MATHEMATICS GRADE 6
School
PANIPUAN ELEMENTARY SCHOOL
Teaching Dates/Week
Week 1
Teacher
ALMA M. LAXAMANA
Quarter
Fourth
I.
Objectives
A. Content Standards
 The learner demonstrates understanding of volume of solid figures and meter reading.
B. Performance Standards
 The learner is able to apply knowledge of order of operations, ratio and proportion, percent,
exponents and integers apply knowledge of volume of solid figures and meter reading in
mathematical problems and real-life situations.
C. Learning Competencies
 The learner determines the relationship of the volume between
1.1 a rectangular prism and a pyramid;
1.2 a cylinder and a cone;
1.3 and a cylinder and sphere (M6ME-IVa-95)
D. Objective
 To determine the relationship of the volume between a rectangular prism and a pyramid, a
cylinder and a cone and a cylinder and a sphere.
II.
Content
 Measurement : Volume of Solid Figures
Learning Resources
A. References
21st Century MATHletes Teacher’s Manual pp. 113-116
21st Century MATHletes Textbook pp. 288-301
B. Other Learning Resources
Skills Enhancer in Mathematics 6 pp. 258 -264
Math Beyond Excellence 6 pp. 381-385
Downloaded reference material – Workbook on Math 6 – PDF)
https://sciencing.com/uses-volumes-daily-life-8692308.html
https://googleimages.com
III.
Procedures
A. Reviewing previous lesson or presenting the new lesson
Hello again! How was your week? I hope you’ve been doing well. Time really flies, doesn’t it? We are already
on the last quarter of this school year. Are you ready for our first lesson this quarter? I bet you are! Let’s begin.
To start with, let us have a review on solid figures. Do you still remember them?
Solid figures are three-dimensional objects having length, width and height. These include
cube, rectangular prism, triangular prism, square-pyramid, rectangular-based pyramid,
triangular-based pyramid, cone, cylinder and sphere.
DRILL
Can you name the solid figure that these real-objects resemble? Write your answer on the blank.
1.
2.
_____________
3.
____________
4.
____________
____________
Turn to the key to correction and check your answers. How many correct answers did you get?
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5.
____________
B. Establishing a purpose for the lesson
Luis would like to put blocks in a box. He would like to find out how
many blocks the box can contain. This situation calls for finding the
volume of a solid figure. The volume of a solid figure is the amount of
space it occupies. It is expressed in cubic units. (cm3, m3, km3, in3 etc.)
C. Presenting examples/instances of the new lesson
Study the situation below.
ENGAGE
This cube was painted on all sides and then cut into 27 smaller cubes.
a. How many smaller cubes have paint on only 2 sides?
b. How many smaller cubes have paint on only 1 side?
EXPLORE
The large cube has 12 edges and 6 faces.
a. After cutting, each edge contains 1 small cube with 2 painted faces; a total of 12.
b. After cutting, each face has 1 small cube with 1 painted face; a total of 6.
EXPLAIN
The volume of a solid figure is the amount of space inside it. Volume is measured in cubic units, which means
how many cubes of a given size it takes to fill the solid figure.
D. Discussing new concepts and practicing new skills #1
RELATIONSHIP BETWEEN THE VOLUME OF A RECTANGULAR PRISM AND PYRAMID
Volume of Prisms
The volume of a prism is the amount of space inside
the prism.
We can use the given diagram below to show why the
formula of any prism works.
To find the volume (V) of a prism, multiply
the number of cubic units needed to cover
the base (B) by the number of layers (h)
Therefore,
Volume (V) = base area (B) x height (h)
V=Bxh
Since B = L x W, then V = L x W x H
Example 1
Find the volume of the refrigerator.
Solution:
V=lxwxh
= (3 m) x (2 m) x (6 m)
V = 36 m3
Thus, the volume of the refrigerator is 36 m3.
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Volume of Pyramids
The volume of a pyramid is the amount of space inside the pyramid. Volume is measured in cubic units which
mean it tells us how many cubes of a given size it takes to fill the pyramid.
Example 2
It takes three pyramids of popcorn to fill the rectangular box. The pyramid and the rectangular
prism have the same base and height.
Therefore,
Volume of the pyramid = 1 x volume of a rectangular prism
3
Volume of a rectangular prism, V = l x w x h
So for a pyramid, V = 1 x l x w x h or l x w x h
3
3
The volume of a pyramid is 1 the volume of a prism with the
3
same base area and height.
