
Pages
3. Textbook Pages
IV. PROCEDURE
A. Reviewing Previous
Advance Learners
Average Learners
lesson or
Translate each phrase Write an expression
presenting new
or sentence to a
for each of the
lesson
mathematical
following.
expression or
1. Add 5 and 7, then
equation.
multiply by 2
1. Four times a
2. Subtract 8 from 16,
number minus twenty then divide by 5.
nine is eleven.
3. The product of 26
2. Seven plus ten
and twice a number.
times an unknown
4. 14 less than 8 times
number.
a number.
3. Twelve added to
5. The quotient of a
three times a number. number and 9.
4. Twice a number
minus seven equals
four.
5. Two plus five times
an unknown number.
151
Show a video of “Basic Algebra Rules”
Original file submitted and formatted by DepEd
club
Visit Depedclub.com.ph
C. Presenting
Janet is twice as old as her sister Grace. The
examples/Instances sum of their ages is 23. How old are they now?
of new lesson
Present the ways in solving equations in the
form ax +b=c. use 2x + 3 =7 as an example.
 Guess and test
 Cover up
 Work backward
 Balancing method
B. Establishing a
Purpose for the
Lesson
D. Discussing New
Concepts and
Practicing New
Skills #1
Define the following terms:

Routine – from the curriculum point of
view, routine problem solving involves
using at least one of the arithmetic
operations and/ or ratio to solve
problems that are practical in nature.
Example:
Nimfa had 32 peso-coins. She gave some to her
friend. Now she has 15 peso-coins. How many
did she give to her friend?

Non-routine- a non-routine problem is
any complex problem that requires some
degree of creativity or originality to solve.
Non-routine problems typically do not
have an immediately apparent strategy
for solving them. Often times, these
problems can be solved in multiple ways.
Example:
There are 50 questions in an exam. For every
correct answer 5 marks awarded and for every
wrong answers 2 marks are deducted. Iñigo
scored 190 marks. How many correct answers
did she give?

Solutions – a number that makes an
algebraic equation true or correct

Introduce the 4 basic rules for solving equation.
1. Addition Property of Equality: If the
same quantity is added to both sides of
152
an equation, the resulting equation is
equivalent to the original equation.
2. Subtraction Property of Equality: If the
same quantity is subtracted from both
sides, the resulting equation is
equivalent to the original.
3. Multiplication Property of Equality: If
both sides of an equation are multiplied
by the same (nonzero) quantity, the
resulting equation is equivalent to the
original equation.
4. Division Property of Equality: If both
sides of an equation are divided by the
same (nonzero) quantity, the resulting
equation is equivalent to the original
equation.
Give the ff. examples to be solved using
different methods
1. N + 7 = -7
2. 2 x + 2 = 8
3. -30 = 18 + d
4. C + 18 = 29
5. -32=15 + d
E. Discussing New
Concepts and
Practicing New
Skills #2
Study another example:
Find the value of -13 = -5g+ 32
Solution:
-13 = -5g +32
-13 -32 =-5g + 32 -32
-45 = -5g + 0
Addition Property
of Equality
Identify Property
of Addition
-45 = -5g
-45 = -5g
-5
-5
9=g
153
Division Property
of Equality
Advance Learners
GROUP ACTIVITY
(Form 4 groups)
Set the norms that
should be followed
during the activity.
Have each group do
this activity.
Average Learners
GROUP ACTIVITY
(Form 4 groups)
Set the norms that
should be followed
during the activity.
Have each group do
this activity.
Find the solution to Find the solution to
each equation.
each equation.
1. 3.ƒ= -2
1. x + 5 = 12
2. -13=-5g+32
2. 3p – 7 =
3. 15 – x = 45
3. h=9
4. x – 10 = 22
5
5. 5y – 2 = 18
4. 85=60+b
5. 4 (x-1)-2(x+2)=6
Let
each
group
Let each group present present their work.
their work.
F. Developing Mastery Advance Learners
Average Learners
(leads to formative
assessment)
Consuelo has PhP500 Sann Shine saved
to buy 8 notebooks
PhP100.00 this week
After
buying
8 from her allowance. If
notebooks, she still has this
amount
is
PhP250 with her. How PhP20.00 more than
much
is
each twice the amount she
notebook?
saved last week, how
much did she save
last week?
G. Finding Practical
Solve:
Applications of
The
price
of
a
Concepts and Skills refrigerator is
₱18 900.00 less than
twice the price of an old
model. If it cost
₱30 500.00 to buy the
new refrigerator, what
is the price of the old
model?
Solve:
The price of onions
and garlic is the
same. If Vincent buys
2kilos of onions and 3
kilos of garlic for
PhP150.00 how much
did he pay per kilo?
Understand:
a. What
is
Understand:
asked?
a. What is asked?
b. What are the
b. What are the
given facts?
given facts?
154
H. Making
Generalizations
and Abstraction
about the Lesson
c. What equations What equations shall
shall we do to we do to solve the
solve
the problem? What is the
problem? What solution to the
is the solution to equation?
the equation?
What are the four basic rules in solving
equation?
An algebraic expression is any combination of
numbers constant and variables with operations
such as addition, subtraction, multiplication or
division.
I. Evaluating Learning
Advance Learners
Average Learners
Solve each problem. Solve and check.
Show your complete Show your complete
solution.
solutions.
1. If twice a number
1. X – 3 = 10
is decreased by
2. 5 x – 8 = 12
13, the result is
3. X + 15 = -32
9.what is the
4. 6 (x – 1) = 30
number?
5. X + 6 = 18
2. In Masbate City
during Rodeo, a
horse ride cost
PhP100.00
per
person for the first
40 minutes and
PhP30.00
for
every additional
15 minutes. If you
spent PhP250.00
for horse ride, for
how long did you
ride?
J. Additional Activities
for Application or
Remediation
Advance Learners
Long is 10 years older
than her youngest
brother. If Long will be n
years after 8 years, find
their total age in terms
of n.
V. REMARKS
VI. REFLECTION
155
Average Learners
Abundio is 4 years
older
than
her
youngest sister. If
Abundio will be n
years after 2 years,
find their total age in
terms of n.
School
Teacher
Time
Week 6 - Day 2
and Date
I.
OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competency
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
page
B. Establishing a
Purpose for the Lesson
C. Presenting
examples/Instances of
new lesson
6
Mathematics
Quarter
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions and equations in
mathematical problems and real life situations.
The learner solves routine and non-routine
problems involving different types of numerical
expressions and equations such as 7+9 =___ +
6.
M6AL-IIIf-19
Solving Routine and Non-routine Problem
Involving Different Types of Numerical
Expressions and Equations.


2. Learner’s
Materials Pages
3. Textbook Pages
IV. PROCEDURE
A. Reviewing
Previous lesson
or presenting new
lesson
Grade Level
Learning Area
K to 12 Mathematics Curriculum Guide
August 2016, page 198
21st Century Mathletes p. 238 - 239
Advance Learners
Simplify each of the
expression
by
combining like terms.
Follow the order of
operations.
1. 8a + 50
=
2. 9x – 5 x
=
3. 10 + 5 + x =
4. 8a + 6a +5b =
5. 7p + 6 – 4p =
Average
Learners
.Simplify each of the
expression
by
combining like terms.
Follow the order of
operations.
1. 2a + 10
=
2. 4x – 3x
=
3. 5 + 2 + x =
4. 2a+3a +2b =
5. 2p + 3 – 3p =
Present “Solving Equation Song"
Show a video “ Solving Equation Song “
www.youtube.com.ph
Consider the ff. verbal sentences.
1. A number increased by 5 is 12.
156
2. The sum of two numbers is 8. If the first
number is 3, what is the second number?
 If we let x be the unknown number, how
can these sentence be translated into
mathematical equations? What is the
value of x?
The first sentence can be translated to
mathematical equation as:
increased by
5
is
12
D. Discussing New
Concepts and
Practicing New
Skills #1
Solving the equation, we have:
x+5
=12
x + 5 – 5 = 12 – 5
Subtract 5 from both
sides.
x+0
=7
x= 7
To check the solution, substitute 7 for x in the
equation.
x + 5 = 12 7 + 5 = 12
12 = 12
The second sentence can be translated to
mathematical equation as: Let x be the second
number. Since, the first number is 3, then, the
equation is 3 + x = 8
Solving the equation, we have:
3+x=8
3–3+x=8–3
Subtract 3 from both
sides.
0+x=5
x=5
To check the solution, substitute 5 for x in the
equation.
3+x =8
3+5=8
8=8
Study these other examples of finding solution to
equations:
1. Find the solution to variable x in the
equation,
x + 5 = 20.
x + 5 = 20 transpose 5 to the other side
of the equation using the inverse operation
x = 20 – 5 x = 15
To check, evaluate x + 5, given x = 15
x + 5 = 15 + 5 = 20 the result is 20, therefore
15 is the value of x in x + 5 = 20.
157
E. Discussing New
Concepts and
Practicing New
Skills #2
F. Developing
Mastery (leads to
formative
assessment)
G. Finding Practical
Applications of
Concepts and
Skills
H. Making
Generalizations and
Abstractions about the
Lesson
Find the value of the variable in 12n + 4n + 10
=58.
12n + 4n + 10 = 58 add like terms 12n and 4n to
get 16n.
16n + 10 = 58 transpose 10 to the other side of
the equation using the inverse operation.
16n = 58 – 10
16n = 48 to find the value of n, divide 48 by 16.
n = 48 ÷16
n=3
To check, evaluate 12n + 4n + 10,
given n=3.
12 (3) + 4 (3) +10 =36 +12 +10 =58
The result is 58, therefore 3 is the value of n in
12n + 4n +10 =58
Notice that we put the known term on one side of
the equation and the unknown on the other side.
The term with variable, 16n is the unknown and
the known terms are 10 and 58.
Advance Learners
Average Learners
Simplify
each
of Simplify
each
of
equation by combining equation
by
like terms. Follow the combining like terms.
order of operation.
Follow the order of
operation.
1.3x + 8 x – 3 – 5x = 6x
–3
1.2x + 5 x – 2 – 4x =
2.6n – 4n + 5 – 4 =
2.3n – 2n + 4 – 3 =
3.10y + 15 – 8 + 5 =
3.5y + 10 – 2 + 5 =
4.15a – 5a + 7 =
4.8a – 4a + 6 =
5.20y + 10 – 3y + 9 =
5.9y + 8 – 2y + 7 =
Advance Learners
Average Learners
GROUP ACTIVITY
GROUP ACTIVITY
Write an algebraic
Creates routine and
equation and solve
non-routine problems
the equation.
involving numerical
During the assembly,
expressions and
the number of boys is
equation.
3 times the number of
girls. How many boys
and girls attended the
meeting if there were
40 people present?
What are the four basic rules in solving equation?
An algebraic expression is any combination of
numbers constant and variables with operations
such as addition, subtraction, multiplication or
division.
158
I. Evaluating
Learning
Advance Learners
Create two routine and
non-routine problems
involving numerical
expressions and
equation.
Average Learners
1. x + 5 = 2
2. x – 10 = 22
3. x- 27 = 8 + 10
4. 5x + (-55) = 20
5. 96 – 4x = -28
J. Additional
Activities for
Application or
Remediation
Do this: Write an expression and solve the
problem.
Roman weights 25 kilograms. His father weights
5 kg less than 3 times Romans weight.
V. REMARKS
VI. REFLECTION
159
School
Teacher
Time
and Date Week 6- Day 3
I.
OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competency
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
page
2. Learner’s
Materials Pages
3. Textbook Pages
IV. PROCEDURE
A. Reviewing
Previous lesson
or presenting
new lesson
C. Presenting
examples/Instances
of new lesson
6
Mathematics
Quarter
Third
The learner demonstrates understanding of
sequence in forming rules, expressions and
equations.
The learner is able to apply knowledge of
sequence, expressions and equations in
mathematical problems and real life situations.
The learner solves routine and non-routine
problems involving different types of numerical
expressions and equations such as 7+9 =___ + 6
( M6AL-IIIf-19)
Solving Routine and Non-routine Problem
Involving
Different
Types
of
Numerical
Expressions and Equations.


K to 12 Mathematics Curriculum Guide
August 2016, page 196
21st Century Mathletes pp. 238-239
Advance Learners
Put the known terms
together on one side and
the unknown terms on the
other side of the equation.
1.
2.
3.
4.
5.
B. Establishing a
Purpose for the Lesson
Grade Level
Learning Area
4a – 8 = a + 28
85 = 60 + b
10p – 8 =
96 – 4x = -28
x – ( -16)= 12 + 13
Average Learners
Put
the
known
terms together on
one side and the
unknown terms on
the other side of the
equation.
1. 4b + 7 = 41
2. 2p – 8 =
3. a – 5 = -2
4. x + 7 = 10
5. 4a + 35 = 51
Ask: What are the steps in solving word
problems?
Why is it important to follow the steps in
solving problems?
Read and solve the problem:
A basket is full of fruits with avocado and orange.
The avocado are 4 times the number of orange.
160
D. Discussing New
Concepts and
Practicing New
Skills #1
How many of each kind of fruits are there, if there
are 50 fruits in the basket?
n = number of orange
The avocado are 4x the number of orange, so if n
is number of orange; the number of avocado is 4n.
4n = number of avocado
Add the number of orange and avocado and we
will have the total number of fruits. Since the total
number of fruits is 50 , therefore, the equation will
be:
4n + n = 50
Discussion: Try to look at how expressions are
simplified.
If we give a value to the variable, we can evaluate
an algebraic expressions. Let’s evaluate 5a + 4b,
if a =3 and b =5.
5a means 5 times a and we write: 5*a or 5 (a)
4b means 4 times b and we write: 4*b or 4 (b)
To evaluate 5a + 4 b, given a=3 and b=5, we may
do this:
5a + 4b = 5 (3) + 4 (5)
= 15 + 20
= 35
Notice that we get a number when we evaluate an
expression. We also need to follow the rule of
operations. That is, starting from left to right,
multiply or divide first before adding or
subtracting.
E. Discussing New
Concepts and
Practicing New
Skills #2
Find the solution to 18 x - 6 =30.
18 x – 6 = 30
transpose 6 to the other side of
the equation using the inverse operation
18 x = 30 + 6
36x = 18 to find the value of x, divide 18 by 36.
x = 36 ÷ 18
x=2
To check, evaluate 18 x – 6, given x= 2.
F. Developing
Mastery (leads to
formative
assessment)
Advance Learners
Group Activity :
Average Learners
Group Activity :
Creates routine and nonroutine problems involving
numerical expressions and
equations using the data
given below.
Creates routine and
non-routine
problems involving
numerical
expressions
and
equations using the
data given below.
161
Item
Price
Fish
150.00
Vegetables 80.00
Meat
250.00
Write the equation.
1. What is the total cost
of fish and meat?
Write the equation
G. Finding Practical
Application of
Concepts and Skills
Item
Price
Candy
10.00
Chocolate 50.00
Soft drinks 16.00
Write the equation.
1. What is the
total cost of 3
candy and 3
soft drinks?
Write
the
equation
Advance Learners
Average Learners
Solve for the variable in Solve
for
the
each equation.
variable in each
equation.
1.3x–6=2x+9
x=_____
1.4(x+5)=12
2.3(m-2)=3m+8 m=_____ x=________
3.10x-6=4x+6x-6 x=_____
2.3n-2
=
n=_________
1
3.2m
-3
=
m=________
5
4.9p+3p=43-19p p=_____
5.5n-28=22
n=_____
4.2p
+
p=________
H. Making
Generalizations and
Abstraction About the
Lesson
I. Evaluating Learning
4=10
5.2x+5=19
x=________
What are the four basic rules in solving equation?
An algebraic expression is any combination of
numbers constant and variables with operations
such as addition, subtraction, multiplication or
division.
Advance Learners
Average Learners
1. 18 = 4 + 7y =
1. 4 = y – 4 =
2. 35 = 8 + 9y =
2. 7 – 2 + (
7x9)+ 8
3. 36 = 5y +1 =
3. (2 x 7 + 4)
4. 7y = 7 = 35
4. 31 + y = 43
5. 8y + 3 = 75
5. 38 – y = 32
162
J. Additional Activities
for Application or
Remediation
Advance Learners
Nimfa has 7 shirts. Five
are green and two are
pink. She arranged them in
three drawers.
3 green in the bottom
drawer
2 green in the middle
drawer.
There are no pink shirts in
the bottom drawer.
How many shirts are in the
top drawer?
V. REMARKS
VI. REFLECTION
163
Average Learners
My dad gave me 50
cents. My
grandfather gave
me 90 cents. How
many cents do I
have now?
School
Teacher
Time
and Date Week 6 - Day 4
I.
OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competency
II. CONTENT
III. LEARNING
RESOURCES
A. References
B. Teacher’s
Guide page
C. Learner’s
Materials
Pages
D. Textbook
Pages
IV. PROCEDURE
A. Reviewing
Previous
lesson or
presenting
new lesson
B. Establishing a
Purpose for the
Lesson
C. Presenting
examples/Instances
of new lesson
Grade Level
Learning Area
6
Mathematics
Quarter
Third
The learner demonstrates understanding of sequence in
forming rules, expressions and equations.
The learner is able to apply knowledge of sequence,
expressions and equations in mathematical problems and
real life situations.
The learner creates routine and non-routine problems
involving numerical expressions and equations.
M6AL-IIIf-20
Creating Routine and Non-routine Problems Involving
Numerical Expressions and Equations


K to 12 Mathematics Curriculum Guide August
2016, page 198
21st Century Mathletes pp. 158-164

Our world of Math, page 183-188
Advance Learners
Average Learners
Simplify each expression.
Simplify each expression.
1. 36c + 11c – 9c + 4d
1. 8 – 1y = 2
2. 5 x – 3y + 2 x – 4y
2. y x 9 = 27
3. 4 = 2 – 6y
3. 8 x 9 – 3 + 3x
4. 12 – 2 x 5 + 3y + y
4. 12 = y x 9
5. 63 + y x 9
5. 3 = 8 – y
How do you create routine and non-routine problems
involving numerical expressions and equations?
Let us find the value of the variable in another equation.
Solve for variable
x in 4 x – 2x = 14.
4x 2x = 14
4x and 2x are two like terms, so
we can subtract to get 2x
2x=14
x, divide 14 by 2.
x=14 ÷2
x=7
To check, let us evaluate 4x-2x, given x = 7
4x-2x= 4 (7) – 2 (7) = 28 – 14
164
D. Discussing
New Concepts and
Practicing New
Skills #1
E. Discussing
New Concepts and
Practicing New
Skills #2
F. Developing
Mastery (leads to
formative
assessment)
G. Finding
Practical Application
of Concepts and
Skills
=14, then 14=14
Therefore, 7 is the solution to the equation 4x-2x=14.
Study these other example: evaluate the expression,
6 x + 4.2 x – 7
given x = 5.
6 x + 4.2 x -7= 6(5) + 8x-7
= 30 + 8 (5) -7
= 30 + 40 – 7
=63
Substitute the value of x and multiply, before adding and
subtracting to get the answer of 63.
The sum of the digits of a 2 digit is 12. If the units digit is
twice the tens digit, what is the number?
Solution:
Let x = tens digit
2x = units digit
Equation:
x+2x = 12
3x = 12
x = 14
2x= 8
Therefore, the number is 48.
Advance Learners
Average Learners
Find the solution of each Find the solution of each
equation.
equation.
1.51 – y = 36
1.3n = 60 + n
2.64 – y = 24
2.2b + 10 = 12
3.38 – y = 32
3.5x + 3y -8
4.46 + y = 77
4.2x + 5 = 19
5. y + 50 = 69
5.x-3 = 4
Advance Learners
Average Learners
GROUP ACTIVITY
GROUP ACTIVITY
Direction: Create a routine Direction:
Arrange
the
and non-routine problem jumbled
phrases/
using the data below.
sentences to form a correct
word problem.
Word Problem
Word Problem
Equation
Solution & Answer
Equation
Solution & Answer
______________________ ______________________
165
Word Problem
A mother is 41 years old
Equation
Solution & Answer
In how many years will the
mother be three times as
old as her daughter?
______________________ and her daughter is 9 years
old.
H. Making
Generalizations and
Abstraction about
the Lesson
IV.
What are the four basic rules in solving equation?
An algebraic expression is any combination of numbers
constant and variables with operations such as addition,
subtraction, multiplication or division.
Evaluating
Advance Learners
Learning
Do this:
Five pupils are recipients of
scholarship. Each receives
₱1,000.00. Write and solve
the equation to find the
total amount of scholarship
given to the pupils.
a. What is asked?
b. What are the given
facts?
c. What equations
shall we do to solve
the problem? What
is the solution to the
equation?
J. Additional
Activities for
Application or
Remediation
Average Learners
Do this:
There are 30 pupils in Sir
Alita’s class. Twelve of
them are boys. Write an
equation to find the number
of pupils who are girls?
a. What is asked?
b. What are the given
facts?
c. What equations
shall we do to solve
the problem? What
is the solution to the
equation?
Create routine and non-routine problem involving
numerical expresssions.
V.REMARKS
VI. REFLECTION
166
School
Teacher
Time and
Date
Week 6 – Day 5
I.OBJECTIVE
A. Content
Standard
B. Performance
Standard
C. Learning
Competency
II. CONTENT
III. LEARNING
RESOURCES
A. References
B. Teacher’s
Guide
C. Learner’s
Material Page
IV. PROCEDURE
A. Reviewing
Previous
Lesson or
Presenting
New Lesson
1. Establishing a
Purpose for the
Lesson
2. Presenting
Examples/Insta
nces of New
Lesson
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of sequence in
forming rules, expressions and equations.
The learner is able to apply knowledge of sequence,
expressions and equations in mathematical problems and
real life situations.
The learner creates routine and non-routine problems
involving numerical expressions and equations.
M6AL-IIIf-20
Creating Routine and Non-routine Problems Involving
Numerical Expressions and Equations
K to 12 Mathematics Curriculum Guide August 2016.
Grade 6, page 198
1. 21st Century Mathletes pp. 239-240
Advance Learners
Flash a problem card for the
learners to answer the
following:
1. Give the facts.
2. Give the operation.
3. Give the number sentence.
4. Give the correct answer.
Average Learners
Flash a problem card for
the learners to answer
the following:
1. Give the facts.
2. Give the operation.
3. Give the number
sentence.
4. Give the correct
Arnel received a monthly
answer.
salary of PhP25 000.00 in
Leslie is able to save
2015. He will receive an
twice as much as what
increase of PhP1 000 every
she saved the week
two years. In what year will he before. If she saves
receive a salary of PhP30 000? PhP100 on the first
week, how much will she
save after four weeks?
How do you create routine and non-routine problems
involving numerical expressions and equations?
Let the learners read the following jumbled phrases or
sentences.
167
For each succeding weeks,
he recieves three times the number
of customers than the previous week.
On the first day of operation
of his new shop, Mr. Gomez receives
5 customers
How many costumers does he
recieve in the seventh week?
3. Discussing
New Concepts
of New Lesson
On the first day of operation of his new shop, Mr. Gomez
receives 5 customers For each succeding weeks, he
recieves three times the number of customers than the
previous week. How many costumers does he recieve in
the seventh week?
1.
2.
3.
4.
5.
4. Discussing
New Concepts
and Practicing
New Skills #2
What is asked in the problem?
What are the given facts?
What operation to be used?
What is the number sentence?
What is the solution of the problem?
Advance Learners
Average Learners
Direction: Create a word Direction:write and solve
problem using the data below the equation for each
model. Use to
Word Problem
represents any variable,
to represent 1, and to
represent -1.
Equation
1.
2.
Solution & Answer
3.
4.
5.
5. Developing
Mastery (leads
to formative
assessment)
Advance Learners
GROUP ACTIVITY
Direction: Create a routine and
non-routine
problem
and
answer
the
following
questions.
168
=
=
=
==
=
Average Learners
GROUP ACTIVITY
Direction: Arrange the
jumbled
phrases/
sentences to form a
correct word problem.
1. What is asked in the
problem?
2. What are the given
facts?
3. What operation to be
used?
4. What is the number
sentence?
5. What is the solution of
the problem?
Four friends share a box
of pens
each recieves 3 pens.
Write and solve the
equation
to find the number of
pens in the box.
H. Making
Generalizations and
Abstraction about the
Lesson
I. Evaluating
Learning
What are the four basic rules in solving equation?
An algebraic expression is any combination of numbers
constant and variables with operations such as addition,
subtraction, multiplication or division
Advance Learners
Average Learners
Do this:
Do this:
1.A family of three children
1.The difference
visited the circus. They went
between two-thirds of a
to the ticket booth to purchase number and one-sixth of
tickets for all the rides and
the same number is
games. The total cost of the
seventy five. What is the
family’s ticket is PhP1 560.00. number?
if an adult ticket cost
PhP280.00, how much is the
ticket cost for each child?
1. What is asked in the
problem?
2. What are the given
facts?
3. What operation to be
used?
4. What is the number
sentence?
5. What is the solution of
the problem?
J. Additional
Activities for
Application or
Remediation
Do this:
Arl can run 12 kilometers per hour, write and solve an
equation to predict how many hours it will take to reach
36 kilometer if he continues at this speed.
V. REMARKS
VI. REFLECTION
169
School:
Teacher:
Time and
Date:
Week 7- Day 1
Grade Level:
Learning Area:
Quarter:
6
Mathematics
Third
I. OBJECTIVES:
A. Content
Standards:
B. Performance
Standards:
C. Learning
Competencies/
Objectives:
The learner demonstrates understanding of rate and speed, and
of area and surface area of plane and space/ solid figures.
The learner is able to apply knowledge of speed, area, surface
area of plane and solid/ space figures in mathematical
problems and real-life situations
The learner calculates speed, distance and time
M6ME-IIIg-17
Calculating Speed
II. CONTENT:
III. LEARNING RESOURCES:
A. References:
1. Teacher’s Guide
Pages:
2. Learner’s Material
Pages:
3. Textbook Pages:
4. Additional
Resources from
Learning Resource
Portal:
B. Other Learning
Resources:
IV. PROCEDURE:
A.
K to 12 Mathematics Curriculum Guide (August, 2016), p.198
21st Century MATHletes Teacher’s Manual, pp.100-102
21st Century MATHletes Textbook, pp.252-259
21st Century MATHletes Textbook, pp.252-259
Power point presentation, printed paper copies, activity card,
manila paper, pentel pen
Advance Learners
Reviewing
Drill:
previous lesson or
Find the value of x in the
Presenting new
following equations:
1. 5x – 2 = 10
lesson:
2. x ÷ 4 = 2x – 1
3. 5x – 6 = 3x – 8
4. 3x + 8 = 20
5. 2x – 4 = 10
Review:
Find the value of a in the
following equation, given that
b = 100 and c = 120:
1. a= b ÷ c
2. 2a = bc ÷ 2
3. a ÷ 2 = b ÷ c
4. a = c ÷ b
5. a = 3c ÷ b
B.
Establishing a
purpose for
the lesson:
Average Learners
Drill:
Find the value of x in the
following equations:
1. x – 10 = 7
2. 5x = 35
3. x ÷ 8 = 9
4. 15 + x = 45
5. 28 – x = 11
Review:
Find the value of a in the
following equation, given that
b = 10 and c = 12:
1. a = b x c
2. 2a = b + c
3. 10a = b x c
4. a = c – b
5. a = b + c
Filipinos are fond of traveling out of town and out of the
country. Because of technology, we can avail of different
170
C.
Presenting
examples/
instances of
the new
lesson:
promos for cheap airfare as well as accommodation. Have you
ever tried to do so?
The pupils will talk about the places they have been to.
They will estimate the distance and time they traveled.
Present the problem:
Present the problem:
A bus covers 216 km
A car travels a distance
in 4 hrs. What is its speed of 500 km in 10 hours. What is
expressed in meter/ second? its speed?
Ask:
 What is asked?
 What is the hidden
question?
 What are given?
 What is the operation to
be used?
 What number sentence
can we use to solve the
problem?
D.
Discussing
new concepts
and practicing
new skills #1:






