West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
Learning Standards
Major Concepts
Week 1
Jan 8 - 11
(6) Geometry and spatial reasoning. The
student uses geometric vocabulary to describe
angles, polygons, and circles. The student is
expected to:
(A) use angle measurements to classify angles
as acute, obtuse, or right;
(B) identify relationships involving angles in
triangles and quadrilaterals; and
(C) describe the relationship between radius,
diameter, and circumference of a circle.
Points
Lines
Angles
Instruction
Key Vocabulary: point, lines, ray, segment, ray, plane,
intersecting lines, parallel lines, skew lines, angle, vertex,
degrees, acute angle, right angle, obtuse angle, straight angle,
perpendicular lines, complementary angles, supplementary
angles, vertical angles, congruent angles, transversal
Math background for teachers:

Geometry is the study of shapes in space and spatial
relationships.

Geometry connects to the students’ world around them.

Although there is a hierarchy of instruction that
progresses through 5 levels of instruction known as the
van Hiele Levels (0 – 4). Levels 3 and 4 are typically
taught at the high school level.

Level 0 – Visualization – classes of shapes

Level 1 – Analysis – Properties of shapes

Level 2 – Informal Deduction - relationships
among properties

Level 3 – Deduction – deductive systems of
properties

Level 4 – Rigor – analysis of deductive
systems

Students should recognize the difference between 1, 2,
Resources
Prentice Hall Course 1 Textbook
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical processes to acquire and
demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Students will work in small group with the
teacher to identify lines and angles
Assessments
Products/Projects
Teacher observation
Chapter 8 – Tools of Geometry
Lesson 1 – Points, Lines, Segments, and
Rays
Lesson 2 –Angles
Lesson 3 Special Pairs of Angles
Protractors
6.11, 6.12. 6.13 are taught every day in all concepts
Students will use coffee stirrers and
toothpicks to make shapes with various
angles. Another option is to use miniature
marshmallows and toothpicks to form angles.
Straws can be used to form and name lines
such as parallel, intersecting, and
perpendicular.
Product/Project
Students will make a
map and label lines and
angles.
Struggling students may find it helpful to
make a foldable describing the types of lines
and angles.
GT: Students will design a robot using
pattern blocks. Students will name points,
lines, and angles.
Page 1
West-Orange Cove ISD






6th Grade Mathematics – 4th Six Weeks
2012 - 2013
and 3 dimensional shapes.
One dimensional shapes are lines – they only have
length
Two dimensional shapes have length and width (they are
flat)
Three dimensional shapes have length, width, and depth
(they are solids)
Some shapes can be combined to make new shapes.
Shapes can be decomposed into other shapes.
Angles size is determined by the spread of the rays
In this lesson stress vocabulary and be sure students are aware of
the symbol for an angle and how angles are named. Provide
many opportunities for students to name angles as well as
measure angles.
Pairs of angles whose sum measures 90˚ are complementary
angles. If the sum of the angles measures 180˚ they are
supplementary angles.
Vertical angles are formed by two intersecting lines.
Congruent angles are angles with equal measures.
Transversal angles crosses two or more lines at different points
while exterior angles are on either side of a transversal outside
of a pair of lines.
Activity: Classroom scavenger hunt to find and name angles
and pairs of angles.
Activity: Students will practice using a protractor to measure
angles both on paper and around the room. Follow the methods
on P. 369 stop students understand that there is more than one
way to measure using a protractor.
Activity: Pattern blocks should be used throughout the
geometry lessons to help students connect the abstract concepts
by first learning then concretely.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 2
6th Grade Mathematics – 4th Six Weeks
West-Orange Cove ISD

2012 - 2013
Measure angles.
o Use a protractor to measure angles from a variety
of orientations (left to right and right to left).
o Use a given picture of a protractor with one or
more given angles to identify the measure of an
angle.
Example: Find the measure of angle BXC. (85º)
B
C
D
A
o
Use a given picture of a protractor with angles as
part of a more complex figure to identify the
measure of an angle.
Example: What is the measure of angle X? (46º)

Classify angles as acute, obtuse, or right.
o Use given or measured angle measurements.
Example: Classify an angle with a measure of 99º
6.11, 6.12. 6.13 are taught every day in all concepts
Page 3
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
as acute, obtuse, or right. (Obtuse)
Example: Measure and classify the given angle.
o
Use pictures of angles.
Example: Classify Angle A as acute, obtuse, or
right. (acute)
A
o
Use pictures of angles as part of a more complex
figure (such as combined angles or as part of a
polygon).
Example: Classify Angle A. (obtuse)
A