Example 3
Find the volume of the given pyramid.
V = 1/3 (l x w)(h)
V = 1/3 (3 x 4)(8)
= 1/3 (12) (8)
= 1/3 (96)
= 96
3
= 32 in³
Therefore, the volume of the pyramid is 32 in³.
Activity 1
Solve for the volume of the figures given below.
Turn to the key to correction and check your answers. How many correct answers did you get?
E. Discussing new concepts and practicing new skills #2
RELATIONSHIP BETWEEN THE VOLUME OF A CYLINDER AND A CONE
Volume of Cylinders
The volume of a cylinder is the amount of space inside a cylinder. Finding the volume of
a cylinder is similar to finding the volume of any other prism.
The volume of a cylinder is the product of the circular base area (B) and the height.
Therefore, V = πr²h
Example 4
Find the volume of the coffee mug.
r = 6 cm
h = 12 cm
So, the volume of this mug is 1 356.48 cm3.
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Solution:
V = πr²h
= 3.14 x 62 x 12
= 3.14 x 36 x 12
= 1 356.48 cm3
Volume of Cones
Study the situation below.
At Five-Six Convenience Store, you can buy a Big Gulp or a Little Gulp juice. The Big Gulp comes in a can,
while the Little Gulp is served in a cone.
r
r
h = 8 in
h
How many bases does a cone have? What is the shape of the base of the cone?
The Big Gulp and the Little Gulp containers have equal radii and equal heights. So, it takes three Little Gulps to
fill one Big Gulp.
Little
Little
Little
Big
=
What fraction of the volume of a Big Gulp is the volume of the Little Gulp?
The volume of a cone is 1 the volume of a cylinder with the same area (base) and height. (h)
3
Volume of a cylinder
Volume of a cone
r
V = πr²h
V=1 b
3
h
h
h
r
base area (b)
The formula for the volume of a cone is 1 the base area times the height.
3
V=
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1
3
B
h
or
V=
1
3
𝜋r²h
Example 5
Find the volume of the given cone.
5 = 2 cm
h = 5 cm
V = 1 𝜋r²h
3
1
V=
x 3.14 x 22 x 5
3
1
V = 3 x 3.14 x 4 x 5
1
V=
3 x 6.28
V = 20.93 cm3
Therefore, the volume of the cone is 20.93 cm3
Activity 2
Solve for the volume of the figures given below.
10 cm
dm
h = 20 cm
dm
Turn to the key to correction and check your answers. How many correct answers did you get?
F. Developing mastery
VOLUME OF SPHERES
Volume is measured in cubic units. A circle on a sphere with the same center as the sphere has an
area of πr². Imagine this same circle as the base of a cylinder that exactly contains the sphere.
The volume of this cylinder would be the area of its base times its height, which is πr² x 2r or 2 r3. The sphere
does not fill the whole cylinder. In fact, its volume is 2 of the volume of the cylinder.
3
Therefore, the volume of a sphere is 4 πr3
3
Example 6
Find the volume of the sphere.
V=
V=
r = 50m
V=
V=
V=
So the volume of the sphere is 523 333.33 m 3
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4
3
4
3
4
3
4
3
𝜋r3
x 3.14 x 503
x 3.14 x 125 000
x 392 500
523 333.33 m3
Try this!
What is the volume of this sphere?
1.2 cm
You should get 7.23456 cm³ as the final answer.
If you got the correct answer, you may proceed with the
next part of the lesson.
If not, I am sorry but you have to go back to the examples
and try all over again.
G. Finding practical applications of concepts and skills in daily living
Whether you're measuring out ingredients for a recipe, filling up a car's gas tank or just
adding detergent to the washing machine, math and volume come are used often in daily life.
From measuring liquids to assessing drinking amounts, volume is necessary. Keep in mind
that volume has nothing to do with weight or mass; it is the measurement of how much space
a liquid or gas takes up. Mass, on the other hand, refers to the quantity or amount of matter in
an object, whereas the volume of a solid can be measured via liquid displacement.
Bottoms Up
One of the main ways volume is used daily is when calculating drinking amounts. Soda pop is bought in 12ounce cans or 20-ounce bottles. At the bar someone might order a pint of beer. Mayo Clinic recommends
people drink a little more than 8 cups of water a day or eight 8-ounce glasses of water, about 1.9 liters.