Ask:
 What is asked?
 What are given?
 What is the operation to be
used?
 What number sentence
can we use to solve the
problem?
Elicit from the pupils how to solve for speed.
Discuss thoroughly the solution to the problem.
Define speed, distance and time.
Explain the relationship among these three
quantities.
Present the table of the units commonly used for
speed and its abbreviations.
Emphasize that conversion of units is done
depending upon the given quantities and what is
asked in the problem.
Think-Pair-Share:
Let the pupils work with a partner and let them help
each other to solve the problem by using the procedures in
solving word problems.
Advance Learners
1. An airplane flies 1050
miles in 1 ½ hours.
What is its speed in
miles per hour?
2. Julia rides her horse
26 km in 3 ¼ hours.
What is her speed?
Average Learners
1. A train travels 140 miles
in 2 ½ hours. What is its
speed in miles per
hour?
2. Mike rides his bike 4
miles in ½ hour. What is
his speed?
Call on a pair to show their solution on the board. Let them
explain their answer.
171
E.
F.
Discussing
new concepts
and practicing
new skills # 2:
Developing
Mastery:
Group Activity:
The pupils will be grouped into five with utmost members
of ten. Each group shall be given an activity card and a fiveminute time allotment to solve the problem. They will identify the
problem, hidden question (if there is any), the given quantities,
operation/s to be used, mathematical equation, solution and
answer. They will write their answers on a ¼ Manila paper
provided by the teacher. After five minutes, a representative from
the group shall present the group’s output. The fastest group to
finish shall receive a reward.
Advance Learners
Average Learners
Group 1:
An airplane flies 2640
km in 2 hours 45 minutes.
What is its speed in kilometers
per hour?
Group 2:
A
minibus
drives
141 miles
in
3 hours
55 minutes. What is its
average speed in miles per
hour?
Group 3:
A van moves 245 miles
in 2 hours 55 minutes. What is
its speed in miles per hour?
Group 4:
An airplane flies 304 km
in 20 minutes. What is its
speed in kilometers per hour?
Group 5:
An
airplane
flies
1620 miles in 135 minutes.
What is its speed in miles per
hour?
Group 1:
Cindy rides her bike
3 km in 15 minutes. What is
her speed in kilometers per
hour?
Group 2:
David rides his bike
44 km in 2 hours 45 minutes.
What is his speed in kilometers
per hour?
Seatwork:
Calculate the
speed of a car, given the
following distances travelled
and time taken:
1. d= 364 km
t = 3 ¼ hrs
Seatwork:
Calculate
the
speed of a car, given the
following distances travelled
and time taken:
1. d= 64 km
t = ½ hrs
2. d = 1440 km
t = 12 ½ hrs
172
Group 3:
Grace rides her horse
7 km in 42 minutes. What is her
speed in kilometers per hour?
Group 4:
Emily rides her horse
6 km in 30 minutes. What is her
speed in kilometers per hour?
Group 5:
Pete roller skates
40 km in 120 minutes. What is
his speed in kilometers per
hour?
2. d = 144 km
t = 1 ½ hrs
3. d = 288 km
t = 2 ¼ hrs
3. d = 30 km
t = ¼ hrs
4. d = 896 km
t = 8 ¾ hrs
G. Finding
practical
application of
concepts and
skills in daily
living:
H.
I.
Making
generalization
and
abstraction
about the
lesson:
Evaluating
Learning:
4. d = 96 km
t = ¾ hrs
5. d = 572 km
t = 5 ½ hrs
5. d = 72 km
t = ¾ hrs
A cyclist covers 950
Noah rides his motorcycle
meters in 5 minutes. Find his
216 miles in 180 minutes.
speed in km/ hour.
What is his speed in miles per
hour?

How are you going to
define speed?
 How is speed related to
the distance travelled?
Time?
 How do we determine
how fast something is
moving?
 What are the units of
measure of speed?
Read and solve. Calculate
for speed:
1. If a car travels 8km in 15
minutes. How fast is it
moving? (express in
km/hr)




What is speed?
What is the relationship
of speed to distance
travelled? Time?
What is the formula to
solve for speed?
What are the units of
measure of speed?
Read and solve. Calculate
for speed:
1. If a motorcycle travels 96
km in 1 ½ hrs. How fast is
it moving?
2. If you run 250 meters in
50 seconds, what is your
speed?
2. If it takes you 96 seconds
to complete a round on the
oval which is 800 meters,
what is your speed?
3.
3.
A plane travels 30,795
meters in 1800 seconds.
What is its speed in
km/hr?
4. It takes Kylie ¼ hours to
drive to school. Her route
is 25 km long. What is
Kylie’s speed on her
drive to school?
A bus travels 100 km in 1
hour 15 minutes. What is
its speed in km/hr?
4. Angel’s house is 1 km
away from school. It takes
her 15 minutes in going to
school every day. How fast
does she walk?
5. Louis
5. It took you 90 seconds to
cross your room from the
other subject, which is
180 meters away. How
fast did you walk?
173
rides his bike
43.5 kilometers in 2 ½
hours. What is his
average speed in miles
per hour?
Assignment:
J.
V.
Assignment:
Additional
Read and solve:
Read and solve:
activities for
applications or
1. John rides his horse 1. Leth drives her car and
remediation:
26.4 km in 176 minutes.
covered a distance of 385
What is his average speed
kilometers in 3 ½ hours.
in kilometers per hour?
What is her speed in
km/hr?
2. LRT-2 train left Santolan
station at 8:00 am and 2. A
car
travels
200
arrived at the Recto station
kilometers in 8 hours.
at 8:30 am. If the distance
Calculate the speed of the
between the two stations is
car in:
13 kilometers, what is the
a. km/hr
speed of the train?
b. m/s
REMARKS
VI.
REFLECTION
A. No. of learners
who earned 80%
on the formative
assessment.
B. No. of learners
who require
additional activities
for remediation
who scored below
80%?
C. Did the remedial
lesson work? No.
of learners who
have caught up
with the lesson.
D. No. of learners
who continue to
require
remediation.
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties
did I encounter
which my principal
or supervisor can
help me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
174
School:
Teacher:
Time and
Date:
Grade Level:
Learning Area:
Quarter:
Week 7- Day 2
6
Mathematics
Third
I. OBJECTIVES:
A. Content
Standards:
B. Performance
Standards:
C. Learning
Competencies/
Objectives:
The learner demonstrates understanding of rate and
speed, and
of area and surface area of plane and space/ solid
figures.
The learner is able to apply knowledge of speed, area,
surface area of plane and solid/ space figures in
mathematical problems and real-life situations
The learner calculates speed, distance and time
M6ME-IIIg-17
Calculating Distance
II. CONTENT:
III. LEARNING RESOURCES:
A. References:
1. Teacher’s Guide
Pages:
2. Learner’s Material
Pages:
3. Textbook Pages:
4. Additional
Resources from
Learning Resource
Portal:
B. Other Learning
Resources:
IV. PROCEDURE:
A. Reviewing
previous
lesson or
Presenting
new lesson:
K to 12 Mathematics Curriculum Guide (August, 2016),
Grade 6, p.198
21st Century MATHletes Teacher’s Manual, pp.100-102
21st Century MATHletes Textbook, pp.252-259
Power point presentation, printed paper copies, activity
card, show-me-boards, manila paper, pentel pen
Checking of Assignment
Review:
“Pass the Paper Cabbage Game”
The class will form a big circle. The teacher
will play a song while the pupils pass along the “paper
cabbage”. The teacher will stop the song and
whoever, among the pupils holds the “paper cabbage”
shall peel a leaf containing a question and shall
answer it. S/he who cannot answer, shall have to take
a consequence. The same routine shall follow until all
the leaves are peeled.
These are the sample problems:
175
Advance Learners
1. Marvin took a 5-hour
bicycle trip. In all, he
travelled 120 km. What
was his speed?
2. A car covered a
distance of 600 km for
7.5 hours. What is its
speed?
3. A car travels 360 km in
4 hours. What is its
speed?
4. You rode your bike 24
km and travelled at an
approximately 2 hours.
What was your speed?
5. A train travels a
distance of 675 km in
2.5 hours. What is its
speed?
B.
Establishing a
purpose for
the lesson:
Average
Learners
1. How fast are you
going if the train you
are on travels 180
kilometers in just 3
hours?
2. How fast are you
going if the bus you
are on drives the 10
kilometers in 15
minutes?
3. How fast are you if
you run 12 km in 2
hours?
4. How fast are you
going if you fly on an
airplane 1500
kilometers in just 2
hours?
5. How fast are you
going when you ride
10 kilometers on
your bicycle in ½
hours?
You have learned on our previous lesson how
fast an object is moving; given the distance travelled and
the time it has taken.
Now, can we determine how far an object could
travel, given the speed of the object and the time?
Let the pupils watch the video clip: Maths
Bitesize- The DST Triangle.
(https://www.youtube.com/watch?v=8glfUANjBbY)
C.
Presenting
examples/
instances of
the new
lesson:
Present the problem:
Present the problem:
Daisy rides her bike
Rico
roller
with a constant speed of 8 skates with a constant
km/h. How far can she speed of 12 miles per
travel in 2 ½ hours?
hour. How far can he
travel in ½ hour?
Ask:
 What is asked?
 What are given?
 What is the operation to
be used?
176
Ask:
 What is asked?
 What are given?

Write the mathematical
equation to solve the
problem.
What is the word clue
used?




D.
Discussing
new concepts
and practicing
new skills #1:

What
is
the
operation to be
used?
What
number
sentence can we
use to solve the
problem?
What is the word
clue used?
Group Activity: (Game)
- A set of standards is established prior to the
activity.
- The class shall be grouped by counting 1-5.
- The teacher shall set a reference point where
each group shall form their lines.
- The first members on the line of each group
will be the first one to answer the question that
the teacher will post on the board.
- Each member shall only be given 2 minutes to
read, analyze and write their answers on the
provided show-me-board.
- After the allotted time, the member will raise
their answers for the teacher to check if it is
correct or wrong.
- If the answer is correct, s/he will move 1 step
forward. But, if the answer is wrong, s/he will
go back to his/ her seat.
- The same process shall continue until all the
members have answered the problems.
- The group who has gone farthest shall be the
winner and shall be rewarded.
- Here are some of the sample problems:
Advance Learners
3. An
owner
jeep
travelling
at
an
average speed of 70
km/h left the town at
2:00 p.m. If it arrived in
another town at 6:00
pm, how far are the
two towns?
4. A bus has an average
speed of 65 km/h. It
travelled for 12 hours.
How far did it travel?
Average Learners
3. A bicycle rider
has a speed of
45 kilometers per
hour
for
3.5
hours. How far
did it travel?
4. Dennis drove his
car at an average
speed of 80 km/h
for 4 hours. How
far did he travel?
5. A taxi driver
travels with a
constant speed
177
5. Jonathan bought a
of 90 km/hr. How
new car. He drove his
far can it travel in
car from Manila to
6 hours?
Baguio City at an
average speed of 65 6. A car travelling at an
km/h, for a total of 3.75
average speed of
hours. How far did he
100 km/h made the
travel?
trip to a certain town
in 7 hours. How far
6. A bus travels at a
did it travel?
speed of 45 km/h. How
far will it travel in 30 7. Ernesto drives his
1
minutes?
car for 2 hours with
2
7. Mike drives his car at a
a
speed
of
80 km/h in
speed of 70 km per
going
to
town.
What
hour. How far will he
is
the
total
distance
cover in 3 hours 30
travelled by him?
minutes?

E.
Discussing
new concepts
and practicing
new skills # 2:
After the game, ask:
- How far is Group 1 away from the
reference point? Group 2? Group 3?
Group 4? Group 5?
- Who among the groups earlier has
moved the farthest? How about the
nearest?
- Rank the groups from the farthest to the
nearest.
- If you are going to look closely on the
problems presented a while ago, what
was it all about?
- Let the pupils define distance.
- What are the units of measure used for
distance?
- How were you able to answer the
problems earlier? (Elicit from the pupils
how to solve for distance travelled, given
the speed and time)
Group Activity: (Different Groupings)
( Norms set shall be observed all throughout the
activity)
The pupils will be grouped into five. Each group
shall have a leader who will pick one among the cards
containing the problem in which they are going to solve.
They will use the POLYA’s step in solving problems. They
will write their answers on a
1
4
Manila paper. After five
minutes, a representative from the group shall present the
group’s output.
178
Advance Learners
Group 1:
An airplane flies with a
constant speed of 760 km/h.
How far can it travel in 4 hours
15 minutes?
Average Learners
Group 1:
Mary rides her
horse with a constant
speed of 20 km/h. How
far can she travel in 1 ½
hours?
Group 2:
A van moves with a Group 2:
A police car
constant speed of 108 km/h.
How far can it travel in 150 drives with a constant
speed of 80 miles per
minutes?
hour. How far can it
travel in 2 ¼ hours?
Group 3:
Bob
rides
his
motorcycle with a constant Group 3:
A taxi hurries
speed of 40 km/h. How far can
with
a
constant
speed
he travel in 240 minutes?
of 84 km/h. How far can
it travel in 5 ¾ hours?
Group 4:
A police car drives with
a constant speed of 68 miles
per hour. How far can it travel Group 4:
How
much
in 210 minutes?
distance will be covered
in 1 ¼ hours at a speed
Group 5:
Pete roller skates with of 120 km/h?
a constant speed of 8 km/h.
How far can he travel in 135
Group 5:
minutes?
Find out the
distance covered when,
speed is 960 km/h and
3
4
time is 1 hours.
179
F.
Developing
Mastery:
Think-Pair-Share
Think-Pair-Share
Calculate the distance
Calculate the
that you would travel if you distance that you would
drove:
travel if you drove:
1. 12 hours at 90 km/h
1. 2 hours at 30
km/h
2. 9 hours at 105 km/h
3. 5 ½ hours at 60 km/h
2. 7 hours at 65
km/h
4. 135 minutes at 85 km/h
3.
1
2
hours at 46
km/h
5. 8 ¼ hours at 95 km/h
4. 45 minutes at
80 km/h
1
5. 1 hours at 55
2
km/h
G. Finding
practical
application of
concepts and
skills in daily
living:
H. Making
generalization
and
abstraction
about the
lesson:
I.
Evaluating
Learning:
Read and solve:
A biker had an average
speed of 30km/h for 3.5 hours
going up the right side of the hill
and had an average speed of
45 km/h for 2.5 hours going
down at the left side of the hill.
What is the total distance
covered by the biker?



How are you going to
define distance?
How is distance related
to speed? Time?
How do we determine
how far something has
travelled?
Read and solve:
6.
A person travels at a
speed of 140 kilometers
per hour. How far will he
travel in 270 minutes?
180
Read and solve:
A bus had an
average speed of 65
km/h for 3 hours in the
morning. And had an
average speed of 70
km/h for 2 hours. What
is the total distance
covered by the bus?



What is distance?
What
is
the
relationship
of
distance travelled
to the speed?
Time?
What
is
the
formula to solve
for distance?
Read and solve:
6. A person travels at a
speed
of
60
kilometers per hour.
How far will he travel
in 4.5 hours?
7. Lilly is driving a scooter
7. Lilly is driving a
with the speed of 80 km/h
scooter with the
for 195 minutes. How far
speed of 60 km/h for
will she travel?
2hours. How far will
she travel?
8. An airplane flies with a
constant speed of 760 8. An airplane flies with
km/h. How far can it travel
a constant speed of
in 235 minutes?
760 km/h. How far
can it travel in 4.5
9. A van moves with a
hours?
constant speed of 108
km/h. How far can it travel
9. A van moves with a
in 195 minutes?
constant speed of 95
km/h. How far can it
10. Ken rides his motorcycle
travel in 2.5 hours?
with a constant speed of
120 km/h. How far can he
travel in 450 minutes?
10. Ken
rides
his
motorcycle with a
constant speed of
80 km/h. How far
can he travel in 3.25
hours?
J.
Additional
activities for
applications or
remediation:
Assignment:
Read and solve:
3. Marlon rides his horse
3km/h in 390 minutes. What
is the distance covered?
4. LRT-2 train left Santolan
station at 5:00 am and
arrived at Recto station at
5:30 am. If the train travels
at 180 km/h, how far did it
travel?
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% on
the formative
assessment.
B. No. of learners who
require additional
activities for
remediation who
scored below 80%?
181
Assignment:
Read and solve:
3. Janet drives her
car and covered a
distance with a
speed of 75 km/h in
1
3 hours. Find the
2
distance traveled.
4. A tricycle travels at
40 km/h in 4 hours.
Calculate
the
distance covered
by the tricycle.
C. Did the remedial
lesson work? No. of
learners who have
caught up with the
lesson.
D. No. of learners who
continue to require
remediation.
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties did
I encounter which
my principal or
supervisor can help
me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
182
School:
Teacher:
Time and
Date:
Grade Level:
Learning Area:
Quarter:
Week 7- Day 3
6
Mathematics
Third
I. OBJECTIVES:
A. Content
Standards:
B. Performance
Standards:
C. Learning
Competencies/
Objectives:
The learner demonstrates understanding of rate and
speed, and of area and surface area of plane and space/
solid figures.
The learner is able to apply knowledge of speed, area,
surface area of plane and solid/ space figures in
mathematical problems and real-life situations
The learner calculates speed, distance and time
M6ME-IIIg-17
Calculating Time
II. CONTENT:
III. LEARNING RESOURCES:
A. References:
1. Teacher’s
Guide Pages:
2. Learner’s
Material
Pages:
3. Textbook
Pages:
4. Additional
Resources
from Learning
Resource
Portal:
B. Other Learning
Resources:
IV. PROCEDURE:
A. Reviewing
previous
lesson or
Presenting
new lesson:
K to 12 Mathematics Curriculum Guide
(August,2016),Grade 6, p.198
21st Century MATHletes Teacher’s Manual, pp.100-102
21st Century MATHletes Textbook, pp.252-259
Power point presentation, printed paper copies, Activity
card, show-me-boards, manila paper, pentel pen
 Drill: How Far Will You Go?
The pupils will answer on their show-meboards after the teacher has read the problem.
Calculate the distance you can travel if:
Advance Learners
6. You rode on a car for 4
hours and 15 minutes
at an average of 100
miles per hour.
7. You fly on a plane for 2
hours 45 minutes at an
average speed of 400
miles per hour?
183
Average
Learners
1. You rode on a
car for 2 hours
at an average
of 100 miles
per hour
2. You fly on a
plane for 4
8. You walk for 30 minutes
at an average speed of
6 km/h?
9. You
ride
on
a
motorcycle
for
60
minutes at a constant
speed of 75 km/h
hours at an
average
speed of 400
miles
per
hour.
3. You walk for 1
1
hours at an
2
average
speed of 6
km/h?
10. You travel on a bus at
a speed of 60 km/h in
4 hours 15 minutes
4. You ride on a
motorcycle for
1
hours at a
4
constant
speed of 75
km/h?
5. You travel
a bus at
speed of
km/h in
hours
on
a
60
3
3
4
 Checking of Assignment
B. Establishing a
purpose for
the lesson:
C. Presenting
examples/
instances of
the new
lesson:
How long do you take in going to school every
day? Are you always punctual or always late?
We Filipinos do not seem to be timeconscious. We are often late for some scheduled
activities. In fact, the term
"Filipino time" connotes this bad habit. (The teacher
shall infuse the value of Time and Punctuality)
But did you know that we can break this bad
habit through calculating how long it will take us to
reach our scheduled activities on time, knowing how
fast we move at a certain distance?
Problem Opener:
Problem Opener:
You need to get to your
class 200 meters away, and
you can only walk in the
hallways at about 1.6 m/s. (if
you run any faster, you’ll be
caught for running). How
much time will it take to get to
your class?
(Express in
You need to get to
your class 80 meters
away, and you can only
walk in the hallways at
about 1.6 m/s. (if you
run any faster, you’ll be
caught for running).
How much time will it
take to get to your
class?
minutes)
Ask:
184


What is asked?
What is the hidden Ask:
 What is asked?
question?
 What are given?
What are given?
is
the
What is the operation to  What
operation
to
be
be used?
used?
Write the mathematical

What
number
equation to solve the
sentence can we
problem.
use to solve the
What is the word clue
problem?
used?
 What is the word
clue used?




