Table of Contents
IL Learning
Standards
Assessment
Objectives
Using Place Value to Read and
Write Whole Numbers . . . . . . . . . 12
6A
6.4.01, 6.4.02
Lesson 2
Characteristics of Numbers . . . . . 17
6A
6.4.09
Lesson 3
Compare and Order
Whole Numbers . . . . . . . . . . . . . . 21
6A
6.4.05, 6.4.09
Adding and Subtracting
Whole Numbers . . . . . . . . . . . . . . 25
6B, 6C, 9B
6.4.10, 9.4.13
Multiplication as Repeated
Addition . . . . . . . . . . . . . . . . . . . . 31
6A
6.4.04
Multiplication and Division
Facts. . . . . . . . . . . . . . . . . . . . . . . 34
6B, 6C
6.4.12, 6.4.15
Lesson 7
Multiplying Whole Numbers. . . . . 39
6B, 6C
6.4.10
Lesson 8
Properties of Addition and
Multiplication . . . . . . . . . . . . . . . . 43
6B, 6C
6.4.14
Equivalent Fractions. . . . . . . . . . . 48
6A
6.4.03
Lesson 10 Compare and Order Fractions . . . 53
6A
6.4.07, 6.4.08
Lesson 11 Add and Subtract Fractions
with Like Denominators . . . . . . . . 58
6B, 6C
6.4.13
Lesson 12 Compare and Order Decimals . . . 62
6A
6.4.06
Lesson 13 Money and Making Change. . . . . 66
6B, 6C
6.4.11
Lesson 14 Using Estimation to Solve
Problems . . . . . . . . . . . . . . . . . . . 71
6B, 6C
6.4.16
Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Test-Taking Checklist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Illinois Assessment Objectives Correlation Chart . . . . . . 8
Chapter 1
Number Sense . . . . . . . . . . . . . . . . . . . . . . . . 11
Lesson 1
Lesson 4
Lesson 5
Lesson 6
Lesson 9
Chapter 1 Review . . . . . . . . . . . . . . . . . . . . 76
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Chapter 2
Measurement . . . . . . . . . . . . . . . . . . . . . . . . 83
Lesson 15 Length . . . . . . . . . . . . . . . . . . . . . 84
7A, 7B, 7C
7.4.02, 7.4.04,
7.4.06
Lesson 16 Perimeter and Area . . . . . . . . . . . 89
7A, 7B, 7C
7.4.03
Lesson 17 Weight and Mass . . . . . . . . . . . . . 95
7A. 7B, 7C
7.4.04, 7.4.06
Lesson 18 Introduction to Volume. . . . . . . . . 99
7A, 7B, 7C
7.4.04, 7.4.05
Lesson 19 Temperature . . . . . . . . . . . . . . . . 104
7A, 7B, 7C
7.4.02
Lesson 20 Elapsed Time . . . . . . . . . . . . . . 109
7A, 7B, 7C
7.4.01, 7.4.02,
7.4.06
Chapter 2 Review . . . . . . . . . . . . . . . . . . 114
Chapter 3
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Lesson 21 Patterns . . . . . . . . . . . . . . . . . . . 122
8A
8.4.01
Lesson 22 Patterns in Tables and
Graphs . . . . . . . . . . . . . . . . . . . . 127
8B
8.4.04
Lesson 23 Completing Number
Sentences . . . . . . . . . . . . . . . . . 132
8C, 8D
8.4.07
Lesson 24 Writing Expressions . . . . . . . . . 136
8A
8.4.02
Lesson 25 Evaluating Expressions . . . . . . . 140
8A
8.4.03
Lesson 26 Solving Word Problems
with Number Sentences. . . . . . . 144
8C, 8D
8.4.06, 8.4.08
Lesson 27 Representations of Numbers . . . 149
8B
8.4.05
Lesson 28 Parallel and Perpendicular
Lines. . . . . . . . . . . . . . . . . . . . . . 160
9A
9.4.07, 9.4.08
Lesson 29 Two-Dimensional Figures . . . . . . 166
9A
9.4.01, 9.4.03
Lesson 30 Transformations . . . . . . . . . . . . . 172
9A
9.4.06
Lesson 31 Symmetry, Congruence,
and Similarity . . . . . . . . . . . . . . . 176
9A, 9B
9.4.05, 9.4.12
Lesson 32 Combining and Dividing
Figures . . . . . . . . . . . . . . . . . . . . 181
9B
9.4.11
Chapter 3 Review . . . . . . . . . . . . . . . . . . . 153
Chapter 4
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Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
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Table of Contents
Lesson 33 Three-Dimensional Figures . . . . 186
9A, 9B
9.4.02, 9.4.09,
9.4.10
Lesson 34 Ordered Pairs on a Grid . . . . . . 192
9A
9.4.04
10A, 10B
10.4.01,
Chapter 4 Review . . . . . . . . . . . . . . . . . . . 196
Chapter 5
Data Analysis, Statistics, and
Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Lesson 35 Tally Charts and Tables . . . . . . . 204
10.4.02
Lesson 36 Bar Graphs and Line Graphs . . 209
10A, 10B
10.4.01,
10.4.02
Lesson 37 Line Plots and Pictographs . . . . 215
10A, 10B
10.4.01,
10.4.02
Lesson 38 Circle Graphs and
Venn Diagrams . . . . . . . . . . . . . . 221
10A, 10B
10.4.01
Lesson 39 Range and Mode . . . . . . . . . . . . 226
10A, 10B
10.4.03
Lesson 40 Probability . . . . . . . . . . . . . . . . . 230
10C
10.4.04,
10.4.05
Chapter 5 Review . . . . . . . . . . . . . . . . . . . 236
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
ISAT Ruler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
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33 Three-Dimensional Figures
Standards: 9A, 9B
Objectives: 9.4.02, 9.4.09, 9.4.10
Getting the Idea
Three-dimensional figures are figures that have length, width, and height.