Include selected response items.
o
Include NOT questions.
Justify selections.
Make conjectures or sort angles using patterns or sets
of examples and non-examples.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 4
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
Learning Standards
Week 2 attributes of angles in triangles.
Explore
(6) Geometry and spatial
Triangles
reasoning. The student uses
geometric vocabulary to
Polygons
 Discuss the sum
of theangles,
anglespolygons,
of a triangle
180º.
describe
and total
 Classify triangles
according
to
side
lengths
(scalene,
circles. The student is expected
isosceles, equilateral).
to:
o Include notation
show
relationships
(A) usetoangle
measurements
tosuch as
right angles
and congruent
angles.
classify
angles as acute,
obtuse,
o Analyze sets
of examples and non-examples.
or right;
 Classify triangles
to angle measures (acute,
(B) according
identify relationships
obtuse, right, equiangular).
involving angles in triangles
o Include notation
to show relationships
such as
and quadrilaterals;
and
congruent (C)
sides.
describe the relationship
o Analyze sets
of examples
and non-examples.
between
radius, diameter,
and
 Find the missing
angle
of
a
triangle
given various
circumference of a circle.
properties.
Instructional
Resources
 Include real-world contexts.
 Include selected response items.
Vocabulary
triangle, acute triangle, obtuse
Prentice Hall Course 1 Textbook:
Key Include
NOT–statements.
triangle, right triangle, congruent segments
equilateral triangle, isosceles triangle, scalene
triangle,selections.
polygon, regular polygon, irregular
Chapter 8- Tools of Geometry
Justify
polygon, quadrilateral, parallelogram, trapezoid,
rectangle, rhombus, square
Lesson 8-4 Classifying Triangles
Explore attributes of angles in quadrilaterals. Lesson 8-5 Exploring and Classifying Polygons
Math background for the teacher:
•
Geometry is the study of shapes in
space and spatial relationships.
•
 Discuss
the Geometry
sum of theconnects
angles to
ofthe
a quadrilateral total
360º.students’ world around them.
Although
there
a hierarchy of
 Find• the missing
angle
of aisquadrilateral.
instruction
that progresses
 Include
real-world
contexts. through 5 levels
of instruction
as the
van Hiele
 Include
selected known
response
items.
Levels
(0
–
4).
Levels
3
and
4 are
 Include NOT statements.
typically taught at the high school level.
•
Level 0 – Visualization – classes
of
shapes
Justify selections
6.11, 6.12. 6.13 are taught every day in all concepts
Processes:
Major Concepts
Jan 14 - 18
2012 - 2013
Mathematical Process Standards. The student uses mathematical processes to acquire and
demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Assessment
Students will work in small groups with the
teacher to:
 classify triangles by their angles,
 classify and sort quadrilaterals
Formal assessment of
triangles and polygons
GT: Polygon prefix scavenger hunt:
students will find examples of polygons
with prefixes:
Product/Project
Students will make a
city skyline using
straws, toothpicks, and
marshmallows and label
each angle, and shape
Triangle, quadrilateral, pentagon
hexagon, heptagon, octagon, nonagon,
decagon, dodecagon
Page 5
West-Orange Cove ISD
•
the rays
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
•
Level 1 – Analysis – Properties of
shapes
•
Level 2 – Informal Deduction relationships among properties
•
Level 3 – Deduction – deductive
systems of properties
•
Level 4 – Rigor – analysis of
deductive systems
•
Students should recognize the
difference between 1, 2, and 3 dimensional
shapes.
•
One dimensional shapes are lines
– they only have length
•
Two dimensional shapes have
length and width (they are flat)
•
Three dimensional shapes have
length, width, and depth (they are solids)
•
Some shapes can be combined to
make new shapes.
•
Shapes can be decomposed into
other shapes.
Angles size is determined by the spread of
For this lesson, students must understand that the
sum of the angles of a triangle measures
180degrees. Triangles may be classified by
angles: acute triangle, obtuse triangle
equilateral triangle has three congruent sides;
an isosceles triangle has at least two congruent
sides, and a scalene triangle has no congruent
sides.
Polygons are closed figures and are named by
the number of sides they have. They can be
considered regular polygons or irregular
polygons.
Quadrilaterals are four-sided polygons
6.11, 6.12. 6.13 are taught every day in all concepts
Page 6
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
classified by parallel sides.
Activity: Create a VD that shows the
relationship of the five special quadrilaterals
(parallelogram, trapezoid, rectangle, rhombus,
and square.)
Activity: Describe how a figure that is not a