D.
Discussing
new concepts
and practicing
new skills #1:
 Elicit from the pupils how to calculate time; given
the speed and distance.
 Let the pupils define time on their own words.
 Explain how to derive the formula for time from
that of the formula for solving speed.
 Present some more sample problems.
 Call on some pupils to do a Board Work.
Advance Learners
Average Learners
1.
A police car drives with
a constant speed of 70
kilometers per hour. How
long will it take to travel a
distance
of
105
kilometers?
1. Rex rides his bike
with a constant
speed of 8 km/h.
How long will he
take to travel a
distance of 4 km?
2.
A van moves with a
constant speed of 56 km/h.
How long will it take to
travel a distance of 140
kilometers?
2. A cycle race is
going on. A cyclist
is moving with the
speed of 2 km/hr.
He has to cover a
distance of 5 km.
How much time
will he need to
reach his destiny?
Jane flies on an
airplane with a constant
speed of 797 km per
hour. How long will it
take her to travel a
distance of 1 594 km?
3.
185
3. Emily rides her
horse
with
a
constant speed of
6 km/h. How long
will she take to
travel a distance of
24 kilometers?
E.
Discussing
new concepts
and practicing
new skills # 2:
Group Activity:
The class will be divided into 5 groups. The
teacher shall post three problems written on a strips of
cartolina on the board. The pupils are going to write
1
their answers on a Manila paper.
4
 Group 1 shall identify what is asked on the
problem and the hidden question (if there is any)
on each problem
 Group 2 shall identify the quantities given on
each problem
 Group 3 shall determine the operations to be
used on each problem
 Group 4 shall write the mathematical equation on
each problem
 Group 5 shall show the solution to solve each
problem
Here are the Sample Problems:
Advance Learners
Average Learners
1. Pia and Sam leave their 1. Dennis drove his
home at the same time.
car at an average
Pia has 180 kilometers
speed of 80 km/h
to travel and drives at
for a total distance
80 km/h. Sam has 2000
of 440 kilometers.
kilometers to travel and
How long did he
also drives at 80 km/h.
travel to cover this
a. How long does
distance?
Pia’s journey take?
b. How much longer
does Sam spend
driving than Pia.
2. A bus has an
average speed of
2. An airplane flies 2600
65
km/h.
It
km with a constant
travelled a distance
speed of 650 km/h and
of 455 kilometers.
another 1680 km with a
How long did the
constant speed of 840
bus travel?
km/h. What is the total
time to be taken to 3. Jane drives at an
travel these distances?
average speed of
60 km/h on a
3. A van travels 33 km
distance of 150
with a constant speed
kilometers.
How
of 120 km/h and
long does it take
another 50 km with a
her to cover this
constant speed of 80
distance?
km/h. How long did it
take for this trip?
186
F.
Developing
Mastery:
Think-Pair-Share
How long does it take
to travel?
Think-Pair-Share
How long
does it take to travel?
6. 224 km at 56 km/h
1. 100 km at 20
km/h
7. 450 km at 75 km/h
2. 180 km at 45
km/h
8. 360 miles at 80 miles
per hour
3. 135 miles at 45
miles per hour
9. 520 km at 65 km/h
4. 240 km at 60
km/h
10. 495 km at 90 km/h
5. 50 km at 40 km/h
G. Finding
practical
application of
concepts and
skills in daily
living:
H. Making
generalization
and
abstraction
about the
lesson:
You are going to travel
to Manila. Your flight is
scheduled at 7:00 am, but you
should be at the airport 30
minutes before boarding. The
airport is 30 km away from your
house. If you leave your house
at 6:00 am and ride on a
motorcycle with a constant
speed of 60 km/h, will you
arrive on time for your flight?
How long will it take you to
travel from your house to the
airport?


It is Sunday
afternoon. You are
going to attend the
mass at 4:00 pm. Your
house is 300 m away
from the church. If you
are going to walk to the
church at the speed of
2 m/s. How long will it
take you to arrive
there? What time are
you going to leave
from your house?
How are you going to 
define time?

How do we determine
how long something
has travelled, given how
fast it travelled and how
far it has travelled?
187
What is distance?
What is the formula
to solve for time,
given the speed
and distance?
I.
Evaluating
Learning:
Read and solve:
11. Eve travels on a plane
at a speed of 135 miles
per hour. How long will
he travel in 270
kilometers?
12. Mark is driving his
motorcycle with the
speed of 80 km/h. How
long will it take him to
travel 180 kilometers?
J.
VII.
Read and solve:
11. Anabelle travels on
a jeepney at a
speed
of
60
kilometers
per
hour. How long will
it take her to travel
180 kilometers?
12. Alex is driving a car
with the speed of
100 km/h. How
long will he travel
225 kilometers?
13. Joseph travels on an
airplane that flies with a
constant speed of 760 13. Ms. Santos rides
an airplane with a
miles per hour. How
constant speed of
long will he travel 2 850
760 miles per hour.
miles?
How long will she
travel 570 miles?
14. Maria rides a van that
moves with a constant
speed of 108 km/h.
How long will it take her 14. John drives his
motorcycle at a
to
travel
189
constant speed of
kilometers?
95 km/h. How long
will he travel 285
15. Ronald rides his bicycle
kilometers?
with a constant speed
of 15 km/h. How long
will
he
travel
6
15. Jenny rides her
kilometers?
scooter with a
constant speed of
50 km/h. How long
will it take her to
travel
175
kilometers?
Mang Kanor is a factory
Shiela is a
worker.
His
work
starts
at
Grade
VI
pupil. She
Additional
exactly
8:00
am.
Mang
Kanor’s
walks
to
school
activities for
applications or house is 15 kilometers away everyday. Her house
from the factory. How many is 540 meters away
remediation:
minutes does it take him to go from the school. If her
to work every day when he average speed in
rides on his motorcycle at 60 walking is 3 m/s, how
km/h? If he leaves his house at many minutes does it
7:30 am, what time does he take her to go to
arrive at the factory?
school?
REMARKS
188
VIII. REFLECTION
A. No. of learners
who earned 80% on
the formative
assessment.
B. No. of learners who
require additional
activities for
remediation who
scored below 80%?
C. Did the remedial
lesson work? No. of
learners who have
caught up with the
lesson.
D. No. of learners who
continue to require
remediation.
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties did
I encounter which
my principal or
supervisor can help
me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
189
School:
Teacher:
Time and
Date:
Grade Level:
Learning Area:
Quarter:
Week 7- Day 4
6
Mathematics
Third
I. OBJECTIVES:
A. Content
Standards:
B. Performance
Standards:
C. Learning
Competencies/
Objectives:
The learner demonstrates understanding of rate and speed,
and of area and surface area of plane and space/ solid
figures.
The learner is able to apply knowledge of speed, area,
surface area of plane and solid/ space figures in
mathematical problems and real-life situations
The learner solves problems involving average rate and
speed.
M6ME-IIIg-18
Solving Problems Involving Average Rate and Speed.
II. CONTENT:
III. LEARNING RESOURCES:
A. References:
1. Teacher’s
Guide Pages:
2. Learner’s
Material
Pages:
3. Textbook
Pages:
4. Additional
Resources
from Learning
Resource
Portal:
B. Other Learning
Resources:
IV. PROCEDURE:
A. Reviewing
previous
lesson or
Presenting
new lesson:
K to 12 Mathematics Curriculum Guide (August 2016)
Grade 6, p.198
21st Century MATHletes Teacher’s Manual, pp.100-102
21st Century MATHletes Textbook, pp.252-259
Power point presentation, printed paper copies, Activity
card, show-me-boards, manila paper, pentel pen
 Drill: How Long Will You Travel?
The pupils will answer on their show-meboards after the teacher has read the problem.
Calculate the time you will travel if:
Advance Learners
1. You ride
on a tricycle at
km/h
2. You ride
on a horse at
km/h.
190
75 kilometers
a speed of 25
18 kilometers
a speed of 4
Average Learners
1. You
ride
50
kilometers
on
a
tricycle at a speed of
25 km/h
2. You
ride
10
kilometers
on
a
horse at a speed of 5
km/h.
3. You
travel
kilometers on a bus
speed of 50 km/hr.
4. You
cycle
kilometers on a bicycle
speed of 15 km/h
5. You
travel
kilometers on a boat
speed of 12 km/h
260
at a
3. You
travel
60
kilometers on a bus
at a speed of 60
km/hr.
4. You
cycle
90
kilometers
on
a
bicycle at an speed
of 20 km/h
5. You
travel
30
kilometers on a boat
at a speed of 12 km/h
105
at an
180
at a
 Checking of Assignment
 Review:
- How do we calculate speed?
- How do we calculate distance, given its speed at
a given time?
- How do we calculate time, given its speed to
cover the distance?
B.
Establishing a
purpose for
the lesson:
Who among you here had spent their vacation out
of town? How far have you travelled? How long did it take
you to reach your destination? How fast was the vehicle you
rode? Did the speed of the vehicle you ride on remained all
throughout your ride, or have you noticed some changes?
In any mode of transportation, the speed does not
always stay constant. There are variables that may alter
how fast it travels at some point. Could you identify some of
these that may speed up or slow down the vehicles? (Elicit
from the pupils the factors and how do these affect speed)
If the speed is changing, we get its average rate to
determine how fast it is really moving.
C.
Presenting
examples/
instances of
the new
lesson:
Problem Opener:
Problem Opener:
John drove for 3 hours at
a speed of 50 kilometers per
hour and for 2 hours at a
speed of 60 kilometers per
hour. What was his average
speed?
Pauline swam for 100
s at a speed of 2.5 m/s.
Then she swam for
another 100 s at a speed
of 1.5 m/s. What is her
average speed?
Ask:
Ask:
 What is asked?
 What is asked?
 What is the hidden  What is the hidden
question, if there is any?
question, if there’s
 What are given?
any?
 What
is/are
the  What are given?
operations to be used?
191


Write the mathematical
equation to solve the
problem.
What is the word clue
used?



D.
Discussing
new concepts
and practicing
new skills #1:
What
is/are
the
operations
to
be
used?
What
number
sentence can we use
to solve the problem?
What is the word clue
used?
 Elicit from the pupils how to calculate the average
speed.
 Clarify and explain that solving an average speed
does not follow the rules in averaging grades and
other quantities.
 Emphasize that average speed is a measure of the
total distance travelled in the entire given period. Or
may be expressed as:
Average speed = total distance travelled
total time taken
 Group Activity:
The teacher shall group the pupils into five.
The teacher shall prepare five pieces of
1
8
sheet of
paper. Each paper shall contain the task to be done
by each group. The paper shall be rolled. The leaders
of the group will be the one to pick among the rolled
papers for the task.
Since the pupils were not able to solve the
problem opener earlier for they have used the
traditional averaging, the pupils shall refer to the
same problem.
Each group will be given a
1
4
Manila paper
and pentel pen for their output. They will only be
given 5 minutes to do it. After the allotted time, a
representative from the group shall report their
answers.
192
Advance Learners
Task 1:
Find the distance
travelled by John for 3
hours at 50 kilometers per
hour
Task 2:
Find the distance
travelled by John for 2
hours at 60 kilometers per
hour
Task 3:
Find the total
distance John travelled
Task 4:
Find the total time
John took driving
Task 5:
Find John’s
average speed
Average Learners
Task 1:
Find the
distance swum by
Pauline at 2.5 m/sec.
for 100 seconds
Task 2:
Find the
distance swum by
Pauline at 1.5 m/sec.
for 100 seconds
Task 3:
Find the total
distance swum by
Pauline.
Task 4:
Find the total
time Pauline took
swimming
Task 5:
Find Pauline’s
average speed
E.
Discussing
new concepts
and practicing
new skills # 2:
Group Activity:
The class will be divided into 5 groups. The
teacher shall post the problem written on a strip of
cartolina on the board. The pupils are going to write their
answers on a
1
2
Manila paper. They will be given 5-7
minutes to finish their activity. Each group shall choose a
presenter of the group output.
Here is the Sample Problem:
Advance Learners
Average Learners
If the distance from point A
Point A and B are
to B, point B to C, and point C
120 m apart. Point B and
to D are equal, and the speed
C are 300 m apart. Ben
from point A to B is 70 miles per ran from point A to B in 15
s. Then he runs from
193
hour. Find the average speed
from point A to D.
Given the time from point A
to B is 3 hours; from point B to
C is 5 hours; and from point C
to D is 6 hours.
Answer:
a. What is asked in the
problem
b. What is/ are the hidden
question/s?
c. What are the given
quantities?
point B to C in 15
seconds. Find Ben’s
average speed for the
distances from Point A to
C.
Answer:
a. What is asked in
the problem
b. What is/ are the
hidden
question/s?
c. What are the
given quantities?
d. What
is/are
the
operation/s to be used?
d. What is/are the
operation/s to be
used?
e. What
is
mathematical
equation?
e. What
is
the
mathematical
sentence?
f.
the
Show your solution in:
Finding the distance
from point A to B;
point B to C; and
point C to D.
- Finding the total
distance from point A
to D.
- Finding the total time
taken from point A to
D.
- Finding the average
speed
-
f.
Show
your
solution in:
- Finding
the
total distance
- Finding
the
total time
- Finding Ben’s
average speed
g. What
is
answer?
the
g. What is the answer?
F.
Developing
Mastery:
Think-Pair-Share
John travels on an airplane
a distance of 8 kilometers. For
half of the distance, the
airplane flies at a speed of
900 km/h. And for the rest of
the distance, it flies at a
speed of 760 km/h. What is
his average speed?
194
Think-Pair-Share
A van moves for 2.2
hours with a constant
speed of 120 km/h, and
then another 5.4 hours
with a constant speed of
67 km/h. What is the
average speed for the
trip?
Answer:
a. What is asked in the
problem
Answer:
a. What is asked in
the problem
b. What is/ are the hidden
question/s?
b. What is/ are the
hidden
question/s?
c. What are the given
quantities?
c. What are the
given quantities?
d. What is/are the
operation/s to be used?
d. What is/are the
operation/s to be
used?
e. What is the mathematical
equation?
f.
Show your solution in:
- Finding the time
John has taken to
travel half the
distance at a speed
of 900 km/h
- Finding the time
John has taken to
travel half the
distance at a speed
of 760 km/h
- Finding the total time
- Finding the average
speed of the
airplane
g. What is the answer?
e. What
is
the
mathematical
equation?
f.
-
-
-
-
-
Show
your
solution in:
Finding the distance
travelled by the van
for 2.2 hours at a
speed of 120 km/h
Finding the distance
travelled by the van
for 5.4 hours at a
speed of 67 km/h
Finding the total
distance travelled
by the van
Finding the total
time the van has
taken to travel
Finding the average
speed of the van.
g. What is the
answer?
G. Finding
practical
application of
concepts and
skills in daily
living:
Mary drives her car for 1.5
hours with a constant speed of
65 k/h. And then for another .75
hours with a constant speed of
80 km/h. What is its average
speed?
(Answer using POLYA’s step in
solving problems)
195
A vehicle travels 30
km with a constant speed
of 60 km/h and another
40 km with a constant
speed of 80 km/h. What is
its average speed?
(Answer using POLYA’s
step in solving problems)
H. Making
generalization
and
abstraction
about the
lesson:
I.
Evaluating
Learning:



How is average speed
defined?
How do we calculate
the average speed?
How do we solve word
problems
involving
average speed?
 A man takes 10 hours to
go to a place and come
back by walking both the
ways. He could have
gained 2 hours by riding
both the ways. The
distance covered in the
whole journey is 18
miles. Find the average
speed for the whole
journey if he goes by
walking and comes back
by riding.
Answer:
a. What is asked in the
problem?
b. What is/ are the
hidden question/s?
c. What are the given
quantities?
d. What is/are the
operation/s to be
used?
e. What is the
mathematical
equation?
f. Show your solution
in:
- Finding the time by
riding both ways
- Finding the time he
goes by walking and
come back riding
- Finding the average
speed?
g. What is the answer?
196

What is average
speed?
What is the formula
to solve average
speed?
What are the steps
in solving problem
involving average
speed?


 An airplane flies
for 3 hours with a
constant speed of
780 miles per hour
and then for
another 1 hour
with a constant
speed of 576 mph.
What is its average
speed for the total
trip?
a.
b.
c.
d.
e.
f.
Answer:
What is asked in
the problem?
What is/ are the
hidden question/s?
What are the given
quantities?
What is/are the
operation/s to be
used?
What is the
mathematical
equation?
Show your solution
in:
- Finding the
distance the
airplane travelled
at constant
speed of 780
mph for 3 hours.
Finding the
distance the
airplane travelled
at constant
speed of 576
mph for 1hour.
- Finding the total
distance
travelled
-
Finding the total
time taken
- Finding the
average speed.
g. What is the
answer?
J.
Solve using POLYA’s steps in
Additional
solving problem:
activities for
applications or
Manny drove at 40 mph for
remediation:
1 hour and then he drove
back home at 10 mph. What
was his average speed for the
entire trip?
VI. REMARKS
VII. REFLECTION
A. No. of learners
who earned 80% on
the formative
assessment.
B. No. of learners who
require additional
activities for
remediation who
scored below 80%?
C. Did the remedial
lesson work? No. of
learners who have
caught up with the
lesson.
D. No. of learners who
continue to require
remediation.
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties did
I encounter which
my principal or
supervisor can help
me solve?
197
Solve using POLYA’s
steps in solving
problem:
Mario drives his car
for 4 hours with a
constant speed of 65
km/h. And then for
another 2 hours with a
constant speed of 80
km/h. What is its
average speed?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
198
School:
Teacher:
Time and
Date:
Grade Level:
Learning Area:
Quarter:
Week 7- Day 5
6
Mathematics
Third
I. OBJECTIVES:
A. Content
Standards:
B. Performance
Standards:
C. Learning
Competencies
/ Objectives:
The learner demonstrates understanding of rate and speed,
and of area and surface area of plane and space/ solid
figures.
The learner is able to apply knowledge of speed, area,
surface area of plane and solid/ space figures in
mathematical problems and real-life situations
The learner solves problems involving average rate and
speed.
M6ME-IIIg-18
Solving Problems Involving Average Rate and Speed.
II. CONTENT:
III. LEARNING RESOURCES:
A. References:
1. Teacher’s
Guide
Pages:
2. Learner’s
Material
Pages:
3. Textbook
Pages:
4. Additional
Resources
from
Learning
Resource
Portal:
B. Other
Learning
Resources:
IV. PROCEDURE:
A. Reviewing
previous lesson
or Presenting
new lesson:
K to 12 Mathematics Curriculum Guide (August 2016)
Grade 6, p.198
21st Century MATHletes Teacher’s Manual, pp.100-102
21st Century MATHletes Textbook, pp.252-259
Power point presentation, printed paper copies, strips of
cartolina, stopwatch, marker, manila paper, pentel pen,
 Checking of assignment
 Review:
Keri rides her bike to school a total distance of
4.5 km. She has to slow down twice to cross the
busy streets, but overall, the journey takes her
0.56 h. What is Keri’s average speed?
Ask:
199





B.
Establishing
a purpose
for the
lesson:
What is asked in the problem?
What are the given quantities?
What is/ are the operations to be used?
What is the mathematical operation to be
used?
What is the answer?
The teacher says, “We are going to have a
race today. But before that, let us set first our norms and
standards in doing the activity. (Elicit from the pupils the
do’s and don’ts in playing. Infuse the value of
Sportsmanship).
Here are the mechanics for the race:
 The pupils shall be grouped into five.
 Each group shall select a runner who will represent
their group in the 200-m race.
 Two members of each group shall be assigned as
time keepers and recorders in every finish line of the
posts
 There will be 4 posts marked from;
a.) 0m-50m
b.) 51m-100m
c.) 101m-150m
d.) 151m-200m
 The time keepers shall be attentive for as soon as
the runner hits the starting points they shall be able
to start their timer and stop it immediately when the
runner hits the finish line in every post
 The recorders shall be able to note the time it took
for the runner to cover the distance in every posts.
 So as for the runners, all they will have to do is to
run as fastest as they can.
 The group with the fastest runner wins and will
receive a reward.
After presenting the mechanics, the whole class
will go out to the 200-m track prepared by the
teacher beforehand for the race. The timers and
recorders will go to their respective posts and the
runners will position themselves at the starting point.
When the teacher says the cue word “Go”, the race
starts.
200
C.
Presenting
examples/
instances of
the new
lesson:
Group Activity:
After the race, the class will go back to their
classroom. Each group shall fill out the table below
using the data gathered during the race. And answer
the questions that follow. They will be given five
minutes to do the activity. They shall write their
answers on a ½ Manila paper.
Speed of Runner in Every Posts
Post
Distance
Time
Rate
(m)
(s)
(m/s)
A
B
C
D
TOTAL
Ask:
Advance
 Did the runner
has constant rate
in
the
entire
duration of the
race?
 How fast was
the runner to cover
point A? point B?
point C? and point
D?
 How were you
able to determine
how fast was the
runner going at
every point?
 At what point did
the runner has the
fastest speed?
 At what point did
the runner has the
slowest speed?
 What was the
average
201
Average
 Did
the
runner
maintained his rate in the
race?
 How fast did he run in
post A? post B? post C? and
post D?
 How did you get his
speed at every post?
 In which post did the
runner ran fastest?
 In which post did the
runner ran the slowest?
 What was the average
speed/ rate of the runner?
 How did you calculate the
average speed/ rate of the
runner?
speed/rate of the
runner?
 How were you
able to determine
the
runner’s
average
speed/
rate?
After the allotted time, one representative of each
group shall present and discuss their answers.
D.
Discussing
new
concepts
and
practicing
new skills
#1:
 The teacher shall process the answers presented by
each group.
 The teacher presents another sample problem:

A
student
travels to reach her
school which is 60
kilometers away. She
rode on a motorcycle
at a rate of 10 km/h
and returns at the rate
of 12 km/h. What is
the average speed of
the motorcycle that
the student ride on?