They are also called solid figures.
Three-dimensional figures can be classified by the number of faces, edges,
and vertices they have. A face is the flat side of a three-dimensional figure.
An edge is where two faces meet. A vertex is the common point where three
or more edges meet.
face
vertex
edge
These three-dimensional figures have only flat faces.
cube
6 square
faces
12 edges
8 vertices
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rectangular
prism
6 faces
12 edges
8 vertices
triangular
prism
5 faces
9 edges
6 vertices
rectangular
pyramid
5 faces
8 edges
5 vertices
triangular
pyramid
4 faces
6 edges
4 vertices
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Lesson 33: Three-Dimensional Figures
These three-dimensional figures have curved surfaces.
cylinder
1 curved surface
2 faces
0 edges
0 vertices
cone
1 curved surface
1 face
0 edges
1 vertex
sphere
1 curved surface
0 faces
0 edges
0 vertices
EXAMPLE 1
How would you classify this figure?
STRATEGY
STEP 1
Find how many faces, edges, and vertices the figure has.
Find how many faces.
The figure has no faces.
STEP 2
Find how many edges.
The figure has no edges.
STEP 3
Find how many vertices.
The figure has no vertices.
The only figure that has no faces, edges, and vertices is a sphere.
SOLUTION
The figure is a sphere.
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EXAMPLE 2
Which polygons form the faces of a rectangular pyramid?
STRATEGY
STEP 1
Look at the figure and identify the faces.
Count the number of faces.
A face is the flat side of a three-dimensional figure. There are
5 faces.
STEP 2
Identify the faces.
4 of the faces are triangles.
1 face is a rectangle.
SOLUTION
The faces of a rectangular pyramid are 4 triangles and 1 rectangle.
A net can be used to make three-dimensional figures from two-dimensional figures.
EXAMPLE 3
Which three-dimensional figure can be made from this net?
STRATEGY
Identify the shapes in the net and match it to a three-dimensional
figure.
The figure has 4 triangles and no other shapes.
The correct three-dimensional figure will have 4 faces that are triangles.
A figure with 4 triangular faces and no others is a triangular pyramid.
SOLUTION
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A triangular pyramid can be made from this net.
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Lesson 33: Three-Dimensional Figures
COACHED EXAMPLE
Which three-dimensional figure could be formed if this net were folded along the
dashed lines?
THINKING IT THROUGH
The net shows __________ faces.
A _______________ and a ______________ _____________ each have this
number of faces.
The shapes of the faces are _________________ and _________________.
Since the solid has 2 different polygons for faces, the figure is not a
________________.
When the net is folded, it forms a ___________________________________.
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Lesson Practice
Choose the correct answer.
1. Which of the following
three-dimensional figures has
4 faces?
3. Which set of characteristics describes
the figure below?
A.
A. 5 faces, 8 edges, 5 vertices
B. 5 faces, 9 edges, 6 vertices
B.
C. 6 faces, 12 edges, 6 vertices
D. 6 faces, 12 edges, 8 vertices
C.
4. Which three-dimensional figure can
be made from this net?
D.
A. cube
2. Which three-dimensional figure is
made of triangles and rectangles?
A. rectangular prism
B. cube
B. sphere
C. cylinder
D. cone
C. triangular pyramid
D. triangular prism
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Lesson 33: Three-Dimensional Figures
5. A tent has 5 faces, 8 edges, and
5 vertices. What figure does the tent
look like?
6. Which three-dimensional figure can
have only one type of polygon for a
face?
A. triangular pyramid
A.
B. sphere
C. rectangular pyramid
D. triangular prism
B.
C.
D.
SHORT-RESPONSE QUESTIONS
7. What is the name of this three-dimensional
figure?
8. How many faces, edges, and vertices does this
figure have?
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