Fueling Up
When you fill up your vehicle, the volume of gasoline your gas tank holds determines your purchase. Whether
you fill up with gallons or liters of gasoline or other fuels, the amount is a volume calculation. On a smaller
scale, when you fill up a gas can to take to another vehicle or to use the gas to power another device, you
again use volume for determining the amount needed.
Cooking and Baking
The number of measuring cups and spoons in the average person's kitchen is indicative of how often volume is
used when cooking. From the 1/4 cup of oil that is needed in a brownie recipe to the quart of chicken broth that
is required for chicken noodle soup, volume is a measurement that is used in almost every recipe.
Cleaning House
Volume is used in most house-cleaning chores. When washing clothes, you add a specific amount of laundry
liquid to the washing machine based on the load or volume of the tub and the clothes being washed. When
using concentrated cleaning detergents, you add a specified amount of the cleaner to a clearly defined amount
of water. Many times you apply a fixed volume of liquid to whatever you are cleaning.
Water Conservation
Water volume plays a huge part in water conservation. Water flow from a shower head is figured in gallons per
minute. If you take a 10-minute shower, you'll likely use about 40 gallons of water, unless you have a watersaving showerhead. Water flow from sprinklers and hoses to determine water usage and conservation in your
yard is also figured in gallons per minutes. Both are volume measurements.
Swimming Pools and Hot Tubs
Once a pool or hot tub is filled with water, maintenance begins. Detailed volumes of cleaners and chemicals
are needed at critical intervals. The volume of chemicals such as chlorine, are adjusted to the pool's capacity
for water.
It’s your turn! Can you also cite some uses of volume in our daily lives?
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H. Making generalizations and abstractions about the lesson
REMEMBER:
The volume of a solid figure is the amount of space inside it. Volume is measured in cubic units,
which means how many cubes of a given size it takes to fill the solid figure.
To find the volume (V) of a prism, multiply the number of cubic units needed to cover the base (B) by the
number of layers (h)
The volume of a pyramid is 1 the volume of a prism with the same base area and height.
3
The volume of a cylinder is the product of the circular base area (B) and the height.
Therefore, V = 𝝅r²h
The formula for the volume of a cone is 1 the base area times the height.
3
The volume of a sphere is 4 πr3.
3
I.
Evaluating learning – Written Work
Solve for the volume of the given figures. Encircle the letter of the correct answer.
1.
L= 20in
A. 600 in3
B. 800 in3
C. 1000 in3
D. 1200 in3
H= 12 in
W = 5 in
2.
A.120 cm3
B. 96 cm3
C. 72 cm3
D. 48 cm3
3.
A.113.04 cm3
B. 96.12 cm3
C. 75.36 cm3
D. 37.68. cm3
.
4.
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A.1 004.80 cm3
B. 966.40 cm3
C. 502.40 cm3
D. 167.46 cm3
A. 38.57963 cm3
B. 40.57963 cm3
C. 42.57963 cm3
D. 44.57963 cm3
5.
J. Additional activities for application or remediation
Work on this additional activity.
Solve for the volume of the given figures.
d=
h=
KEY TO CORRECTION
Reviewing previous lesson or presenting the new lesson
DRILL
Can you name the solid figure that these real-objects resemble? Write your answer on the blank.
1. rectangular prism
2. Sphere
3. Cylinder
4. Cone
5. Triangular prism
Activity 1
Solve for the volume of the figures given below.
Solution:
V=lxwxh
= 10 cm x 2 cm x 3 cm
= 60 cm3
Activity 2
Solve for the volume of the figures given below.
Solution:
V = 𝜋r²h
= 3.14 x 102 x 20
= 3.14 x 100 x 20
= 6 280 cm3
Solution:
V=
1
3 x l x w x h
= 1 x 7 x 8 x 12
3
= 1 x 372
3
= 672
3
= 224 cm3
Solution
V = 1/3 𝜋r²h
= 1/3 x 3.14 x 72 x 18
= 1/3 x 3.14 x 49 x 18
= 1/3 x 2 769.48
= 923.16 dm3
Section J. Additional activities for application or remediation
Enrichment
1. V = 16 956 mm3
2. V = 523.33 m3
3. V = 103.62 cm3
Prepared by:
Reviewed and checked by:
Noted by:
ALMA M. LAXAMANA
Teacher III
EDNA T. SUAREZ
Master Teacher I
MARIA LUZ L. DACOCO
Principal
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