Peter
drives
120
kilometers at 60 km/h and then
drives the next 120 120
kilometers at 40 km/h. What is
his average speed?
 Group Activity: “The Problem Seekers”
The teacher shall group the pupils into five. The
teacher shall prepare five strips of colored cartolina.
Each cartolina shall contain the task to be done by
each group. The cartolina shall be placed by the
teacher under the armchairs randomly. Each group
will search among the the armchairs. They shall
perform the task indicated in the the strip they get.
Each group will be given a
1
Manila
4
paper and
pentel pen for their output. They will only be given 5
minutes to do it. After the allotted time, a
representative from the group shall report their
answers.
202
Advance Learners
E.
Discussing
new
concepts
and
practicing
new skills #
2:
Average Learners
Task 1:
Find how long the
motorcycle covered the 60
kilometers at a speed of 10
km/h
Task 1:
Find how long
Peter covered the
120 kilometers at a
speed of 60 km/h
Task 2:
Find how long the
motorcycle covered the 60
kilometers at a speed of 12
km/h
Task 2:
Find how long
Peter covered the
120 kilometers at a
speed of 40 km/h
Task 3:
Find the total
distance the motorcycle
covered
Task 3:
Find the total
distance Peter
covered
Task 4:
Find the total time
the motorcycle took on a
roundtrip
Task 4:
Find the total
time Peter took
driving
Task 5:
Find the motorcycle’s
average speed on the entire
trip
Task 5:
Find Peter’s
average speed
Group Activity:
The class will be divided into 5 groups. The
teacher shall post the problem written on a strip of
cartolina on the board. The pupils are going to write their
1
answers on a Manila paper. They will be given 5-7
2
minutes to finish their activity. Each group shall choose a
presenter of the group output.
Here is the Sample Problem:
Advance Learners

A biker covers
18 kilometers at 10
km/h, 16 kilometers
at 8 km/h, and 30
203
Average Learners

A biker rode up a 20
kilometer hill in 2 hours and
down the hill in 0.5 hour
kilometers at 6 km/h.
without stopping. What was
Find the average
his average speed?
speed of the biker in
covering the whole
Answer:
distance.
a. What is asked in the
Answer:
problem
a. What is asked in
the problem
b. What is/ are the hidden
question/s?
b. What is/ are the
hidden
c. What are the given
question/s?
quantities?
c. What are the
d. What
is/are
the
given
operation/s to be used?
quantities?
d. What is/are the
operation/s to
be used?
e. What is the mathematical
sentence?
f.
e. What is the
mathematical
equation?
f.
Show
your
solution in:
- Finding the
time taken to
cover 18 km
at 10 k/h
- Finding the
time taken to
cover 16 km
at 8 km/h
- Finding the
time taken to
cover 30 km
at 6 km/h
- Finding the
total distance
covered
- Finding the
total
time
taken
to
cover
the
whole
distance
- Finding the
average
speed.
g. What is the
answer?
204
Show your solution in:
Finding
the
total
distance
- Finding the total time
- Finding the biker’s
average speed
-
g. What is the answer?
F.
Developing
Mastery:
Seatwork:
Seatwork:
Nena drove 40
On the first part of her
kilometers to see
trip, Lyka rode her bike 16
her cousin at a
kilometers and on the
speed of 20 km/h.
second part of her trip, she
The trip took Nena
rode her bike 42 kilometers.
2 hours. And then
Her total time for the trip was
she drove from her
5 hours. What is her average
cousin’s
house
speed?
another
30
kilometers to the Answer:
store at a speed of
a. What is asked in the
problem
10 km/h. It took
Nena 3 hours to
b. What is/ are the hidden
arrive at the store.
question/s?
What was Nena’s
average speed for
c. What are the given
the entire trip?
quantities?
Answer:
a. What is asked in
d. What
is/are
the
the problem
operation/s to be used?
b. What is/ are the
hidden question/s?
e. What is the mathematical
equation?
c. What are the given
quantities?
f.
d. What is/are the
operation/s to be
used?
e. What is the
mathematical
equation?
f.
Show your solution
in:
- Finding the
total distance
Nena
travelled
- Finding the
total time
Nena took to
cover the
whole
distance
- Finding the
Nena’s
205
Show your solution in:
-
-
Finding
the
total
distance covered by
Lyka
Finding the average
speed for the entire
trip.
g. What is the answer?
average
speed
g. What is the
answer?
Read and solve:
Lola Sarah
rides on a tricycle in
travelling
from
Masbate proper to
Brgy. Biyong. The
trip took 1 hour at a
rate of 30 km/h. And
it took another 3
hours at the speed of
60 km/h on her way
from Brgy. Biyong to
the municipality of
Aroroy. What was
the average speed of
her whole trip?
G. Finding
practical
application
of concepts
and skills in
daily living:
H.
Making
generalization and
abstraction about
the lesson:
I. Evaluating
Learning:

How
do
we
determine
the
average speed/ rate
of a moving body?
Read and solve:
 Dianne took a nonstop flight to visit
her grandmother.
The 750-mile trip
took 3 hours and
45 minutes.
Because of the
bad weather, the
return trip took 4
hours and 45
minutes. Find her
average speed.
Answer:
a. What is asked in
the problem?
b. What is/ are the
hidden
question/s?
c. What are the
given quantities?
206
Read and solve:
Julie joined a Skate-RowBike race. Her time and distance
for each leg of the race are
entered in the chart:
Leg of
race
Time
(h)
Distance
Skate
1.25
20
Row
0.75
6
Bike
2.5
100
(km)
Find her average speed/ rate