polygon is different from one that is a polygon.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 7
West-Orange Cove ISD
Week 3
6th Grade Mathematics – 4th Six Weeks
Learning Standards
Major Concepts
Jan 22 - 25
(6) Geometry and spatial reasoning. The student uses
geometric vocabulary to describe angles, polygons, and
circles. The student is expected to:
(A) use angle measurements to classify angles as acute,
obtuse, or right;
(B) identify relationships involving angles in triangles and
quadrilaterals; and
(C) describe the relationship between radius, diameter, and
circumference of a circle.
Congruent and Similar Figures
Line Symmetry
Transformations
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical processes to
acquire and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the
workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number
sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and language as
appropriate;
(E) create and use representations to organize, record, and communicate
mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical
ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Instruction
Resources
Interventions
Extensions
Assessment
Key Vocabulary: Congruent figures, similar figures, line symmetry,
line of symmetry, transformation, image, translation, reflection, line of
reflection, rotation, center of rotation, tessellation
Prentice Hall Course 1 Textbook
Formal - Geometry
Math background for the teacher:
Chapter 8 – Geometry Tools
Students will work with the teacher to
trace pattern blocks with irregular
shaped figures. Students should trace
rotated figures as well as a flipped
figure.
•
Geometry is the study of shapes in space and spatial relationships.
•
Geometry connects to the students’ world around them.
•
Although there is a hierarchy of instruction that progresses through 5
levels of instruction known as the van Hiele Levels (0 – 4). Levels 3 and 4
are typically taught at the high school level.
•
Level 0 – Visualization – classes of shapes
•
Level 1 – Analysis – Properties of shapes
•
Level 2 – Informal Deduction - relationships among properties
•
Level 3 – Deduction – deductive systems of properties
•
Level 4 – Rigor – analysis of deductive systems
•
Students should recognize the difference between 1, 2, and 3
dimensional shapes.
•
One dimensional shapes are lines – they only have length
•
Two dimensional shapes have length and width (they are flat)
6.11, 6.12. 6.13 are taught every day in all concepts
Lesson 8-6 Congruent and Similar
Figures
Lesson 8-7 Line Symmetry
Lesson 8-8 Transformations
Products/Project
Tessellations
GT: Students will take a picture from
a magazine and glue it onto poster
board. Next students will make a
template to create a puzzle out of the
picture using as many geometric
shapes as possible. Students will cut
out their puzzle and challenge their
classmates to put them together and
name all the geometric figures and
angles that were used.
Page 8
West-Orange Cove ISD
•
solids)
•
•
•
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
Three dimensional shapes have length, width, and depth (they are
Some shapes can be combined to make new shapes.
Shapes can be decomposed into other shapes.
Angles size is determined by the spread of the rays
Congruent figures have the same size and shape.
Similar figures have the same shape but not necessarily the same size.
Corresponding angles are congruent but corresponding sides are proportional.
Activity: Students will design and cut out figures that have 2, 4, 6, and 8 lines
of symmetry.
Activity: Students will practice translations using pattern blocks.
Activity: Students will design a quilt using a tessellation.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 9
West-Orange Cove ISD
Week 4 – 6
6th Grade Mathematics – 4th Six Weeks
Learning Standards:
Jan 28 – Feb 15
(8) Measurement. The student solves application problems
involving estimation and measurement of length, area, time,
temperature, volume, weight, and angles. The student is
expected to:
(A) estimate measurements (including circumference) and
evaluate reasonableness of results;
(B) select and use appropriate units, tools, or formulas to
measure and to solve problems involving length (including
perimeter), area, time, temperature, volume, and weight;
(C) measure angles; and
(D) convert measures within the same measurement system
(customary and metric) based on relationships between units.
Instruction
Key Vocabulary: metric system, meter, mass, gram, capacity, liter,
converting, perimeter, area, base of a parallelogram, height of a
parallelogram, base of a triangle, height of a triangle, circle, circumference,
radius, diameter, three dimensional figure, prism, cube, pyramid, cylinder,
cone, sphere, net, surface area, volume, cubic unit
Math background for teachers:


When students develop formulas, they gain conceptual understanding
of ideas and relationships involved.
Remind students of the arrays in multiplication for finding the area.
The metric system uses meter for measuring length, gram for measuring
mass, and liter for measuring capacity.
The metric system is a decimal system. All measurements are based on
powers of 10. You can convert one unit with a measurement type by
multiplying or dividing by a power of 10. To convert to smaller units,
multiply. To convert to larger units you divide.
6.11, 6.12. 6.13 are taught every day in all concepts
Major Concepts
Measurement
Converting measurements
Perimeter
Area
Circumference
Surface area of prisms
Resources
Prentice Hall Course 1
Textbook
Chapter 9 – Geometry
and Measurement
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Students will work with the teacher to
convert measurements within the same
system (metric or customary).
Assessment
Formal assessment
Students will work with the teacher using
formulas to find the area of complex
figures and circles.
Measurement stations should be set up
around the room where students can
explore different kinds of measurements.
GT: Students will collect several cans of
different sizes. Students will find the ratio
for each circle to the nearest tenth.
Students will then compare the weight in
the can with the ratio. Students will create
a graphic illustration and explain their
findings.
Product/Project:
Students will identify
geometric shapes in the
classroom and find the
surface area.
Concept Map
Page 10
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
In 6th grade students begin to use formulas in problem solving. Be sure to
provide and refer to the STAAR Chart daily as students work.
Also new to 6th grade students is to convert measurement units. Again,
have students to refer to the STAAR Chart.
Activity: Students find the area of irregular figures by deconstructing the
figure into familiar figures and find the area of each then add the areas
together.
Activity: Students will make a foldable showing when to use
measurements for distance, weight, and volume in both metric and
customary units.
Activity: Students will bring in artifacts and practice measuring the area
of several parallelograms and the area of triangles.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 11
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
Learning Standards:
Major Concepts
(9) Probability and statistics. The student uses experimental
and theoretical probability to make predictions. The student is
expected to:
(A) construct sample spaces using lists and tree diagrams; and
(B) find the probabilities of a simple event and its
complement and describe the relationship between the two.
(10) Probability and statistics. The student uses statistical
representations to analyze data. The student is expected to:
(A) select and use an appropriate representation for presenting
and displaying different graphical representations of the same
data including line plot, line graph, bar graph, and stem and
leaf plot;
(B) identify mean (using concrete objects and pictorial
models), median, mode, and range of a set of data;
(C) sketch circle graphs to display data; and
(D) solve problems by collecting, organizing, displaying, and
interpreting data.
Instruction
Probability and Statistics
Week 7 & 8
Feb 18 – Mar 1
Key Vocabulary: complement of an event, compound event, counting
principle, dependent event, equally likely outcomes, event, experimental
probability, independent events, outcome, permutation, population,
probability of an event, sample, sample space, simulation, tree diagram
Resources
Prentice Hall Course 1
Textbook
Chapter 10 – Exploring
Probability
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Formal assessment
Students will work in small groups with
the teacher using manipulatives to list all
the possible outcomes – roll a number
cube and then toss a coin.
Math background for teachers:
The occurrence of an event can be characterized as impossible to certain.
Product/Project:
Using a taco menu,
students will make a tree
diagram to list all the
possible types of taco
toppings.
Probability is about predictions over time rather than individual events.
Two events are either independent or dependent. They are considered
independent if one event does not influence the occurrence of the other
event.
You can use the counting principle to find the number of ways to make one
choice followed by a second choice. (The counting principle states that if
6.11, 6.12. 6.13 are taught every day in all concepts
Assessment
GT: Students will write an algebraic
formula to represent the counting principle
for a three-stage probability experiment.
(M x N x O = total outcomes)
Page 12
West-Orange Cove ISD
6th Grade Mathematics – 4th Six Weeks
2012 - 2013
there are ‘m’ ways of making one choice and ‘n’ ways of making a second
choice then there are m x n ways to make the first choice followed by the
second choice.
A tree diagram can be used to find the probability of two or more events.
Probability is expressed as a number from 0 to 1 that estimates how often
an event will occur.
Probability may be written as fractions, decimals, or percent.
Experimental probability is based on the results of an actual experiment.
Theoretical probability is based on the assumption that certain outcomes
are equally likely.
Probability can help you make predictions about what may happen but can
not guarantee you the results.
Activity: Present students with several different spinners. Students will
list all the possible outcomes if they were to spin the spinner 3 times.
Activity: Provide students with a cup. Ask them to predict all the possible
ways it could land if they tossed it in the air and let it land on the floor. Of
the possibilities, which one to they think is most and least likely? Why?
Next let them toss the cup 20 times and record how it lands. Students
should agree on how to toss it so the results are not biased. Students will
compare their results with their classmates. Pool the data and compute the
three ratios (upside down, right side up, and on the side).
6.11, 6.12. 6.13 are taught every day in all concepts
Page 13