How do we calculate the
average speed/ rate?
Read and solve:
 Dianne took a non-stop
trip to visit her
grandmother. The 540-km
trip took 3 hours Because
of the bad weather, the
return trip took 6 hours.
Find her average speed.
Answer:
a. What is asked in the
problem?
b. What is/ are the
hidden question/s?
c. What are the given
quantities?
d. What is/are the
operation/s to be
used?
e. What is the
mathematical
equation?
f. Show your solution
g. What is the answer?
d. What is/are the
operation/s to be
used?
e. What is the
mathematical
equation?
f. Show your
solution
g. What
is
the
answer?
J.
Additional
activities for
applications
or
remediation:
Read and solve:
A cyclist rides along a
straight road. For the
first 5 kilometers, the
cyclist warms up at a
rate of 16 kilometers
per hour. For the
second 5 kilometers,
the cyclist’s rate is 26
kilometers per hour.
Find his average
speed.
VI. REMARKS
VII. REFLECTION
A. No. of learners
who earned 80%
on the formative
assessment.
B. No. of learners
who require
additional
activities for
remediation who
scored below
80%?
C. Did the remedial
lesson work? No.
of learners who
have caught up
with the lesson.
D. No. of learners
who continue to
require
remediation.
E. Which of my
teaching
strategies worked
well? Why did
these work?
207
Read and solve:
An aircraft carrier made a trip
to Davao and back. The trip
there took 3 hours at 8 km/h
and the trip back took 4 hours
at a speed of 6 km/h. Find its
average speed.
F. What difficulties
did I encounter
which my
principal or
supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover
which I wish to
share with other
teachers?
208
School:
Teacher:
Dates and Day:
I.OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Week 8- Day 1
Grade Level:
Learning
Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of ratio
and speed, and of area and surface area of plane
and solid / space figures
The learner is able to apply the knowledge of
speed, area and surface area of plane and solid /
space figures in mathematical problem and real-life
situations
The learner finds the area of composite figures
formed by two or more of the following: triangle,
square, rectangle, circle and semi -circle.
M6ME – IIIh – 89
II.CONTENT
Finding the Area of Composite Figures Formed by
Two or More of the Following: Triangle, Square,
Rectangle, Circle and Semi -Circle.
III. LEARNING
RESOURCES
A .References
K to 12 Math Curriculum Guide 2016. Grade 6,
page 198
21st Century Mathletes 6, pages 263-271
1.Teacher’s Guide Pages 21st Century Mathletes 6 TM, pages 103-108
2.Learner’s Materials
Pages
3.Textbook Pages
21st Century Mathletes 6, pages 263-271
4. Additional Materials
from Learning
Resources (LR) Portal
B. Other Learning
Resources
Activity card, flash cards, manila paper, power
point presentation
IV. PROCEDURES
A. Review Previous
Lessons
A. Have the pupils solve the following:
Find the area. Show complete solutions
1. What is the area of the square room with
a side of 16 meters?
209
2. A triangular structure has a base of 40
meters and a height of 70 meters. What
is it’s area?
(Have the children solve on the board )
B. Establishing purpose
for the Lesson
A. Present a problem, like:
1. Find the area of the
figure
Discussion:
1. A figure or shape that can be
divided into more than one of the
basic figures is said to be
composite figure.
2. To find the area of composite
figures, you can sometimes
separate it into figures with areas
you know how to find.
C. Presenting Examples
/ instances of the new
lesson
Advance Learners
Average Learners
1. Father was to paint
the façade of the house.
He needs to find out the
area so that he would
know the amount of
paint to buy. The side of
the square is fourteen
meters and the height of
the triangle is fifteen
meters .What is the area
of the façade of the
house? What figures
are
used
in
the
structure?
To find the area of the
structure, we need to
find the area of each
figure.
Area of the square
=sxs
= 14x14
= 196 square meters
1. Father was to paint the
façade of the house. He
needs to find out the area
so that he would know
the amount of paint to
buy. The side of the
square is 12 meters and
the height of the triangle
is 15 meters .What is the
area of the façade of the
house? What figures are
used in the structure?
To find the area of the
structure, we need to find
the area of each figure.
Area of the square
=sxs
= 12x12
= 144 square meters
210
Area of the triangle
= ½ bh
= ½ ( 14x15)
= ½ (210)
= 105 square meters
Area of the triangle
= ½ bh
= ½ ( 12x15)
= ½ (180)
= 90 square meters
Area of the façade of the
house = area of a
square + area of a
triangle
= 210 square meters +
105 square meters
= 301 square meters
Area of the façade of the
house = area of a square
+ area of a triangle
= 144square meters + 90
square meters
= 234 square meters
(power
presentation)
D. Discussing new
concepts and practicing
new skills # 1
point
Pair Teaching
Find the area of each composite figures :
1. Find the area of the composite figure.
Valuing: Teacher infuses the value of being
cooperative.
Does working together make your work easier?
Why?
E. Discussing New
Concepts and Practicing
New Skills # 2
Group Activity
Study the composite figure below:
 Group 1
 Group members will give the shapes used
to solve the area of the composite figures.
211
 Group 2
 Group members will give the formula in
finding the area of the shapes identified by
the group 1.
 Group 3
 The group members will show the
solutions on how to find the area of the
composite figures,.
 The pupils will present their output after 5
minutes.
 The teacher will check the answer of the pupils.
 Asks:
a. How did you find the activity?
b. Did all the group members participate in
the activity?
c. What did you do to find the correct
answer?
F. Developing Mastery
Find the area of each composite figure.
G. Finding practical
Application
The diagram shows the floor of a school canteen. If
wall to wall carpeting is installed. How many
square feet of carpeting is needed?
212
H. Making
Generalizations
-What is composite figure?
-How do we find the area of the composite figures?
Find the area of the following composite figures.
I. Evaluating Learning
1.
J. Additional
Activities
for Application and
Remediation
2.
Solve the area of the following composite figures.
1.)
2.)
V. REMARKS
VI. REFLECTIONS
213
School:
Teacher:
Dates and Day: Week 8- Day 2
I. OBJECTIVES
A. Content Standards
Grade Level: 6
Learning
Area: Mathematics
Quarter: Third
The learner demonstrates understanding of ratio and
speed, and of area and surface area of plane and
solid / space figures
B. Performance Standards
The learner is able to apply the knowledge of speed,
area and surface area of plane and solid / space
figures in mathematical problem and real-life
situations..
C. Learning Competencies
The learner finds the area of composite figures
formed by two or more of the following: triangle,
square,
rectangle,
circle
and
semi-circle.
M6ME – IIIh – 89
II.CONTENT
Finding the Area of Composite Figures Formed by
Two or More of the Following: Triangle, Square,
Rectangle, Circle and Semi -Circle.
SUBJECT INTEGRATION: EPP
(Health and Cleanliness )
III. LEARNING
RESOURCES
A .References
1.Teacher’s Guide Pages
2.Learner’s Materials
Pages
3.Textbook Pages
4. Additional Materials
from Learning Resources
(LR) Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6,
page 198
st
21 Century Mathletes 6, pages 263-271
21st Century Mathletes 6 TM, pages 103-108
21st Century Mathletes 6, pages 263 - 271
Activity card, flash cards, manila paper,
power point presentation
IV. PROCEDURES
A. Review Previous
Lessons
Find the area of the composite figure.
214
1. Study the composite figure.
B. Establishing purpose
for the Lesson
Asks:
1. What are the shapes used in the figure?
2. How are you going to find the area?
C. Presenting Examples /
instances of the new
lesson
Father is working to cover the kitchen floor to look it
neat and clean .How many square foot tiles are
needed to cover this kitchen floor?
A. Group Activity
(Cite the norms in having a group activity)
1 – Give the shape of the kitchen floor.
2 – Find the area of the kitchen floor.
3 – Find the number of tiles needed to cover the
kitchen floor.
B. Presentation of Outputs
D. Discussing new
concepts and practicing
new skills # 1
Study this example:
.
Mang Kardo is building a shed. How many square
feet of wood are needed to build the back of the
shed shown below?
215
E. Discussing New
Concepts and Practicing
New Skills # 2
 To deepen pupil’s understanding, let them
answer the following.
 Pair activity
A ground floor is shown below. Each end is semicircle, what is it’s area?
1. Find the area of the rectangle.
2. Find the area of the circle.
 After (10) ten minutes, pupils will present their
output.
 The teacher will check the pupil’s answers.
F. Developing Mastery
G. Finding Practical
Application
1. Two diagonals divide a square carpet into 4
congruent triangles. The base of each triangle is 10
feet and the height is 5 feet. What is the area of the
entire carpet?
216
H. Making Generalizations
1. What is a composite figure?
2. How do we find the area of the composite figure?
I. Evaluating Learning
Advance Learner
Average Learner
Solve the problem.
Find the area?
How much material is
required to make a
circular skirt if the
waist hole has a
circumference of 60.5
cm and the diameter of
the circular skirt is 12.5
cm?
J. Additional Activities
for Application and
Remediation
Find the area of the following composite figures.
1.)
V. REMARKS
VI. REFLECTION
217
2.)
Grade
Level:
Learning
Area:
Quarter:
School:
Teacher:
Dates and Day:
Week 8- Day 3
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
II.CONTENT
6
Mathematics
Third
The learner demonstrates understanding of
ratio and speed, and of area and surface area
of plane and solid / space figures.
The learner is able to apply the knowledge of
speed, area and surface area of plane and solid
/ space figures in mathematical problem and
real-life situations.
The learner finds the area of composite figures
formed by two or more of the following: triangle,
square, rectangle, circle and semi-circle.
M6ME – IIIh – 89
Finding the Area of Composite Figures Formed
by Two or More of the Following: Triangle,
Square, Rectangle, Circle and Semi -Circle.
SUBJECT INTEGRATION: ESP
Sportmanship
III. LEARNING
RESOURCES
A .References
1.Teacher’s Guide Pages
K to 12 Math Curriculum Guide 2016. Grade 6,
page 198
21st Century Mathletes 6, pages 263-171
K to 12 Grade 6 TM, 21st Century
Mathletes 6, page103
2.Learner’s Materials
Pages
3.Textbook Pages
21st Century Mathletes 6, pages 263 - 271
4. Additional Materials
from Learning Resources
(LR) Portal
B. Other Learning
Resources
Activity card, flash cards, manila paper,
colored
papers, power point presentation
218
IV. PROCEDURES
A. Review Previous
Lessons
B. Establishing purpose
for the Lesson
1. Recall the formula on finding the area
of the: triangle, square, rectangle semicircle and circle.
2.Recall the steps/ formula on how to
find the area of the composite figure
a. Present the problems:( power point
presentation)
1. How much larger is a pizza made in a10inch square molder than a pizza in a 10inch-diameter circular molder?
Solutions:
First we make illustration of each. Then
compute the areas.
The area of the square is:
A = s2
A =s x s
A = 10 in x 10 in
A = 100 in
The area of the circle is:
𝑨 = 𝜋𝑟 2
A=3.14 x 5 x5
A=3.14 x 25
A= 78.5 square in
The square pizza is larger than by about
100square in – 78.5 square in = 21.5 square in.
Answer: 21.5 square in.
219
A. What is the area of the unshaded region?
C. Presenting Examples /
instances of the new
lesson
Solution : Area of the circle
𝐴 = 𝜋𝑟 2
A = 3.14 X4X4
A = 3.14 X16
A = 50.24 square cm
Area of the square is:
A= s2
A =sxs
A =8X8
A = 64 square cm
64 square cm - 50.24 square cm
ANSWER: 13.76 square cm
To find the answer subtract the area of the
circle from the area of the square.
B. Find the area of the shaded region.
Area of small rectangle is :
A=lxw
= 3 x10
= 30
Area of big rectangle is :
A=lxw
= 7 x12
= 84
Answer: 114 square cm.
To find the answer separate the small
rectangle from the big rectangle. Get the area
of each rectangle. Then add the area of the
small rectangle and the area of the big
rectangle
220
C. Group Activity ( 4 groups )
Have each group form a composite figure by
any of two or more of the following: triangle,
square, rectangle, circle or semi- circle.
a. Set norms in doing group activity
b. Have them present their output in 5 minutes
c .Check the learners answer
D. Discussing new
concepts and practicing
new skills # 1
Advance Learners
How many square
centimeters of tiles are
needed to cover this
dining floor
E. Discussing New
Concepts and Practicing
New Skills # 2
Average Learners
Find the area of the
shaded region
below.
Pair Activity
Each pair in the first row will form a composite
figure with indicated size of area. The second
row will do the solution to find the area of
composite figure made by the first row
A. Guide them in presenting and checking
their answers.
F. Developing Mastery
Find the area of the following composite
figures.
G. Finding Practical
Application
Peter was assigned by his boss to create a new
logo for their company. The logo is a rectangle
that has a semicircular piece removed. What is
the approximate area of the shaded part of the
logo?
221
H. Making Generalizations
1. What is a composite figure?
2. How to find the area of the composite
figure?
I. Evaluating Learning
Find the area of the figures.
a. Divide the figure into familiar shapes.
b. Find the area of each shape.
1.)
J. Additional Activities for
Application and
Remediation
2.)
Solve the composite area of the following
figures.
V. REMARKS
VI. REFLECTION
222
School:
Teacher:
Dates and Day:
I.OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competencies
Week 8- Day 4
Grade Level:
Learning
Area:
Quarter:
6
Mathematics
Third
The learner demonstrates understanding of ratio and
speed, and of area and surface area of plane and
solid / space figures.
The learner is able to apply the knowledge of speed,
area and surface area of plane and solid / space
figures in mathematical problem and real-life
situations
The learner solves routine and non-routine problems
involving area of composite figures formed by two
or more of the following: triangle, square,
rectangle,
circle
and
semi-circle.
M6ME – IIIh – 90
II.CONTENT
Solving Routine and Non-Routine Problems Involving
Area of Composite Figures Formed by Two or More
of the Following: Triangle, Square, Rectangle, Circle
and Semi -Circle.
Unpacked Learning Competency:
Solves Routine and Non-Routine Problems Involving
Area of Composite Figures Formed by Two or More
of the Following: Triangle, Square, and Rectangle.
III. LEARNING
RESOURCES
A .References
1.Teacher’s Guide
Pages
2.Learner’s Materials
Pages
3.Textbook Pages
4. Additional Materials
from Learning
Resources (LR) Portal
B. Other Learning
Resources
K to 12 Math Curriculum Guide 2016. Grade 6,
page 198
st
21 Century Mathletes 6, pages 103
21st Century Mathletes 6, pages
Activity card, flash cards, manila paper, colored
papers, power point presentation
223
IV. PROCEDURES
A. Review Previous
Lessons
A. Group Game
Solve situation. Show complete solution.
1. What is the area of a square room with a side
of 14 meters?
2. The width of a rectangle is 8 meters. Its length
is twice its width. What is its area?
B. Establishing
purpose for the
Lesson
A. As what you have learned in your previous
grades or lessons, the area is measured in
square units, such as square inches or square
centimeters.
Ask the learners on remember how to find the
area of:
1. Rectangle
2. Square
3. Triangle
C. Presenting
Examples / instances
of the new lesson
Advance Learners
1. A figure (or shape)
that can be divided
into more than one
of the basic figures
is said to be a
composite figures
(or shapes).
Suppose
a
swimming pool at
the figure below
looks like this. How
do you find the
area
of
this
swimming pool? Is
it possible to find
the area?
224
Average Learners
1. A figure (or shape) that
can be divided into more
than one of the basic
figures is said to be a
composite figures (or
shapes).
Suppose a covered court
at the figure below looks
like this. How do you find
the area of this covered
court? Is it possible to
find the area?
1. The pupils will present their output after 10
minutes.
2. The teacher will check their answer.
D. Discussing new
concepts and
practicing new skills #
1
To find the area of composite figures, you can
sometimes separate it into figures with areas you
know how to find.
Show example:
Find the area of each shaded region. Assume that all
angles that appear to be right angles are right
angles.
6 cm
a.
7 cm
We can separate the figures into two: a triangle and
a square. Now let us find the area of each figure.
Solution:
Area of the triangle
A= 1 • b • h
2
6 cm
Area of the square
A=s•s
= 7 cm • 7 cm
= 1 • 7 cm • 6 cm
2
= 1 • 42 cm²
2
A = 21 cm²
225
= 49 cm²
7 cm
We can see that the area of
49 cm²
+
=
21 cm
Therefore, the area of the composite figure is 70 cm²
3 ft
b. 6 ft
3 ft
3 ft
3 ft
6 ft
4ft
10 ft
We can identify two rectangles from the figure, one
that measures 3 feet by 4 feet (the smaller) and the
10 feet by 6 feet rectangle (the larger) where the
smaller one overlapped.
Let us solve the area of each rectangle.
Area of the smaller rectangle
A=l•w
4 ft
= 4 ft • 3 ft
3 ft
A (smaller) = 12 ft²
Area of the larger rectangle
A=l•w
= 10 ft • 6 ft
6 ft
A (larger) = 60 ft²
10 ft
To get the area of the shaded region, subtract the
area of the smaller rectangle from the area of the
larger rectangle.
226
A (shaded) = A (larger) - A (smaller)
= 60 ft² - 12 ft²
= 48 ft²
The area of the shaded region is 48 ft²
E. Discussing New
Concepts and
Practicing New Skills
#2
Group Activity
Problem:
The length of a rectangle is 12 cm and its width is 2
cm less than 3 of its length.
4
Find the area of the rectangle.
 Group 1
 Group members will give the data needed in
solving word problem, following the steps
given.
 Group 2
 Group members will show the solution in
finding the complete answer of the problem
given togroup 1.
 Group 3
 The group members will do the checking of
the given answer of group 2.
 The pupils will present their output after 7
minutes.
 The teacher will check the answer of the pupils.
 Asks:
d. How did you find the activity?
e. Did all the group members participated in
the activity?
f. What did you do to find the correct
answer?
Valuing: Teacher infuses the value of being
cooperative.
227
F. Developing Mastery
Advance Learners
To develop pupil’s understanding, let them answer
the following:
1. Mang Pedro walks off a patch of garden for
tomatoes. He walks 14 feet north, 7 feet west, and
then 15 feet straight back to where he started.
What is the area of Mang Pedro’s tomato patch?
*The pupils will show their solutions on a piece of
paper and the teacher may call in a volunteer to solve
the given word problem on the board.
Average Learners
2. The length of a rectangle is 52 cm and its
perimeter is 200 cm. What is the area of the
rectangle?
G. Finding Practical
Application
Mary is in charge of calculating the area of the new
faculty room. The figure below shows Mary divided
the composite figure representing the faculty room
into regions.
a. How many figures Mary formed?
b. Show the solution on a piece of paper.
H. Making
Generalizations
State how to find the area of composite figures and
solve routine problems involvingarea of composite
figures formed by any two or more of the following:
triangle, square and rectangle.
228
I. Evaluating
Learning
Advance Learners
1. A photograph
measuring 10 cm
by 4 cm is
mounted on a
rectangular
cardboard, leaving
a margin of 3 cm
all around.
J. Additional Activities
for Application and
Remediation
a. What is the area of
the photograph?
b. What is the area of
the cardboard?
c. What area of the
cardboard is NOT
covered by the
photograph?
The
area
of
the
playground is shown
below. Find the area of
the playground.
V. REMARKS
VI. REFLECTION
229
Average Learners
1. How many square
centimeters of tiles are
needed to floor a
hexagonal terrace if each
side is 30 cm long and
the
radius
of
the
inscribed circle is 15.5
cm?
School:
Teacher:
Dates and Day: Week 8- Day 5
I.OBJECTIVES
A. Content Standards
B. Performance Standards
C. Learning Competencies
II.CONTENT
Grade Level: 6
Learning
Area: Mathematics
Quarter: Third
The learner demonstrates understanding of ratio
and speed, and of area and surface area of plane
and solid / space figures.
The learner is able to apply the knowledge of speed,
area and surface area of plane and solid / space
figure in mathematical problem and real-life
situations
The learner solves routine and non-routine
problems involving area of composite figures
formed by two or more of the following: triangle,
square, rectangle, circle and semi-circle.
M6ME – IIIh – 90
Solving Routine and Non-Routine Problems
Involving Area of Composite Figures Formed by Two
or More of the Following: Triangle, Square,
Rectangle, Circle and Semi -Circle.
Unpacked Learning Competency:
Solves Routine and Non-Routine Problems Involving
Area of Composite Figures Formed by Two or More
of the Following: circle and Semi- Circle
III. LEARNING
RESOURCES
A .References
1.Teacher’s Guide Pages
K to 12 Math Curriculum Guide 2016. Grade 6,
page 198
21st Century Mathletes 6, pages 103 - 208
2.Learner’s Materials
Pages
3.Textbook Pages
21st Century Mathletes 6, pages 263-270
4. Additional Materials
from Learning Resources
(LR) Portal
B. Other Learning
Resources
Activity card, flash cards, manila paper, colored
papers,
Power point presentation.
230
IV. PROCEDURES
A. Review Previous
Lessons
B. Establishing purpose
for the lesson
1. Group Games
Solve situation. Show complete solution
a. What is the area of the square room with
a side of 14 meters?
b. The width of a rectangle is 8 meters. Its
length is twice its width. What is its area?
Ask the learners on how to find the area of:
1.Circle
2. Semi-circle
Find the area of the window in the living room.
C. Presenting Examples /
instances of the new
lesson
D. Discussing new
concepts and practicing
new skills # 1
A roller-rink floor is shown below. Each end is a
semi-circle. What is its area? If hardwood flooring
costs ₱220.00 per square foot, how much will be the
following cost?
Let’s analyze and identify the figures. The figures
that we can easily identify are the rectangle and the
two semi-circles.
Now let’s find the area of each figure:
Area of rectangle:
A = lxw
85 ft x 40 ft
A= 3400 square feet
231
Combining the two semi-circles on both ends of the
figure will result to a circle. Having this, the
combined area of both end is :
A=πr2
= π ●r ● r
= ( 3.14 ) ( 20ft ) ( 20ft)
= ( 3.14 ) (4000ft ) ft2
= 1256 ft2
the total area of the floor
A = A ( rectangle ) +
A 9 circle)
= 3400 ft2+ 1256 ft2
A= 4556
ft2
If hardwood flooring costs ₱ 220.00nper square foot
then 4656 ft2●₱ 220 = ₱ 1 024 320.00 is the total
flooring cost.
E. Discussing new
concepts and practicing
new skills # 2
How much larger is a leche flan made in a 12-inch
square moulder than a leche flan made in a 12 inch
diameter circular moulder?
(Use π – 3.14)
Solution:
First, we make illustration of each. Then compute
the areas.
232
The area of the square is
A =s2
A=s ● s
= 12 in ● 12 in
A= 144 in2
The diameter of the circle is 12 inches, so the radius
is 6 inches. The area of the circle is:
A= π●r●r
= (3.14)(6 in.)(6 in.)
= (3.14)(36) in2
The square leche flan is larger by about 144in2–
113.04 in2= 30.96 in2
F. Developing Mastery
G. Finding Practical
Application
To develop pupil’s understanding , let them answer
the following:
1.) A circular wall clock with a circumference of
88 cm is mounted on the wall. How much
area of the wall did it occupy?
( Use π = 22/ 7)
2.) The new HedCen field is a rectangle , 100
yards by 40 yards, with a semicircle at each
of the shorts sides. A running track 10 yards
wide surrounds the field. What is the area of
the running track.
 The pupils will show their solutions on a
piece of paper and the teacher may call in a
volunteer to solve the given word problem on
the board.
Problem:
How much larger is a pizza made in circular pan
with a 14 inch diameter than a pizza made in square
pan with sides measuring 14 inches?
 The pupils will present their output after 7
minutes.
 The teacher will check the answer of the pupils.
 Ask:
a.) How did you find the activity?
b.) Did all the group members participate in the
activity?
c.) What did you do to find the correct answer?
Valuing: Teacher infuses the value of being
cooperative.
233
H. Making Generalizations
State how to find the area of composite figures and
solve routine problems involving area of composite
figures formed by any two or more of the following:
circle and semi-circle.
I. Evaluating Learning
Advance learners
Solve the Problems.
A rectangular
wrapping cloth has a
length of 26 inches and a
width of 24 inches. Two
circular cloth with a
diameter of 8 inches will
be cut from it. How much
cloth will be left?
J. Additional Activities for
Application and
Remediation
Average learners
Find the area of each
figure.
Read, illustrate, and solve to find the area.
How much material is required to make a circular
skirt if the waist hole has the circumference of 30.5
cm and the diameter of the circular skirt is 6.5?
V. REMARKS
VI. REFLECTION
234
School
Teacher
Time and Date
Week 9-Day 1
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competency
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s
Materials Pages
3. Textbook Pages
4. Additional
Materials from
Learning Resource
(LR) Portal
B. Other Learning
Resources
IV.
PROCEDURE
A. Reviewing
Previous Lessons
or Presenting New
Lesson
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of rate
and speed, and of area and surface area of
plane and solid/space figures.
The learner is able to apply knowledge of
speed,
area, and surface area of plane and
solid/space figures in mathematical problems
and real-life situations
The learner visualizes and describes surface
area and names the unit of measure used for
measuring the surface area of solid / space
figures
M6ME-IIIi-91
Visualizing and Describing Surface Area and
Naming the Surface Area of Solid/Space
Figures
K to 12 Math Curriculum Guide 2016. Grade 6,
page 199
21ST Century Mathletes, 108-112
21st Century Mathletes 6, p. 272-285
21st Century Mathletes 6, p. 272-285
Mathletes 6 textbook, power point presentation
Mental Computation Drill: Solving for Areas of
Plane Figures
Play “Pass-It-On”
a)Teacher divides the class into 6 groups (per
column).
b)Teacher instructs the pupils in front to
prepare a piece of paper ( 41 sheet), which will
be the group’s answer sheet.
c)Teacher shows a picture of a plane figure with
given dimensions. For example:
5m
235
4m
8m
6m
20 m
10 m
d)Pupils in front solve mentally for the area and
write their answer on the piece of paper, with
the proper label.
e)Teacher shows another picture of a plane
figure with given dimensions.
f)The pupils in front pass the paper to the one
behind them who, in turn, solve mentally for the
area.
g)Continue this until everyone in the group or
column has participated.
h)Teacher gives the correct answers.
i)The group with the correct answer and label
gets 2 pts.
j)The group with the most number of points
wins.
Review: Formulas in Solving for the Areas of
the Following: Square, Rectangle,
Parallelogram, Trapezoid, Triangle
Give one example each for the above shapes.
These may be in the form of a word problem or
a picture with given dimensions. Let the class
solve for the area of each.
B. Establishing a
Purpose for the
Lesson
Show nets of solid figures.(Cube, rectangular
prism, triangular prism)
Ask the following for each solid figure.
1) How many faces does it have?
2) What is the shape of each face?
3) Are the faces congruent?
4) What is the formula for the area of square?
c) Show a cylinder, cone, pyramid, and sphere.
Ask questions similar to the ones above.
C. Presenting
Present the ff. problem in the class.
Examples/Instance
1. Mother is celebrating her birthday. Her
s of New Lesson
children prepared a gift for her. They
have a gift wrapping paper that
measures 900 square inches. Each edge
of the box is 12 inches. Do you think the
children have enough wrapping paper to
cover the gift?
The pupils will investigate the following:
a. Name of the solid
b. Number of faces
c. Shapes of faces
236
D. Discussing New
Concepts and
Practicing New
Skills # 1
Call one pupil and let him hold a ‘cube’. Let him
count the faces of the cube then ask if each
face is similar in terms of size to other faces of
the cube.
Call again another pupil and let him hold a
rectangular prism. Let him count the faces of
the prism then ask if each face has the same
size of the other faces of the rectangular prism.
Show the following table. Let the pupils study
the table. (Elaborate and discuss the
information given with the use of actual solid
figure to describe the surface area of each
figure.)
Name of
Lateral Faces/Curved Surface
solid figure
Cube
6 congruent faces
Rectangular 4 lateral faces; 2 bases
prism
Triangular
2 congruent triangular faces; 3
prism
congruent rectangular faces
E. Discussing New
Concepts and
Practicing New
Skills #2
Square
pyramid
4 congruent lateral faces; 1
square base
Cylinder
Curved surface
Cone
Curved surface
Sphere
1 curved surface
In measuring the length of each side of surface
area of a solid figure, we use different kinds of
unit of measure. We can use ruler, meter stick,
tape measure and other measuring tools to
know the length of any side of a space figure.
Show and let them study the table below.
Unit of measure
Abbreviation used
Millimetre
mm
Centimetre
cm
Inch
in
decimeter
dm
foot/feet
ft
meter
m
kilometer
km
Mile
mi
237
F. Developing
mastery
(Leads to
Formative
Assessment)
G. Finding practical
applications of
concepts and skills
in daily living
H. Making
generalizations
and abstractions
about the lesson
I. Evaluating
Learning
Discuss the following example:
Aling Marikit wants to measure the length of
the sides of her shoe box in order for her to
know the surface area of the box. What
measuring tool can be used and what unit of
measure should be used? (Expected answers:
1. ruler, tape measure/
2. centimeter, inch, millimeter, etc.)
Note: Use square units in measuring area and
surface area. For example, cm2, ft2, in2, m2,
mm2, km2
Advanced Learners
Average Learners
Activity (in groups of 5) Activity (in groups of
1) Give each group a
5)
spatial figure. For
1) Give each group a
example, a shoe box.
spatial figure. ( A shoe
2) Let each group
box).
measure the
2) Let each group
dimensions of their
measure the
spatial figure and let
dimensions of the
them decide what
given figure using a
measuring tool they will ruler and “inch” will be
use. Let them use
used as unit of
”centimeter” as unit of
measure.
measure
3) Presentation of
3) Presentation for
each group.
each group follows
Advanced Learners
Average Learners
What solid figure can
What solid figure can
be formed with the
be formed with the
given nets?
given nets?
1)Net of a triangular
1)Net of a cube
prism
2)Net of a cylinder
2)Net of a square
pyramid
What is surface area?
The surface area of a solid object is a measure
of the total area that the surface of the object
occupies.
How do we find the surface area of cubes?
Prisms?
A cube is a rectangular prism where all its sides
are the same.
Name the solid figure formed with the following
nets:
1)
238
2)
3.
J. Additional
activities for
application and
remediation
V.
REMARKS
VI.
REFLECTION
Name the solid figure formed with the following
nets:
1.
2.
239
School
Teacher
Time and Date
Week 9-Day 2
I.
OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competency
II.
CONTENT
LEARNING
RESOURCES
A. References
1. Teacher’s Guide
Pages
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The Learner demonstrates understanding of rate and
speed, and of area and surface area of plane and
solid/space figures.
The learner is able to apply knowledge of speed, area,
and surface area of plane and solid/space figures in
mathematical problems and real-life situations
The learner derives a formula for finding the surface
area of cubes, prisms and cylinders
M6ME-IIIi-92
Deriving a Formula in Finding the Surface Area of
Cubes, Prisms and Cylinders
III.
2. Learner’s Materials
Pages
3. Textbook Pages
4. Additional Materials
from Learning
Resource (LR)
Portal
B. Other Learning
Resources
IV.
PROCEDURE
A. Reviewing Previous
Lessons or
Presenting New
Lesson
B. Establishing a
purpose for the
lesson
K to 12 Math Curriculum Guide 2016. Grade 6,
page 199
21ST Century Mathletes, 108-112
21st Century Mathletes 6, p. 272-285
21st Century Mathletes 6, p. 272-285
Mathletes 6 Textbook, Powerpoint Presentation
Show a net of a cube, a rectangular prism, and a
cylinder.
Ask: What solid figure can be formed with given nets?
Expected answers: ( cube/ rectangular prism/ cylinder)
a) Show a cube.
Ask:
1) How many faces does it have?
2) What is the shape of each face?
3) Are the faces congruent?
4) What is the formula for the area of square?
b) Show a rectangular prism.
Ask:
1) How many faces does it have?
2) Which faces are congruent?
3) What is the shape of each face?
4) What is the formula for the area of a rectangle?
240
c) Show a cylinder, cone, pyramid, and sphere. Ask
questions similar to the ones above.
C. Presenting
Present the ff. problem in the class.
Examples/Instances
3. Mother is celebrating her birthday. Her children
of new lesson
prepared a gift for her. They have a gift
wrapping paper that measures 900 square
inches. Each edge of the box is 12 inches. Do
you think the children have enough wrapping
paper to cover the gift?
The pupils will investigate the ff.
a.Name of the solid figure
b.Number of faces
c.Shapes of faces
D. Discussing new
Ask the ff. questions:
concepts and
a. What is the name of the solid figure? (cube)
practicing new skills
b. How many faces does it have?(6 faces)
#1
c. What is the shape of the faces? (square)
d. How do we know that the wrapping paper is
enough? Present to the class the net of the
cube.
Find the area of each face. Explain the solution.
Area of a square= s x s
= 12 x 12
=144 square inches
Total area of all faces = 144 x 6 = 864 sq. inches
Therefore, the children have enough wrapping paper
to cover the gift. How do you call the total area of all
the faces of a solid figure?
a. Define surface area. Surface Area is the sum of the
areas of the base and the lateral face of a solid figure.
b. Based on the answers to the above questions,
derive the formula for the surface area of a cube.
E. Discussing new
concepts and
practicing new skills
#2
a. Present a problem
Gerald owns an antique shop. He is refinishing a
rectangular jewelry box shown below. The can of
varnish he is using is enough liquid left in it to cover 30
cm2 is there enough varnish left in the can to refinish
the jewelry box?(Show the picture of the box)
241
Ask:
1. How many sides (or faces) does the box have?
2. How many faces does it have?
3. What are the shapes formed?
Let the pupils derive the formula in finding the surface
area of a prism.
Calculating Surface Area
One way to find the surface area of a prism is to use
the lateral area and base areas. Lateral area (L.A.) of
a prism is the sum of the areas of lateral faces.
*When you find the surface area of a prism, it is a
good idea to find the lateral area first.
S.A.= L.A. + B
Discuss further in finding the lateral area of prism.
b. Show a can of a sardines. Tell them that it is a
concrete example of a cylinder.
Then show a net of a cylinder.
Ask questions about the net of the cylinder:
1. What shapes are formed?
2. What is the formula in finding the area of a circle?
Of a rectangle? Area of a circle= 2πr, Area of a
rectangle=lxw
Ask:What will you do in order to find the surface area
of a cylinder? (Expected answer: Add the area of the 2
circles and the area of the rectangle)
Let the pupils derive the formula in finding the surface
area of a cylinder.
SA= 2πrh + 2(πr2)
(Use 3.14 for pi/π)
Give a problem in finding the surface area of a
cylinder, then let the pupils derive the formula with the
guide of the teacher.
F. Developing mastery
Advance Learners
(Leads to Formative Activity (in groups of 5)
1) Give each group a
Assessment)
spatial figure. For
example, a cylinder.
2) Let each group
measure the
dimensions of their
spatial figure and solve
for its surface area.
242
Average Learners
Activity (in groups of 5)
1) Give each group o
spatial figure. For example
a shoe box.
2) Let each group solve for
its surface area.
(Measurement of
dimensions are already
given)
G. Finding practical
applications of concepts
and skills in daily living
3)Presentation for each
group follows
3)Presentation for each
group follows
Advance Learners
Group Activity: Write the
formula then solve.
Write the unit of
measure to be used in
each problem.
1.)Cubic lunch box:
s=18cm
2.Rectangular shoe
box: l=18 cm, w= 7 cm,
h=9 cm
Average Learners
Group Activity: Write the
formula then solve. Write
the unit if measure to be
used in each problem.
1)a square box whose edge
is 10 cm
2)Rectangular shoe box
with: l=12m, w=8m, h=9m
3.)cylindrical water tank
r=4m
l=10m
w=6mg
G. Making
generalizations and
abstractions about
the lesson
H. Evaluating Learning
I. Additional activities
for application and
remediation
V.
REMARKS
VI.
REFLECTION
l=7in
w=4in
h=5in
What is surface area?
The surface area of a solid object is a measure of the
total area that the surface of the object occupies.
How do we find the surface area of cubes?
Prisms?Cylinders?
A cube is a rectangular prism where all its sides are
the same. The formula to find the surface area of a
rectangular prism is A = 2wl + 2lh + 2hw, where w is
the width, the l is the length, and the h is the height.
To use this formula, we plug in our values and then
evaluate.
Write the formula and find the surface area of the
following solid figures:
1. Cube side = 15cm
2. Rectangular prism l=12m w=8m h=10m
3. Cylinder radius= 3in l=7in w=5in
Write the formula and find the surface area of the
following:
1. Cylinder radius=4cm, l=6cm, w=4cm
2. Cube side= 20in
3. Rectangular prism l=15m, w=9m, h=10m
243
School
Teacher
Time and Date
Week 9 - Day 3
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Standards
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of rate
and speed, and of area and surface area of
plane and solid/space figures.
The learner is able to apply knowledge of speed,
area, and surface area of plane and solid/space
figures in mathematical problems and real-life
situations
The learner derives a formula for finding the
surface area of pyramids, cones and spheres
M6ME-IIIi-92
Deriving a Formula in Finding the Surface Area of
Pyramids, Cones and Spheres
K to 12 Math Curriculum Guide 2016. Grade 6,
page 199
ST
21 Century Mathletes, 108-112
21st Century Mathletes 6, p. 272-285
2. Learner’s
Materials pages
3. Textbook pages
21st Century Mathletes 6, p. 272-285
4. Additional
Materials from
Learning Resource
(LR) Portal
B. Other Learning
Mathletes 6 textbook, power point presentation
Resources
IV. PROCEDURE
A. Reviewing
Drill: Match the picture w/ the formula for the area:
Previous Lessons
Plane Figure
Area Formula
or Presenting
1)
A. s2
2)
B. b x h
3)
C. π r2
4)
5)
D. bh
2
E. lw
6)
F. ½ h(b1+b2)
Review:
244
Find the surface area of a cube with a side of
length 3 cm
Solution:
Given that s = 3
Surface area of a cube = 6s2 = 6(3)2 = 54 cm2
Calculate the surface area of triangular prism.
Solution:
There are 2 triangles with the base = 4 cm and
height = 3 cm.
Area of the 2 bases
= 12 cm2
1 rectangle with length = 7 cm and width = 5 cm
Area = lw = 7 × 5 = 35 cm2
1 rectangle with length =7cm and width 3m
Area = lw = 7 × 3 = 21 cm2
1 rectangle with length = 7 cm and width 4m
Area = lw = 7 × 4 = 28 cm2
The total surface area is 12 + 35 + 21 + 28 = 96
cm2
We can also use the formula
Surface area of prism = 2 × area of base +
perimeter of base × height
= 2 × 6 + (3 + 4 + 5) × 7 = 96 cm2
B. Establishing a
The teacher will show picture of a tent, actual
purpose for the
globe or ball and a party hat. Tell the pupils that
lesson
these are examples of space figures.
C. Presenting
Show a net of a pyramid, cone and sphere.
Examples/Instance Ask : ( for each figure )
s of new lesson
1. What shapes are formed?
2. How many faces does it have?
3. Which faces are congruent?
4. What is the shape of each face?
5. What is the formula for the area of each
face?
(depending on the shape of each face)
D. Discussing new
concepts and
practicing new
skills #1
a. Surface Area of Pyramids:
The surface area of a pyramid is the sum of the
areas of all the faces, including the base. We can
use the net to find a general formula that will help
us find the surface area of a pyramid.
Show to the class a picture and a net of a pyramid
To find the surface area (S.A), we need to find the
lateral area (L.A) and the area of the base(B), then
add. S.A.=L.A. + B.
b. Surface Area of Cones:
The surface area of a cone is the sum of the
lateral (L.A.) and area of its base (B).
S.A=L.A. + B
245
To find L.A., imagine cutting the lateral surface
into wedges and arranging the wedges to form a
figure like parallelogram.
Show a cone or a picture of a party hat.
E. Discussing new
concepts and
practicing new
skills #2
The base of the new figure is πr and the height is
the slant height of the curved surface. So, L.A.=
πrs
S.A.= L.A. + B
= πrs+ πr2
a.Surface Area of Spheres
The area of the circle that contains the center of
the sphere is πr2. It would take exactly 4 of these
circles to wrap the sphere completely.
The surface area of a sphere with radius ( r ) is
S.A.= 4πr2
Say: This is a net of a sphere.
Further discuss the ways to derive the formula in
finding the surface area of the sphere.
F. Developing
mastery
(Leads to
Formative
Assessment)
Advance Learners
Activity (in groups of 5)
1)Give each group a
spatial figure. For
example, a ball, a cone, a
paper weight shaped like
a pyramid.
2)Let each group
measure the dimensions
of their spatial figure and
solve for its surface area.
3.) Write the correct unit
of measure of each
object.
4)Presentation for each
group follows
246
Average Learners
Activity (in groups of
5) 1)Give each group
a spatial figure. For
example, a ball, a
cone, a paper weight
shaped like a pyramid.
2)Let each group
measure the
dimensions of their
spatial figure and
solve for its surface
area.
3.) Write the correct
unit of measure of
each object.
4)Presentation for
each group follows
G. Finding practical
applications of
concepts and skills
in daily living
Advance Learners
Group Activity: Write the
formula then solve. Write
the unit of measure to be
used in each problem.
1. Ball radius=5dm
2. Cone of ice cream
radius 4cm,
s=6cm
3. Rectangular
pyramid (m)
Average
Learners
Group Activity: Write
the formula then
solve. Write the unit of
measure to be used in
each problem.
1. Square pyramid
side=5m,
h=7m,
2. Ball radius 3
cm
3. Cone of Ice
cream radius=
2dm, s=4dm
H. Making
generalizations
and abstractions
about the lesson
What is surface area?
The surface area of a solid object is a measure of
the total area that the surface of the object
occupies.
How do we find the surface area of a Pyramid,
Cone and Sphere?
How do we find the surface area of a pyramid?
There is no formula for a surface area of a nonregular pyramid since slant height is not defined.
To find the area, find the area of each face and
the area of the base and add them.
How do we find the surface area of a cone?
To find the surface area of a cone, find the sum of
the lateral area and the area of its base.
How do we find the surface area of a sphere?
To find the surface area, just use the formula:
S.A.= 4πr2, (the value of pi is 3.14)
I. Evaluating
Learning
Post pictures of the following.
Direction: Write the formula to get surface area of
each figure:
1.
2.
3.
J. Additional
activities for
Write the formula to find the surface area of the
following space figure:
247
application and
remediation
VI. REMARKS
VII. REFLECTION
248
School
Teacher
Time and Date
Week 9- Day 4
I.
OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competency
II.
CONTENT
LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of rate
and speed, and of area and surface area of
plane and solid/space figures.
The learner is able to apply knowledge of
speed, area, and surface area of plane and
solid/space figures in mathematical problems
and real-life situations
The learner finds the surface area of cubes,
prisms and cylinders
M6ME-IIIi-93
Finding the Surface Area of Cubes, Prisms and
Cylinders
III.
2. Learner’s Materials
pages
3. Textbook pages
4. Additional Materials
from Learning
Resource (LR)
Portal
B. Other Learning
Resources
IV.
PROCEDURE
A. Reviewing Previous
Lessons or
Presenting New
Lesson
B. Establishing a
Purpose for the
Lesson
C. Presenting
Examples/Instances
of new lesson
K to 12 Math Curriculum Guide 2016. Grade 6,
page 199
ST
21 Century Mathletes, 108-112
21st Century Mathletes 6, p. 272-285
21st Century Mathletes 6, p. 272-285
Mathletes 6 Textbook, Powerpoint Presentation
Internet website / https://guro.ako.com
Give the formula in finding the area of the
following:
 Circle
 Square
 Rectangle
 Triangle
Review on formulas in finding the surface area
of cubes, prisms, and cylinders.
The teacher will show a cube, a ball and can of
milk. Tell the pupils that these are examples of
space figures.
Present the nets of cube, rectangular/triangular
prism, and cylinder. Ask:
1. What shapes are formed?
2. How many faces does it have?
3. What is the shape of each face?
249
D. Discussing new
concepts and
practicing new skills
#1
E. Discussing new
concepts and
practicing new skills
#2
4. What is the formula for the area of each
face?
The teacher will ask: How can you derive the
formula in finding the surface area for the cube,
prisms, and cylinder. (The pupils will answer
based on what they have learned on previous
lessons.)
Present a problem:
Charmie is wrapping a gift for her mother on
Teacher’s day. The box she is using is a cube
with 5 inches length on each side. Find how
many square inches of paper she needs to wrap
the entire box?
Explain how to get the surface area of a cube.
Solve for the surface area using the formula:
S.A.= 6s2
Let us solve for the surface area:
What are the given facts? ( side of the cube:5
inches)
S.A.= 6x(5)2
= 6x25
= 150 in2
Therefore, Charmie needs 150 in2 of to wrap the
entire box.
Give another problem in finding the surface area
of a cube. Let the pupils answer the problem
with the guide of the teacher.
Present a problem.
A library has an aquarium in the shape of a
rectangular prism. Its base is 6 ft. by 2 ft. The
height is 4 ft. How many sq. ft. of glass was
used to build the aquarium?
Discuss how to get the surface area of a
rectangular prism. L.A. or lateral area of a prism
is the sum of the areas of lateral faces.
Let us solve for the surface area of the prism.
Given facts: base of the aquarium: l=6 ft w=2ft. ;
height=4 ft.
6 ft.
S.A.= L.A.+2B
250
To find the lateral area (L.A.), add the
areas of the 4 lateral faces with rectangular
shape.
There are 2 pairs of congruent lateral areas.
Area of 1st pair of lateral faces
A=lxw
= 6x4 = 24 ft. 2
24x2=48 ft2
Area of the 2nd pair of lateral faces
A=lxw
=4x2
= 8 ft2
8x2= 16 ft2
Total area of 4 lateral faces: 64 ft2
To find the area of the base with rectangular
shape,
Use the formula lxw. A=lxw
Area of the 2 bases:
A=lxw
= 6x2 = 12 ft2 12x2= 24 ft2
Add the areas of the base and lateral faces to
find the surface area of the rectangular
aquarium:
S.A. = L.A. + 2B
= 64 + 24
= 88 ft2
Therefore, 88 ft2 of glass is needed to build the
aquarium.
Next Activity : Discuss on how to find the
surface area of a cylinder.
F. Developing mastery
(Leads to Formative
Assessment)
Advance Learners
Activity ( in groups of 5)
1)Give each group a
solid figure. For
example, cube,
rectangular prism, a
cylinder.
2)Let each group
measure the
dimensions of their
spatial figure and solve
for its surface area.
3.) write the correct unit
of measure of each
object.
4)Presentation for each
group follows
251
Average Learners
Activity ( in groups of
5)
1.Give each group a
solid figure. For
example, cube,
rectangular prism,
and a cylinder.
2)The measurement
of the dimensions is
given. Let each group
solve for its surface
area.
3.) Write the correct
unit of measure of
each object.
4)Presentation for
each group follows
G. Finding practical
applications of
concepts and skills
in daily living
Advance Learners
Group Activity: Write
the formula then solve.
Write the unit of
measure to be used in
the following problem.
Calculate the surface
area of a cylindrical
water tank with a radius
of 6 ft and a height of
10 ft.
H. Making
generalizations and
abstractions about
the lesson
What is surface area?
The surface area of a solid object is a measure
of the total area that the surface of the object
occupies.
I. Evaluating Learning
Read and solve.
1. What is the minimum amount of
cardboard needed to make a tissue cube
with a side length of 4 centimeters?
2. A cylinder shaped water pitcher has a
radius of 5 inches and a height of 12
inches. Find the surface area of the
pitcher?
3. Calculate the surface area of a
rectangular shoe box with a base of 10
cm by 4 cm; and a height of 5 cm.
Solve for the following:
 Find the amount of tin needed to make a
milk tin can that has a radius of 3
centimeters.
 Find the surface area of a refrigerator
with a base of 3 ft. by 2 ft. ; and a height
of 6 ft.
J. Additional activities
for application and
remediation
V.
REMARKS
VI.
REFLECTION
252
Average Learners
Group Activity: Write
the formula then
solve. Write the unit
of measure to be
used in each
problem.
Find the surface area
of jewelry box that
measures 6 cm on
each side.
School
Teacher
Time and date
Week 9-Day 5
I.
OBJECTIVES
A. Content Standards
B. Performance
Standards
C. Learning
Competency
II.
CONTENT
LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
Grade Level
Learning Area
Quarter
6
Mathematics
Third
The learner demonstrates understanding of
rate and speed, and of area and surface area
of plane and solid/space figures
The learner is able to apply knowledge of
speed, area, and surface area of plane and
solid/space figures in mathematical problems
and real-life situations
The learner finds the surface area of cones,
spheres, and pyramids
Finding the Surface Area of Cones, Spheres,
and Pyramids
M6ME-IIIi-93
III.
2. Learner’s Materials
pages
3. Textbook pages
4. Additional Materials
from Learning
Resource (LR)
Portal
B. Other Learning
Resources
IV.
PROCEDURE
A. Reviewing Previous
Lessons or
Presenting New
Lesson
B. Establishing a
Purpose for the
Lesson
C. Presenting
Examples/Instances
of new Lesson
K to 12 Math Curriculum Guide 2016. Grade 6,
page 199
st
21 Century Mathletes, 108-112
21st Century Mathletes 6, p.272-285
21st Century Mathletes 6, p.272-285
Internet website / https://guro.ako.com
Review on how to find the surface area of
prisms, cylinder and cubes.
Show actual objects of solid figures. For
example, cone, sphere, and pyramids.
Show the nets of cone, sphere, and pyramid.
Ask:
1. What shapes are formed?
2. How many faces does it have?
3. What is the shape of each face?
4. What is the formula for the area of each
face?
The teacher will ask: How can you derive the
formula in finding the surface area for the
253
D. Discussing New
Concepts and
Practicing New
Skills #1
E. Discussing New
Concepts and
Practicing New
Skills #2
F. Developing Mastery
(Leads to Formative
Assessment)
cube, prisms, and cylinder. (The pupils will
answer based on what they have learned on
previous lessons.)
Present a problem:
John works in a company that makes tents.
His boss assigned him to design tents for
mountaineers. He need to keep them light. To
decide what fabrics are acceptable to
mountaineers, he needs to know the amount
of fabric it takes to construct a rectangular tent
whose base is 4m by 1.5m and a height of 3
meters. How much fabric is required to
construct this tent?
Let us use the formula below to find the
surface area of the rectangular pyramid.
S.A.=L.A.+ B
Discuss and explain further to find the surface
area of the tent.
Give another problem in finding the surface
area of a cone. Let the pupils answer the
problem with the guide of the teacher.
Present another problem:
Find the area of the basketball with a radius of
5 decimeters.
Solution: Use the formula S.A. = 4πr2
S.A.= 4πr2
= 4(3.14)(52)
= 314 dm2
Answer: The surface area of the basketball is
314 dm2.
Advance Learners
Average Learners
Activity ( in groups of Activity ( in groups of
5)
5)
1. Give each group a 1. Give each group a
solid figure. For
solid figure. For
example, cone,
example, cone,
sphere, and a
sphere, and a pyramid.
pyramid.
2)Let each group
2)Let each group
measure the
measure the
dimensions of their
dimensions of their
spatial figure and solve
spatial figure and
for its surface area.
solve for its surface
3.) write the correct
area.
unit of measure of
3.) write the correct
each object.
unit of measure of
4)Presentation for
each object.
each group follows
4)Presentation for
each group follows
254
G. Finding Practical
Applications of
concepts and Skills
in Daily Living
Advance Learners
Group Activity: Write
the formula then
solve.
Calculate the surface
area of a globe with
a diameter of 12.5
centimeters.
H. Making
Generalizations and
Abstractions About
the Lesson
What is surface area?
The surface area of a solid object is a
measure of the total area that the surface of
the object occupies.
I. Evaluating Learning
Average Learners
Group Activity: Write
the formula then solve.
Calculate the surface
area of a ball with a
radius of 6
centimeters.
How do we find the surface area of a cone?
The first step in finding the surface area of a
cone is to measure the radius of the circle part
of the cone. The next step is to find the area of
the circle, or base. The area of a circle is 3.14
times the radius squared (πr2). Now, you will
need to find the area of the cone itself. In
order to do this, you must measure the side
(slant height) of the cone. Make sure you use
the same form of measurement as the radius.
You can now use the measurement of the side
to find the area of the cone. The formula for
the area of a cone is 3.14 times the radius
times the side (πrl).
So the surface area of the cone equals the
area of the circle plus the area of the cone and
the final formula is given by:
SA = πr2 + πrl
How do we find the surface area of a cone?
To find the surface area of a sphere, use the
formula (4πr2), where r = the radius of the
circle
How do we find the surface area of a pyramid?
To find the surface area of a pyramid, we need
to find the lateral area (L.A.) and the area of
the base (B), then add: S.A. = L.A. + B.
Write the formula then solve.
1.Find the surface area of the ice cream cone
with a radius of 2 cm and slant height of 6 cm.
2.Calculate the surface area of a basketball
with a radius of 4 decimeters.
3.Compute for the surface area of a tent with a
rectangular base that measures 3 meters wide
and 4 meters long; and a height of 2 meters.
255
J. Additional Activities
for Application and
Remediation
Solve for the following:
A spherical tank for natural gas has a radius of
6 feet. Calculate its surface area.
VI. REMARKS
VII. REFLECTION
256
School:
Teacher:
Grade Level: 6
Learning Mathematics
Area:
Quarter: Third
Teaching
Dates and Week 10 – Day 1
Time:
I. OBJECTIVES
A. Content Standard
B. Performance Standard
C. Learning
Competencies /
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
3. Textbook pages
4. Additional Materials
from Learning
Resource (LR) Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrates understanding of rate and
speed, and of area and surface area of plane and
solid/space figures
The learner is able to apply knowledge of speed, and
of area and surface area of plane and solid/space
figures in mathematical problems and real- life
situations
The learner solves word problems involving
measurement of surface area
M6ME-IIIj-94
Solving Word Problems Involving Measurement of
Surface Area of Prism
K to 12 Mathematics Curriculum Guide 2016,
Grade 6 pp. 200
21st Century Mathletes pp. 272-285
Math for A Better Life pp. 294-300
Flashcards, manila paper, strips of cartolina
Advance Learners
Find the surface area.
h=25 cm
b- 11 cm
16 dm
12.5 m
20.5 m
B. Establishing a purpose
for the lesson
Ask:
-
Average Learners
1. Distribute strips of
cartolina with 3D shapes
and formula of surface
area written on it.
2. Have each pupils find
its partner.
3. Let each partner
show to the class what
they have.
4. The class will check if
their classmates are
correct.
When is your mother’s birthday?
What did you do to make her happy? Did you give
her gifts?
What gift did you give?
257
C. Presenting
Examples/Instances of
new lesson
D. Discussing new
concepts and
practicing new skills #1
Present the problem.
- Wendel wants to surprise her mother on her
birthday. He bought a pair of sandals placed in
a 32 cm by 18 cm by 15 cm box. If he wants to
cover it with birthday wrapper, what must he
do? How many wrappers are needed to cover
the box?
Ask:
- Who has a birthday?
- What birthday present did Wendel bring?
- What kind of son is Wendel?
- If you were Wendel, will you do the same?
Why?
Answer the following questions:
1. What is asked?
2. What are given?
3. What operation to be used?
4. What is the number sentence?
5. What is the solution?
6. What is the complete answer?
Advance Learners
Average Learners
Read and analyze the
problem.
- Find the surface
area of a cube with
a side of 21.60
centimeter.





E. Discussing new
concepts and
practicing new skills #2
What is asked in the
problem?
 the surface area of
the cube
What are the given
facts?
 side of the cube
21.60 cm
What operation will be
used?
 multiplication
What is the number
sentence?
 S2 x 6 = n
What is the solution
and the answer?
 (21.60 cm)2 x 6 = n
 466.56 cm x 6 = n
 2 799.36 cm2
Advance Learners
Group Activities.
Group the pupils into 2.
Setting of standards.
258
Read and analyze the
problem.
-





Find the surface
area of a cube
with a side of 6
centimeter.
What is asked in the
problem?
 the surface area
of the cube
What are the given
facts?
 side of the cube
6 cm
What operation will
be used?
 multiplication
What is the number
sentence?
 S2 x 6 = n
What is the solution
and the answer?
 (6 cm)2 x 6 = n
 36 cm x 6 = n
 216 cm2
Average Learners
Group Activities.
Group the pupils into 2.
Setting of standards.
Group 1
1. Ben bought a cube with
a side of 14 centimeter. He
wants to cover it with
plastic cover. How much
plastic cover will be used?
2. A rectangular water
tank, 15 meters by 23
meters by 10 meters is to
be painted all over. How
much surface is to be
painted?
F. Developing mastery
(Leads to Formative
Assessment)
Advance Learners
Read and analyze the
problem.
 How many square
centimeter of gift
wrapper are needed to
cover the box which is
29 centimeters by 21
centimeters by 32
centimeters?
- What is asked in the
problem?
- What facts are given?
- What operation to be
used?
- What is the mathematical
sentence?
- What is the solution and
the answer?
G. Finding practical
applications of
concepts and skills in
daily living
Group 1
1. Ben bought a cube
with a side of 9
centimeter. He wants to
cover it with plastic
cover. How much plastic
cover will be used?
2. A rectangular water
tank, 5 meters by 3
meters by 12 meters is
to be painted all over.
How much surface is to
be painted?
Average Learners
Read and analyze the
problem.
 How many square
centimeter of gift
wrapper are needed
to cover the box
which is 11
centimeters by 7
centimeters by 2
centimeters?
Advance Learners
Answer the problem below
with the following
questions:
1) What is asked in the
problem?
2) What facts are given?
3) What operation to be
used?
4) What is the
mathematical sentence?
5) What is the solution and
answer?
What is asked in the
problem?
- What facts are given?
- What operation to be
used?
- What is the
mathematical sentence?
- What is the solution
and the answer?
Average Learners
Answer the problem
below with the following
questions:
1) What is asked in the
problem?
2) What facts are given?
3) What operation to be
used?
4) What is the
mathematical sentence?
5) What is the solution
and answer?
- Josie needs a sewing box
for her sewing materials.
She used an empty milk
can 756 centimeters by
182 centimeters by 69
- Josie needs a sewing
box for her sewing
materials. She used an
empty milk can 75.6
centimeter by 18.2
259
centimeters. She wanted to
cover it with attractive wall
paper. How much will she
use to cover it?
centimeter by 9
centimeter. She wanted
to cover it with attractive
wall paper. How much
will she use to cover it?
H. Making generalizations
and abstraction about
the lesson.
What is surface area?
How do you find the surface area of prism?
What are the steps in solving word problem?
I.
Advance Learners
Analyze and solve.
1. What is the surface area
of a cube whose side is
32.5 decimeter?
2. Find the surface area of
a rectangular box with a
length of 120 cm and a
width of 34 cm.
Advance Learners
- You are painting a room
that is 540 cm long, 420
cm wide and 240 cm high.
Find the surface area of
the four walls that you are
going to paint.
Evaluating Learning
J. Additional activities for
application and
remediation
V. REMARKS
VI. REFLECTIONS
A. No. of learners who
earned 80% on the
formative assessment
B. No. of learners who
require
additional
activities
for
remediation
who
scored below 80%
C. Did
the
remedial
lessons work? No. of
learners
who
have
caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did this work?
F. What difficulties did I
encountered which my
principal or supervisor
can help me solve?
260
Average Learners
Analyze and solve.
1. What is the surface
area of a cube whose
side is 12.5 decimeter?
2. Find the surface area
of a rectangular box with
a length of 18 cm and a
width of 30 cm.
Average Learners
- You are painting a
room that is 54 cm long,
42 cm wide and 24 cm
high. Find the surface
area of the four walls
that you are going to
paint.
G. What innovation or
localized materials did I
use/discover which I
wish to share with other
teachers?
261
School:
Grade 6
Level:
Learning Mathematics
Area:
Quarter: Third
Teacher:
Teaching
Dates and Week 10 – Day 2
Time:
I. OBJECTIVES
A. Content Standard
B. Performance Standard
C. Learning
Competencies /
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages
2. Learner’s Materials
pages
3. Textbook pages
B. Additional Materials
from Learning
Resource (LR) Portal
C. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrates understanding of rate and
speed, and of area and surface area of plane and
solid/space figures
The learner is able to apply knowledge of speed, and of
area and surface area of plane and solid/space
figures in mathematical problems and real- life
situations
The learner solves word problems involving
measurement of surface area
M6ME-IIIj-94
Solving Word Problems Involving Measurement of
Surface Area of Pyramid
K to 12 Mathematics Curriculum Guide 2016. Grade 6,
pp. 200
21st Century Mathletes pp. 272-285
Math for Life pp. 294-300
Flashcards, manila paper, strips of cartolina
Advance Learners
a. Drill:
1. Group the pupils into 5
members each.
2. Distribute strips of
cartolina with word problem.
3. Let each member of the
group answer the problem
following the steps in
solving word problem.
 1st member-will answer
what is asked
 2nd member- what facts
are given
 3rd member-operation
to be used
262
Average Learners
a. Drill:
1. Group the pupils into
5 members each.
2. Distribute strips of
cartolina with word
problem.
3. Let each member of
the group answer the
problem following the
steps in solving word
problem.
 1st member-will
answer what is
asked

4th member-will answer
the number sentence
 5th member- will solve
the problem.
Sample word problem.
- Find the surface area of a
box with a height of 150 dm,
75 dm width and a height of
125 dm.
- Mara made a cube for her
project in math. The side is
150 cm Find the surface
area of the cube.
b. Checking of assignment
B. Establishing a purpose
for the lesson
C. Presenting
Examples/Instances of
new lesson
L
(dm)
25
W
(dm)
16
H
(dm)
15
SA
Side
80
Advance Learners
Present the problem.
- What is the surface area
of a square pyramid whose
side is 120 meters and a
height of 225 meters?
1. What is asked in the
problem?
 surface area of the
square pyramid
2. What are the given facts?
 side is 120 meters
height is 225 meters
4. What operation will you
use?
 addition,
multiplication and
division
4. What is the mathematical
sentence?
263
2nd memberwhat facts are
given
 3rd memberoperation to be
used
 4th member-will
answer the
number
sentence
 5th member- will
solve the
problem.
Sample word problem.
- Find the surface area
of a box with a height of
15 dm, 7.5 dm width
and a height of 12.5 dm.
- Mara made a cube for
her project in math. The
side is 22 cm. Find the
surface area of the
cube.
b. Checking of
assignment
Advance Learners
Complete the table.
Advance Learners
Complete the table.
Space
figure
Rectang
ular
prism
cube

Space
figure
Rectan
gular
prism
cube
L
(dm)
12
W
(dm)
8
H
(dm)
9
SA
Side
25
Average Learners
Present the problem.
- What is the surface
area of a square
pyramid whose side is 9
meters and a height of
12 meters?
1. What is asked in the
problem?
 surface area of
the square
pyramid
2. What are the given
facts?
 side is 9 meters
 height is 12
meters
5. What operation will
you use?
 1202 + 4(120)(225) ÷
2=n
5. What is the solution and
the answer?
14 400 + 108 000 = n
2
 122 400 ÷ 2 = n
 61 200 m2
D. Discussing new
concepts and
practicing new skills #1
Advance Learners
Analyze and solve.
- The boy scouts are setting
up a tent. The tent is in the
shape of rectangular
pyramid with a height of 15
meters, a width of 3 meters
and with a length of 12
meters. What is the surface
area of the tent?
E. Discussing new
concepts and
practicing new skills #2
Advance Learners
Group Activity.
1. Group the pupils into 2.
2. Setting of standards
Problem #1
- A box in the shape
of rectangular
pyramid has a
length of 74 cm,
width of 45 cm and a
height of 50 cm.
What is the surface
area of the box?
Problem #2
- A square pyramid
has a side of 125
dm and a height of
1175 dm. Find the
surface area of the
pyramid.
3. Presentation of output.
4. Ask: How did you find the
activity?
- What formula did you use
to solve the problem?
264
 addition,
multiplication
and division
4. What is the
mathematical sentence?
 92 + 4(9)(12) ÷ 2
=n
5. What is the solution
and the answer?
 81 + 432 = n
2
 513 ÷ 2 = n
 256.5 m2
Average learners
Analyze and solve.
- The boy scouts are
setting up a tent. The
tent is in the shape of
rectangular pyramid
with a height of 2.5
meters, a width of 1.2
meters and with a
length of 7 meters.
What is the surface area
of the tent?
Average learners
Group Activity.
1. Group the pupils into
2.
2. Setting of standards
Problem #1
- A box in the
shape of
rectangular
pyramid has a
length of 24 cm,
width of 18 cm
and a height of
35 cm. What is
the surface area
of the box?
Problem #2
- A square
pyramid has a
side of 24 dm
and a height of
16 dm. Find the
surface area of
the pyramid.
3. Presentation of
output.
4. Ask: How did you find
the activity?
- What formula did you
use to solve the
problem?
F. Developing mastery
(Leads to Formative
Assessment)
Advance Learners
Analyze and solve:
- A pyramid has a side of
125 cm and a height of
1250 cm. What is its
surface area?
G. Finding practical
applications of
concepts and skills in
daily living
Advance Learners
Analyze the problem by
answering the given
questions.
- Find the surface area of
the pyramid whose base is
212m and the slant height
of 175m.
a. What is asked in the
problem?
b. What are the given facts?
c. What is the operation to
be used?
d. What is the mathematical
sentence?
e. What is the solution and
the answer?
H. Making generalizations
and abstraction about
the lesson.
I.
Evaluating Learning
Average Learners
Analyze and solve:
- A pyramid has a side
of 25 cm and a height of
36 cm. What is its
surface area?
Average Learners
Analyze the problem by
answering the given
questions.
- Find the surface area
of the pyramid whose
base is 3.5m and the
slant height of 7.25m.
a. What is asked in the
problem?
b. What are the given
facts?
c. What is the operation
to
be used?
d. What is the
mathematical
sentence?
e. What is the solution
and
the answer?
What is the formula for finding the surface area of
square pyramid and rectangular pyramid?
What are the steps in solving word problems involving
measurement of surface area?
Advance Learners
Average Learners
Read, analyze and solve
Read, analyze and
the problem.
solve the problem.
1) A square pyramid has a
1) A square pyramid
side of 102 dm and a slant
has a side of 10.2 dm
height of 205 dm. Find the
and a slant height of
surface area of the pyramid. 21.5 dm. Find the
2) Find the surface area of
surface area of the
pyramid whose side is 125
pyramid.
cm and a height of 80 m.
2) Find the surface area
of pyramid whose side
is 17.2 cm and a height
of 11.6 cm.
265
J. Additional activities for
application and
remediation
Advance Learners
Read, analyze and solve.
- John has a pyramid. The
base is 122 cm and the
slant height is 90 cm. Find
the total surface area of the
pyramid.
V. REMARKS
VI. REFLECTIONS
A. No. of learners who
earned 80% on the
formative assessment
B. No. of learners who
require
additional
activities
for
remediation
who
scored below 80%
C. Did
the
remedial
lessons work? No. of
learners
who
have
caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did this work?
F. What difficulties did I
encountered which my
principal or supervisor
can help me solve?
G. What innovation or
localized materials did I
use/discover which I
wish to share with other
teachers?
266
Average Learners
Read, analyze and
solve.
- John has a pyramid.
The base is 15 cm and
the slant height is 22
cm. Find the total
surface area of the
pyramid.
School:
Grade 6
Level:
Learning Mathematics
Area:
Quarter: Third
Teacher:
Teaching
Dates and Week 10 – Day 3
Time:
I. OBJECTIVES
A. Content Standard
B. Performance
Standard
C. Learning
Competencies /
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
3. Textbook pages
4. Additional
Materials from
Learning
Resource (LR)
Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
The learner demonstrates understanding of rate and speed,
and of area and surface area of plane and solid/space
figures
The learner is able to apply knowledge of speed, and of area
and surface area of plane and solid/space figures in
mathematical problems and real- life situations
The learner solves word problems involving measurement of
surface area
M6ME-IIIj-94
Solving Word Problems Involving Measurement of Surface
Area of Cone
K to 12 Mathematics Curriculum Guide 2016. Grade 6,
pp. 200
21st Century Mathletes pp. 272-285
Math for Life pp. 294-300
Flashcards, manila paper
Advance Learners
1. Drill: Write the fomula or
equation then solve the
surface area of the
following:
Average Learners
1. Drill: Write the fomula or
equation then solve the
surface area of the following:
16 cm
26 dm
16 cm
12 m
26 dm
12 m
11 dm
35 m
2. Analyze and solve.
- A pyramid has a square
base of 14.75 m and a
height of 29.16 m. Find the
surface area of pyramid
267
11 dm
35 m
2. Analyze and solve.
- A pyramid has a square base
of 14.75 m and a height of
29.16 m. Find the surface area
of pyramid
B. Establishing a
purpose for the
lesson
C. Presenting
Examples/Instance
s of new lesson
Advance Learners
Present a problem.
- A cone of ice cream has a
radius of 5.5 cm and a slant
height of 36 cm. Find the
surface area of cone.
Advance Learners
Analyzing the problem.
1. Understand:
a. What is asked?
 surface area of
cone
b. What are the given
facts?
 r = 5.5 cm
 h = 36 cm
2. Plan:
a. Which formula shall
we use to solve the
problem?
 SA=πr2 + πrs
3. Solve:
SA=3.14(5.5)2 + 3.14(5.5)(36)
= 3.14(30.25) + 3.14(198)
= 94.985 + 621.72
= 716.705 cm2
D. Discussing new
concepts and
practicing new
skills #1
E. Discussing new
concepts and
practicing new
skills #2
Pair Activity:
- Find the surface area of a
cone whose radius is 21 cm
and the slant height is 80
cm.
1. Understand:
a. What is asked?
b. What are the given
facts?
2. Plan:
a. Which formula will
you use to solve the
problem?
3. Solve:
4. Look back
Advance Learners
Group Activity:
1. Group the pupils into 2.
Setting of standards.
Group 1:
- A conical shape tent
has a diameter of 35
meters and a height
of 45 meters. Find
the surface area of
the tent.
Group 2:
- Find the surface
area of an ice cream
268
Average Learners
Present a problem.
- A cone of ice cream has a
radius of 3.5 cm and a slant
height of 16 cm. Find the
surface area of cone.
Average Learners
Analyzing the problem.
1. Understand:
a. What is asked?
 surface area of
cone
b. What are the given
facts?
 r = 3.5 cm
 h = 16 cm
2. Plan:
a. Which formula shall we
use to solve the
problem?
 SA=πr2 + πrs
3. Solve:
SA=3.14(3.5)2 + 3.14(3.5)(16)
= 3.14(12.25) + 3.14(56)
= 38.465 + 175.84
= 214.305 cm2
Pair Activity:
- Find the surface area of a
cone whose radius is 6 cm and
the slant height is 8 cm
1. Understand:
a. What is asked?
b. What are the given
facts?
2. Plan:
a. Which formula will
you use to solve the
problem?
3. Solve:
4. Look back
Advance Learners
Group Activity:
1. Group the pupils into 2.
Setting of standards.
Group 1:
- A conical shape tent
has a diameter of 3.25
meters and a height of
7.5 meters. Find the
surface area of the
tent.
Group 2:
- Find the surface area
of an ice cream cone
cone with a diameter
with a diameter of 9 cm
of 9 cm and a slant
and a slant height of 16
height of 16 cm.
cm.
2. Presentation of output.
2. Presentation of output.
3. Ask:
3. Ask:
- How did you find the
- How did you find the activity?
activity?
- What did you do to find the
- What did you do to find the answer?
answer?
F. Developing
Advance Learners
Average Learners
mastery
Read, analyze and solve.
Read, analyze and solve.
(Leads to Formative - Find the surface area of a
- Find the surface area of a
Assessment)
conical shape roof of a
conical shape roof of a waiting
waiting shed with a radius
shed with a radius of 3.75
of 75 meters and a slant
meters and a slant height of
height of 125 meters
7.5 meters
G. Finding practical
Advance Learners
Average Learners
applications of
Analyze and solve:
Analyze and solve:
concepts and skills - The base of a conical
- The base of a conical shape
in daily living
shape hat is 52 cm in
hat is 21 cm in diameter and
diameter and with a height
with a height of 15 cm. Find
of 125 cm. Find the surface the surface area of the hat.
area of the hat.
H. Making
1. What is the formula for finding the surface area of cone?
generalizations
2. What are the steps in solving word problems involving
and abstraction
measurement of surface area?
about the lesson.
a. Understand the problem
1. What is asked?
2. What are the given facts?
3. What operation to be used?
b. Plan
1. What is the number sentence?
c. Solve
d. Look back
I. Evaluating
Advance Learners
Average Learners
Learning
Read and analyze the
Read and analyze the
problem.
problem.
1. A cone has a radius of 45 1. A cone has a radius of 12
cm and 210 cm height. Find cm and 20 cm height. Find the
the surface area.
surface area.
2. The base of a conical
2. The base of a conical shape
shape funnel has a radius
funnel has a radius of 7 dm
of 32 dm and with a height
and with a height of 14 dm.
of 45 dm. Find the surface
Find the surface area.
area.
J. Additional
Advance Learners
Average Learners
activities for
Analyze and solve.
Analyze and solve.
application and
- The base of the cone has
- The base of the cone has a
remediation
a diameter of 114 dm and
diameter of 14 dm and with a
with a slant side of 245 dm. slant side of 25 dm. What is its
What is its surface area?
surface area?
269
V. REMARKS
VI. REFLECTIONS
A. No. of learners who
earned 80% on the
formative
assessment
B. No. of learners who
require additional
activities
for
remediation
who
scored below 80%
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners who
continue to require
remediation
E. Which
of
my
teaching strategies
worked well? Why
did this work?
F. What
difficulties
did I encountered
which my principal
or supervisor can
help me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
270
School:
Grade 6
Level:
Learning Mathematics
Area:
Quarter: Third
Teacher:
Teaching
Dates and Week 10 – Day 4
Time:
I. OBJECTIVES
A. Content Standard
B. Performance
Standard
C. Learning
Competencies /
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
3. Textbook pages
B. Additional Materials
from Learning
Resource (LR)
Portal
C. Other Learning
Resources
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
The learner demonstrates understanding of rate and
speed, and of area and surface area of plane and
solid/space figures
The learner is able to apply knowledge of speed, and of
area and surface area of plane and solid/space figures
in mathematical problems and real- life situations
The learner solves word problems involving
measurement of surface area
M6ME-IIIj-94
Solving Word Problems Involving Measurement of
Surface Area of Cylinder
K to 12 Mathematics Curriculum Guide 2016.
Grade 6, pp. 200
21st Century Mathletes pp. 272-285
Math for Life pp. 294-300
Flashcards, manila paper
Advance Learners
1. Drill:
Identify the solid figure
and give the formula for
finding the surface area.
1)
3)
120 dm
160 cm
Average Learners
1. Drill:
Identify the solid figure
and give the formula for
finding the surface area.
1)
25 dm
3)
30 cm
75 cm
11 cm
45 dm
9 dm
2)
20 m
4)
35 m
2)
14 m
180 m
35 m
271
4)
6m
B. Establishing a purpose
for the lesson
C. Presenting
Examples/Instances of
new lesson
Advance Learners
Present a problem.
- A can of sardines has a
radius of 65 cm and a
height of 85 cm. How much
tin can was used?
Advance Learners
Analyzing the problem.
1. Understand
a. What is asked?
 surface area of
can of sardines
b. What are the given
facts?
 radius 65 cm
 height 85 cm
2. Plan
a. Which formula will
you use to solve the
problem?
 SA=2πr2 + 2πh
b. What is the
mathematical
sentence?
2(3.14)(65)2 + 2(3.14)(85)=n
3. Solve:
D. Discussing new
concepts and
practicing new skills #1
E. Discussing new
concepts and
practicing new skills #2
=2(3.14)(4225)+2(266.9)
=2(13266.5)+533.8
= 26532 + 533.8
= 27065.8
Advance Learners
1. Pair Activity.
- The diameter of the base
of a cylinder is 120 cm and
the height is 65 cm. Find
the surface area.
2. Discussion of the
answer of each partner.
Advance Learners
A. Group Activity.
1. Group the pupils into 2
2. Let them select their
leader, secretary and
reporter.
3.Have each group answer
the problem.
Group 1.
- A flourescent bulb
has a diameter of 5
cm and a length of
112 cm. Find the
surface area.
Group 2.
272
Average Learners
Present a problem.
- A can of sardines has a
radius of 5 cm and a height of
12 cm. How much tin can was
used?
Average Learners
Analyzing the problem.
1. Understand
a. What is asked?
 surface area of
can of sardines
b. What are the given
facts?
 radius 5 cm
 height 12 cm
2. Plan
a. Which formula will
you use to solve the
problem?
 SA=2πr2 + 2πh
b. What is the
mathematical
sentence?
2(3.14)(5)2 + 2(3.14)(12)=n
3. Solve:
=2(3.14)(25)+2(37.68)
=2(78.5)+75.36
= 157 + 75.36
= 232.36
Average Learners
1. Pair Activity.
- The diameter of the base of
a cylinder is 18 cm and the
height is 21 cm. Find the
surface area.
2. Discussion of the answer
of each partner.
Average Learners
A. Group Activity.
1. Group the pupils into 2
2. Let them select their
leader, secretary and
reporter.
3.Have each group answer
the problem.
Group 1.
- A flourescent bulb has
a diameter of 5 cm
and a length of 75 cm.
Find the surface area.
Group 2.
- What is the surface
area of a pen if the
-
F. Developing mastery
(Leads to Formative
Assessment)
G. Finding practical
applications of
concepts and skills in
daily living
H. Making generalizations
and abstraction about
the lesson.
I.
Evaluating Learning
J. Additional activities for
application and
remediation
What is the surface
radius is 0.5 cm and a
area of a pen if the
height of 12 cm.
radius is 0.75 cm
B.Presentation of output.
and the height of 42 C. Ask:
cm.
- How did find the
B.Presentation of output.
activity?
C. Ask:
- What did you do to
- How did find the
find the answer? What
activity?
formula did you use?
- What did you do to
find the answer?
What formula did
you use?
Advance Learners
Average Learners
Analyze and solve.
Analyze and solve.
- A milk can has a diameter - A milk can has a diameter of
of 45 cm and a height of
5 cm and a height of 13 cm.
112 cm. Find the surface
Find the surface area.
area.
Advance Learners
Average Learners
Analyze and solve.
Analyze and solve.
- A cylinder is 75 cm tall
- A cylinder is 15 cm tall and
and the radius of its
the radius of its circular base
circular base is 24 cm.
is 8 cm. What is its surface
What is its surface area?
area?
1. What is the formula for finding the surface area of cone?
2. What are the steps in solving word problems involving
measurement of surface area?
a. Understand the problem
1. What is asked?
2. What are the given facts?
3. What operation to be used?
b. Plan
1. What is the number sentence?
c. Solve
d. Look back
Advance Learners
Average Learners
Answer the following
Answer the following
problems. Follow the steps problems. Follow the steps in
in solving word problem.
solving word problem.
1. A can is 94 cm tall and
1. A can is 24 cm tall and its
its base has a radius of 32 base has a radius of 5.2 cm.
cm. How much paper is
How much paper is needed to
needed to cover the can?
cover the can?
2. What is the surface area 2. What is the surface area of
of the cylindrical tank that
the cylindrical tank that is
is 375 m in high and 80 m
3.75 m in high and 1.25 m in
in diameter?
diameter?
Advance Learners
Average Learners
Analyze and solve.
Analyze and solve.
- A cylindrical shape basket - A cylindrical shape basket
has a radius of 63 dm and
has a radius of 14 dm and a
a height of 35 dm. Find its
height of 32 dm. Find its
surface area.
surface area.
273
V. REMARKS
VI. REFLECTIONS
A. No. of learners who
earned 80% on the
formative assessment
B. No. of learners who
require
additional
activities
for
remediation
who
scored below 80%
C. Did
the
remedial
lessons work? No. of
learners
who
have
caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did this work?
F. What difficulties did I
encountered which my
principal or supervisor
can help me solve?
G. What innovation or
localized materials did I
use/discover which I
wish to share with other
teachers?
274
School:
Grade 6
Level:
Learning Mathematics
Area:
Quarter: Third
Teacher:
Teaching
Dates and Week 10 – Day 5
Time:
I. OBJECTIVES
A. Content
Standard
B. Performance
Standard
C. Learning
Competencies /
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
2. Learner’s
Materials
pages
3. Textbook
pages
B. Additional
Materials from
Learning
Resource (LR)
Portal
C. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
The learner demonstrates understanding of rate and speed,
and of area and surface area of plane and solid/space
figures
The learner is able to apply knowledge of speed, and of area
and surface area of plane and solid/space figures in
mathematical problems and real- life situations
The learner solves word problems involving measurement of
surface area
M6ME-IIIj-94
Solving Word Problems Involving Measurement of Surface
Area of Sphere
K to 12 Mathematics Curriculum Guide 2016. Grade 6,
pp. 200
21st Century Mathletes pp. 272-285
Math for Life pp. 294-300
Flashcards, manila paper
1. Drill: Match column A with column B.
A
B
1. Pyramid
a. 2LW + 2WH + 2HL
2. Cylinder
b. S2 + 4SH
2
3. Cube
c. 2(Area of ) + (Area of
4. Cone
d. 2πr2 + 2πh
5. rectangular prism
e. πr2 + πrs
2. Checking of assignment
B. Establishing a
purpose for the
lesson
Advance Learners
Ask: Who has a basketball at
home? Do you know how much
rubber is used in that ball? What
275
Average Learners
Ask: Who has a
basketball at home?
Do you know how
)
will you do to know how much
rubber is used?
C. Presenting
Examples/Instance
s of new lesson
D. Discussing new
concepts and
practicing new
skills #1
E. Discussing new
concepts and
practicing new
skills #2
Advance Learners
Present a problem.
- A basketball has a radius of
11.5 cm. How much rubber is
used?
Ask: What is the shape of the
basketball? What formula will you
use to get the needed rubber?
Analyzing the problem.
1. Understand:
a. What is asked?
b. What are the given
facts?
2. Plan:
a. Which formula will
you use to solve the
problem?
b. What is the
mathematical
sentence?
3. Solve
4. Look back
Advance Learners
- The diameter of a globe is 21.5
dm. What is its surface area?
Advance Learners
Group Activity
1. Let each group answer the
following problems.
2. Setting of standards.
Group 1
- Find the surface area of a
plastic - ball with a radius
of 84 cm.
Group 2
- What is the surface area
of the sphere with a
radius of 90 dm?
3. Presentation of output.
4. Ask: How did you find the
activity? What did you do to solve
the problem?
276
much rubber is used in
that ball? What will you
do to know how much
rubber is used?
Average Learners
Present a problem.
- A basketball has a
radius of 5 cm. How
much rubber is used?
Ask: What is the shape
of the basketball? What
formula will you use to
get the needed rubber?
Analyzing the problem.
1. Understand:
a. What is asked?
b. What are the
given facts?
2. Plan:
a. Which formula
will you use to solve
the problem?
b. What is the
mathematical sentence?
3. Solve
4. Look back
Average Learners
- The diameter of a
globe is 4 dm. What is
its surface area?
Average Learners
Group Activity
1. Let each group
answer the following
problems.
2. Setting of standards.
Group 1
- Find the surface
area of a plastic
ball with a
radius of 24 cm.
Group 2
- What is the
surface area of
the sphere with
a radius of 16
dm?
3. Presentation of
output.
4. Ask: How did you
find the activity? What
did you do to solve the
problem?
F. Developing
mastery
(Leads to Formative
Assessment)
G. Finding practical
applications of
concepts and skills
in daily living
Advance Learners
- Find the surface area of a ball
with a radius of 72 dm.
H. Making
generalizations
and abstraction
about the lesson.
1. What is the formula for finding the surface area of cone?
2. What are the steps in solving word problems involving
measurement of surface area?
a. Understand the problem
1. What is asked?
2. What are the given facts?
3. What operation to be used?
b. Plan
1. What is the number sentence?
c. Solve
d. Look back
Advance Learners
Average Learners
Read the problem. Analyze and
Read the problem.
solve.
Analyze and solve.
1) A ball has a radius of 78 cm. 3) A ball has a radius
What is its surface area?
of 18 cm. What is its
2) What is the surface area of a
surface area?
sphere with a diameter of 35 4) What is the surface
dm?
area of a sphere
with a diameter of
11 dm?
I.
Evaluating
Learning
J. Additional
activities for
application and
remediation
Advance Learners
Analyze and solve the problem.
- What is the surface area of a
softball with a radius of 42 dm?
Advance Learners
Analyze and solve the problem.
- Find the surface area of a
sphere that has a diameter of
127 cm.
V. REMARKS
VI. REFLECTIONS
A. No. of learners who
earned 80% on the
formative
assessment
B. No. of learners who
require additional
activities
for
remediation
who
scored below 80%
277
Average Learners
- Find the surface area
of a ball with a radius
of 24 dm
Average Learners
Analyze and solve the
problem.
- What is the surface
area of a softball with a
radius of 9 dm?
Average Learners
Analyze and solve the
problem.
- Find the surface area
of a sphere that has a
diameter of 27 cm.
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners who
continue to require
remediation
E. Which
of
my
teaching strategies
worked well? Why
did this work?
F. What
difficulties
did I encountered
which my principal
or supervisor can
help me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?
278
TABLE OF SPECIFICATION
POST-TEST
Third Quarter
Mathematics 6
AREA OF CONTEXT / COMPETENCIES
1. Visualizes and describes the different solid figures: cube,
prism, pyramid, cylinder, cone, and sphere. M6GE – IIIa – 27
2. Differentiates solid figures from plane figures. M6GE – IIIa –
28
3. Illustrates the different solid figures using various concrete
and pictorial models. M6GE – IIIb – 29
4. Identifies the faces of a solid figure. M6GE – IIIb – 30
5. Visualizes and describes the different solid figures: cube,
prism, pyramid, cylinder, cone, and sphere. M6GE – IIIc – 31
6. Identifies the nets of the following figures: cube, prism,
pyramid, cylinder, cone, and sphere using plane figures.
M6GE – IIIc – 32
7. Formulates the rule in finding the nth term using different
strategies (looking for a pattern, guessing and checking,
working backwards). E.g. 4, 7, 13, 16, …. n (the nth term is
3n+1) M6AL – IIId – 7
8. Differentiates expression from equation. M6AL – IIId – 15
9. Gives the translation of real-life verbal expressions and
equations into letters or symbols and vice versa. M6AL – IIIe
– 16
10. Defines a variable in an algebraic expression and
equation. M6AL – IIIe – 17
Time
Allot
ment
Weig
ht in
Perce
ntage
Tota
l No.
Cognitive Process Dimension
Item
Place
ment
20%
Compr
ehensi
on
30%
Know
ledge
Appli
cation
Analys
is
Evalua
tion
Sysn
thesis
20%
10%
10%
10%
Item
s
2
5
1-2
(0.40)2
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
3-4
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
5-6
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
1
2.5
7
(0.20)1
(0.30)
(0.20)
(0.10)
(0.10)
(0.10)
1
2
5
8-9
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
10-11
(0.40)2
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
12-13
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)2
2
1
2.5
14
(0.20)2
(0.30)
(0.20)
(0.10)
(0.10)
(0.10)
1
2
5
15-16
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
17-18
(0.40)1
(0.60)1
(0.40)
(0.20)
(0.20)
(0.20)
2
279
11. Represents quantities in real-life situations using algebraic
expressions and equations. M6AL – IIIe – 18
12. Solves routine and non-routine problems involving different
types of numerical expressions and equations such as 7+a=
__+6. M6AL – IIIf – 19
13. Creates routine and non-routine problems involving
numerical expressions and equations. M6AL – IIIf – 20
14. Calculates speed, distance, and time. M6ME – IIIg – 17
15. Solves problems involving average, rate, and speed.
M6ME – IIIg – 18
16. Finds the area of composite figures formed by any two or
more of the following: triangle, square, rectangle, circle, and
semi-circle. M6ME – IIIh – 89
17. Solves routine and non-routine problems involving area of
composite figures formed by any two or more of the
following: triangle, square, rectangle, circle, and semi-circle.
M6ME-IIIh-90
18. Visualizes and describes surface area and names the unit
of measure used for measuring the surface area of
solid/space figures. M6ME – IIIi – 91
19. Derives a formula for finding the surface area of cubes,
prisms, pyramids, cylinders, cones, and spheres. M6ME-IIIi92
20. Finds the surface area of cubes, prisms, pyramids,
cylinders, cones, and spheres. M6ME – IIIi – 93
21. Solves word problems involving measurement of surface
area. M6ME – IIIj – 94
Total
2
5
19-20
(0.40)
(0.60)
(0.40)2
(0.20)
(0.20)
(0.20)
2
2
5
21-22
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
23-24
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)2
2
2
5
25-26
(0.40)
(0.60)
(0.40)
(0.20)1
(0.20)1
(0.20)
2
2
5
27-28
(0.40)
(0.60)
(0.40)1
(0.20)
(0.20)1
(0.20)
2
2
5
29-30
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
31-32
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
33-34
(0.40)1
(0.60)1
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
35-36
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
37-38
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)2
(0.20)
2
2
5
38-40
(0.40)
(0.60)
(0.40)2
(0.20)
(0.20)
(0.20)
2
40
100
40
8
12
8
4
4
4
40
280
PRE-TEST
Third Quarter
Direction: Read and solve each problem carefully and choose the letter of the correct
answer.
1. How many edges do we have in the figure?
a. 4
c. 8
Figure
b. 6
d. 12
1
2. In figure 1 above, how many vertices can you count?
a. 4
b. 6
c. 8
d. 12
3. What is the solid figure if circles and rectangles will be combined?
a. cube
b. pyramid
c. prism
d. cylinder
4. If we combine square and triangle, what geometric solid will be formed?
a. cube
b. pyramid
c. prism
d. cylinder
5. What kind of solid figure is the ice
a. cube
b.
cylinder
cube ?
pyramid
c. prism
6. Refrigerator is a real-life example of what solid figure below.
a. cube
b. pyramid
c. prism
d. cylinder
7. The triangular pyramid has
a. 3
c. 5
b. 4
d. 6
lateral faces?
8. A prism composed of two rectangular bases
rectangular lateral faces.
and four
a.
b.
c.
d.
d.
9. A solid figure with a curved surface and that has two circular bases that are
congruent and parallel.
a.
b.
c.
d.
10. The net that can be formed a cube.
a.
b.
c.
d.
11. The base is a square and it has four triangular faces. This net
can form a
.
a. square pyramid
c. triangular pyramid
b. rectangular pyramid
d. Egyptian’s pyramid
281
12.
1 3 5 7
, , ,
5 5 5 5
2x𝑛−1
a.
5
…. n. The nth rule for this sequence is
b.
𝑛+1
5
c.
.
5
𝑛+2
d.
5
𝑛+1
13. What rule can be used to find nth term of this sequence?
1 4 9 16
, , , …. n
15 15 15 15
2x𝑛
𝑛2
𝑛𝑥𝑛
𝑛3
a.
b.
c.
d.
15
14.
15
15
15
is a mathematical phrase that uses variables, numerals and operation
symbols while
is a mathematical sentence with an equal sign (=) which
shows that two expressions or both sides are equal.
a. Variable and constant
c. Expression and
equation
b. Numerical value and algebra
d. Phrase and sentence
15. Ray is b years old now. Her daughter’s age is 7 more than one-fifth her age.
What is the algebraic expression for her daughter’s age?
𝑏
5
𝑏
5
a. 7 +
b. 7 +
c. – 7
d. – 7
5
𝑏
5
𝑏
16. John Ray took a pre-test and post-test to measure his proficiency in Math. His
score in the pre-test was 90 and his score in the post test was n. If the average of
the two tests is 91, what is an equation that can be used to solve for his post-test
score?
90+𝑛
90−𝑛
a.
= 91
c.
= 91
b.
2
91+𝑛
2
= 90
d.
2
91−𝑛
2
= 90
17. 5y -2, the variable in the algebraic expression is
.
a. 5
b. 2
c. 18
d. y
18. Which of the following are the variables of 7x – 2 = 5y + 18?
a. x and y
b. 7 and -2
c. x and 5
d. y and 18
19. Mrs. Cruz, when asked about her age, replies “I am six years older and twice the
age of my youngest child”. Express her age in algebraic equation if her age is
now 50.
a. 2a – 6 = 50 b. 2a + 50 = 6 c. 2a – 50 = 6 d. 2a + 6 = 50
20. Write an algebraic expression for the cost of each n liter of crude oil if the total
cost of 11 liters is P825.00.
825
11
𝑛
11
a. n =
b. n =
c. 825 =
d. 825 =
11
825
11
𝑛
21. If thrice a number is increased by 11, the result is 35. What is the number?
a. 8
b. 9
c. 10
d. 11
22. If twice my allowance will be increased by P300.00, it would become P1,000.00.
How much is my current allowance?
a. P350.00
b. P300.00
c. P1000.00 d. P600.00
23.
x + 10 = 20. Using this equation, what is the correct word problem?
a. x increased by 10 is equal to 20 c. x decreased by 10 is equal to 20
b. x more than 20 is equal to 10
d. x is equal to 10 and 20
282
24.
𝑦+3
2
, the word phrase for this algebraic expression is
a. y increased by 3 all over 2
c. y decreased by 3 all over 2
b. y more than 2 all over 3
d. y over 2 increased by 3
.
25. Calculate the distance of your travel if you’ll drive 2 hours at 50 km/h.
a. 50 km
b. 100 km
c. 150 km
d. 200 km
26. A car travels 100 km in 4 hours. Calculate the average speed of the car in
kilometres per hour.
a. 100 km/h b. 75 km/h
c. 50 km/h
d. 25 km/h
27. A bus has an average speed of 45 kph. If travelled a distance of 450 km. How
long did the bus travel?
a. 5 hours
b. 10 hours
c. 15 hours
d. 20 hours
28. John Ray took a 2-hour bicycle trip. He travelled 60 km. What was the average
rate of speed of John Ray’s trip?
a. 30 km/h
b. 60 km/h
c. 90 km/h
d. 120 km/h
29.
10cm
What is the area of this figure?
a. 22 cm2
c. 200 cm2
2
b. 35 cm
d. 225 cm2
5c
m
20cm
30.
Find the area of this composite figure.
a. 4 m2
c. 37.56 m2
2
b. 25 m
d. 10 m2
2m
5m
31.
8 cm
2 cm
How many square centimetres of tiles are
needed to cover this kitchen floor?
a. 12 cm2
c. 48 cm2
2
b. 24 cm
d. 112 cm2
6 cm
16c
m
32. A rectangular wrapping cloth has a length of 15 dm and a width of 10 dm. Two
circular cloth with a diameter of 4 inches will be cut from it. How much cloth will
be left?
a. 150 dm2
b. 162.56 dm2
c. 200 dm2
d. 12.56 dm2
33. A solid figure whose surface area is the sum of the lateral area and the areas of
the two bases.
a. prism
b. pyramid
c. cylinder
d. cone
34. The unit of measure used for measuring the surface area of space figure is
.
a. unit
b. square unit
c. cubit unit
d. volume
283
35. The formula to find the surface area of a pyramid is
.
a. S.A. = L.A.+2B
c. S.A. = 4πr2
4
b. S.A. = πr2
d. S.A. = L.A. + B
3
36. Which formula below to find the surface area of a cube?
4𝑠ℎ
a. S.A. = s2 +
c. S.A. = s2 x 6
4
b. S.A. = πr2
3
2
d. S.A. = πrs + πr2
37. What is the surface area of a cube if its edge is 4 m?
a. 16 m2
b. 96 m2
c. 150 m2
d. 200 m2
38. Find the surface area of a sphere that has a radius of 5dm.
a. 314 dm2
b. 78.5 dm2 c. 100 dm2
d. 12.56 dm2
39. A rectangular box has a length of 8 inches, a width of 6 inches, and a height of 10
inches. What is the surface area?
a. 48 in2
b. 60 in2
c. 80 in2
d. 376 in2
40. Rayneli is wrapping a can of chocolates for her youngest brother. If the can is 10
cm high and has a diameter of 4 cm, how many square centimetres of wrapping
paper will she use completely in covering the can?
a. 25.12 cm2 b. 125.6 cm2 c. 150.72 cm2 d. 250 cm2
284
TABLE OF SPECIFICATION
POST-TEST
Third Quarter
Mathematics 6
AREA OF CONTEXT / COMPETENCIES
1. Visualizes and describes the different solid figures: cube,
prism, pyramid, cylinder, cone, and sphere. M6GE – IIIa – 27
2. Differentiates solid figures from plane figures. M6GE – IIIa –
28
3. Illustrates the different solid figures using various concrete
and pictorial models. M6GE – IIIb – 29
4. Identifies the faces of a solid figure. M6GE – IIIb – 30
5. Visualizes and describes the different solid figures: cube,
prism, pyramid, cylinder, cone, and sphere. M6GE – IIIc – 31
6. Identifies the nets of the following figures: cube, prism,
pyramid, cylinder, cone, and sphere using plane figures.
M6GE – IIIc – 32
7. Formulates the rule in finding the nth term using different
strategies (looking for a pattern, guessing and checking,
working backwards). E.g. 4, 7, 13, 16, …. n (the nth term is
3n+1) M6AL – IIId – 7
8. Differentiates expression from equation. M6AL – IIId – 15
9. Gives the translation of real-life verbal expressions and
equations into letters or symbols and vice versa. M6AL – IIIe
– 16
Time
Allot
ment
Weig
ht in
Perce
ntage
Tota
l No.
Cognitive Process Dimension
Item
Place
ment
20%
Compr
ehensi
on
30%
Know
ledge
Appli
cation
Analys
is
Evalua
tion
Sysn
thesis
20%
10%
10%
10%
Item
s
2
5
1-2
(0.40)2
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
3-4
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
5-6
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
1
2.5
7
(0.20)1
(0.30)
(0.20)
(0.10)
(0.10)
(0.10)
1
2
5
8-9
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
10-11
(0.40)2
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
12-13
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)2
2
1
2.5
14
(0.20)2
(0.30)
(0.20)
(0.10)
(0.10)
(0.10)
1
2
5
15-16
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
285
10. Defines a variable in an algebraic expression and
equation. M6AL – IIIe – 17
11. Represents quantities in real-life situations using algebraic
expressions and equations. M6AL – IIIe – 18
12. Solves routine and non-routine problems involving different
types of numerical expressions and equations such as 7+a=
__+6. M6AL – IIIf – 19
13. Creates routine and non-routine problems involving
numerical expressions and equations. M6AL – IIIf – 20
14. Calculates speed, distance, and time. M6ME – IIIg – 17
15. Solves problems involving average, rate, and speed.
M6ME – IIIg – 18
16. Finds the area of composite figures formed by any two or
more of the following: triangle, square, rectangle, circle, and
semi-circle. M6ME – IIIh – 89
17. Solves routine and non-routine problems involving area of
composite figures formed by any two or more of the
following: triangle, square, rectangle, circle, and semi-circle.
M6ME-IIIh-90
18. Visualizes and describes surface area and names the unit
of measure used for measuring the surface area of
solid/space figures. M6ME – IIIi – 91
19. Derives a formula for finding the surface area of cubes,
prisms, pyramids, cylinders, cones, and spheres. M6ME-IIIi92
20. Finds the surface area of cubes, prisms, pyramids,
cylinders, cones, and spheres. M6ME – IIIi – 93
21. Solves word problems involving measurement of surface
area. M6ME – IIIj – 94
Total
2
5
17-18
(0.40)1
(0.60)1
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
19-20
(0.40)
(0.60)
(0.40)2
(0.20)
(0.20)
(0.20)
2
2
5
21-22
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
23-24
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)
(0.20)2
2
2
5
25-26
(0.40)
(0.60)
(0.40)
(0.20)1
(0.20)1
(0.20)
2
2
5
27-28
(0.40)
(0.60)
(0.40)1
(0.20)
(0.20)1
(0.20)
2
2
5
29-30
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
31-32
(0.40)
(0.60)
(0.40)1
(0.20)1
(0.20)
(0.20)
2
2
5
33-34
(0.40)1
(0.60)1
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
35-36
(0.40)
(0.60)2
(0.40)
(0.20)
(0.20)
(0.20)
2
2
5
37-38
(0.40)
(0.60)
(0.40)
(0.20)
(0.20)2
(0.20)
2
2
5
38-40
(0.40)
(0.60)
(0.40)2
(0.20)
(0.20)
(0.20)
2
40
100
40
8
12
8
4
4
4
40
286
POST- TEST
Third Quarter
Direction: Solve the problems carefully. Choose the correct answer and write the
letter only.
1. How many edges do we have in the figure?
a. 12
c. 4
Figure 1
b. 6
d. 8
2. In figure 1 shown above, how many vertices can you count?
a. 6
b. 12
c. 8
d. 4
3. What is the solid figure if rectangles and triangles will be combined?
a. cube
b. pyramid
c. prism
d. cylinder
4. If we combine two squares, what geometric solid will be formed?
a. cube
b. pyramid
c. prism
d. cylinder
5. What kind of solid figure is the
a. cube
b. pyramid
aquarium?
c. prism
d. cylinder
6. Pail is a real-life example of what solid figure below.
a. cube
b. pyramid
c. prism
d. cylinder
7. The rectangular pyramid has
a. 3
c. 5
b. 4
d. 6
lateral faces?
8. A 3-dimensional solid object that has a circular base and a single vertex.
a.
b.
c.
d.
9. A geometrical figure that is perfectly round, 3-dimensional and circular-like a ball .
a.
b.
c.
d.
10. The net that can be formed a rectangular prism.
a.
b.
c.
d.
11. The base is a rectangle and it has four triangular faces. This net can form a
.
a. square pyramid
c. triangular pyramid
b. rectangular pyramid
d. Egyptian’s pyramid
1 4 5
7 7 7
12. , , …. n. The nth rule for this sequence is
a.
n+2
7
b.
𝑛+1
7
.
c.
7
𝑛+2
13. What rule can be used to find nth term of this sequence?
1 6 9 12
, , , …. n
13 13 13 13
2𝑛
𝑛2
5𝑛
a.
b.
c.
13
13
13
287
d.
7
𝑛+1
d.
3𝑛
13
14.
is a mathematical statement wherein two expressions show equality while
is a mathematical phrase which combines numbers, variables and operations to
show the value of something.
a. equation and expression
c. sentence and phrase
b. algebraic expression and numerical expression d. constant and variable
15. Cassie is c years old now. Her mother’s age is 6 more than twice as much as her
age. What is the algebraic expression for her mother’s age.
a. 6c + 2
b. 2c + 6
c. 6c2
d. 2c - 6
16. Marga got the following scores in her Mathematics quizzes: 90, 95, n. If the
average of the three quizzes is 94, what is an equation that can be used to solve
for his 3rd quiz score?
90+95+𝑛
90+95−94
a.
= 94
c.
= 90
3
b. 3(90 + 95 + 𝑛) = 94
d.
𝑛
94+90+𝑛
3
= 95
17. 3x - 5, the variable in the algebraic expression is
.
a. 3
b. 5
c. x
d. -
18. Which of the following are the variables of 5y – 3 = 4z + 9?
a. y and z
b. y and -3
c. z and 9
d. -3 and 9
19. Gen. Marcial de Leon is ten years older and twice the age of his eldest daughter.
If his age now is 58, express his age in algebraic equation.
a. 10a + 2 = 58
b. 2a - 10 = 58
c. 2(a + 10) = 58
d. 2a + 10
= 58
20. Write an algebraic expression for the cost of each n liter of gasoline if the total
cost of 15 liters is ₱900.00.
900
15
𝑛
15
a. n =
b. n =
c. 900 =
d. 900 =
15
900
15
𝑛
21. If a quadrupled number is decreased by 15, the result is 65. What is the number?
a. 15
b. 20
c. 25
d. 30
22. After I got failing grades in my subjects, my weekly allowance decreased to
₱2,500.00 which is 1 500 less than my previous allowance. How much is my
allowance before?
a. ₱4,000.00
b. ₱3,500.00
c. ₱3,000.00
d.
₱5,000.00
23. 3x = 60. Using this equation, what is the correct word problem?
a. x increased by 3 is equal to 60
c. thrice the number is equal to
60
b. x less 3 is equal to 60
d. x is equal to 3 and 60
24.
𝑦+7
5
, the word phrase for this algebraic expression is
.
a. y increased by 7 all over 5
c. y decreased by 7 all over 5
b. y more than 5 all over 7
d. y over 5 increased by 7
25. Calculate the distance of your travel if you’ll drive 3 hours at 80km/h.
a. 150km
b. 180km
c. 210km
d. 240km
288
26. A car travels 400km in 5 hours. Calculate the average speed of the car in
kilometres per hour.
a. 80km/h
b. 60km/h
c. 90km/h
d. 120km/h
27. A bus has an average speed of 70kph. If travelled a distance of 630km. How long
did the bus travel?
a. 9 hours
b. 10 hours
c. 11 hours
d. 12 hours
28. Christopher took a 2-hour bicycle trip. He travelled 80km. What was the average
rate of speed of Christopher’s trip?
a. 20km/h
b. 30km/h
c. 40km/h
d. 50km/h
29.
What is the area of this figure?
a. 330cm2
c. 306cm2
b. 350cm2
d. 390cm2
6c
m
10cm
30cm
30.
Find the area of this composite figure.
a. 30m2
c. 37.56 m2
b. 61m2
d. 75.25m2
5m
6m
cm
31.
7cm
3cm
How many square centimetres of tiles
are needed to cover this kitchen floor?
a. 45cm2
c. 35cm2
2
b. 75cm
d. 105cm2
5cm
15c
32. A rectangular mwrapping cloth has a length of 20dm and a width of 30dm. Five
circular cloth with a diameter of 40cm will be cut from it. How much cloth will be
left?
a. 568.6dm2
b. 560dm2
c. 580dm2
d.
2
575.6dm
33. It is the sum of all areas of the surface of a 3-dimensional solid figure.
a. perimeter
b. circumference
c. surface area
d. volume
34. In measuring the surface area of space figure, the unit used is
.
a. square unit
b. cubic unit
c. unit
d. area
35. The formula to find the surface area of a cone is
.
a. S.A. = L.A.+2B
c. S.A. = πrs + πr2
4
b. S.A. = πr2
d. S.A. = L.A. + B
3
36. Which formula below to find the surface area of a cylinder?
4𝑠ℎ
a. S.A. = s2 +
c. S.A. = 2πr2 + 2πrh
4
3
2
b. S.A. = πr2
d. S.A. = πrs + πr2
37. A side of a cube measures 5cm. Find its surface area.
a. 36cm2
b. 180cm2
c. 25cm2
289
d. 150cm2
38. Find the surface area of a sphere that has a radius of 10dm.
a. 1,256dm2
b. 125.6dm2
c. 100dm2
2
12.56dm
d.
39. A rectangular cabinet has a length of 3 metres, a width of 4 metres, and a height
of 5 metres. What is the surface area?
a. 48m2
b. 60m2
c. 80m2
d. 94m2
40. Romina is wrapping a can of sardines for her stepdaughter. If the can is 15cm
high and has a diameter of 10cm, how many square centimetres of wrapping
paper will she use completely covering the can?
a. 628cm2
b. 162.8cm2
c. 150cm2
d. 25cm2
290