Download Developed in Consultation with Virginia Educators

Developed in Consultation
with Virginia Educators
Table of Contents
Virginia Standards of Learning
Correlation Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Virginia Standards of Learning
Chapter 1 Number and Number Sense
Lesson 1
Use the Order of Operations to
Simplify Numerical Expressions . . . . . . . . 10
Lesson 2
8.1a
Use Properties of Operations to
Simplify Numerical Expressions . . . . . . . . 14
8.1a
Lesson 3
Scientific Notation . . . . . . . . . . . . . . . . . . . 19
8.1b
Lesson 4
Compare and Order Numbers. . . . . . . . . . 24
8.1b
Lesson 5
Real Numbers . . . . . . . . . . . . . . . . . . . . . . 28
8.2
Chapter 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 2 Computation and Estimation
Lesson 6
Solve Real-World Problems. . . . . . . . . . . . 38
8.3a, 8.3b
Lesson 7
Evaluate Algebraic Expressions . . . . . . . . 45
8.4
Lesson 8
Perfect Squares and
Square Roots. . . . . . . . . . . . . . . . . . . . . . . 50
8.5a, 8.5b
Chapter 3 Measurement
Lesson 9
Vertical, Supplementary, and
Complementary Angles . . . . . . . . . . . . . . . 60
8.6a, 8.6b
Lesson 10
Solve Volume Problems. . . . . . . . . . . . . . . 67
8.7a
Lesson 11
Solve Surface Area Problems . . . . . . . . . . 74
8.7a
Lesson 12
Effects of Changing Dimensions . . . . . . . . 81
8.7b
Chapter 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Chapter 4 Geometry
Lesson 13 Transformations . . . . . . . . . . . . . . . . . . . . . 94
8.8a, 8.8b
Lesson 14
Construct a Three-Dimensional Model . . 102
8.9
Lesson 15
The Pythagorean Theorem . . . . . . . . . . . 108
8.10a, 8.10b
Lesson 16
Area and Perimeter of
Composite Figures . . . . . . . . . . . . . . . . . 113
8.11
Chapter 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4
Duplicating any part of this book is prohibited by law.
Chapter 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Virginia Standards of Learning
Chapter 5 Probability and Statistics
Lesson 17 Probability . . . . . . . . . . . . . . . . . . . . . . . . 126
Lesson 18
8.12
Picture Graphs, Bar Graphs, and
Line Graphs . . . . . . . . . . . . . . . . . . . . . . . 133
8.13a
Frequency Distributions and
Histograms. . . . . . . . . . . . . . . . . . . . . . . . 140
8.13a
Lesson 20
Circle Graphs . . . . . . . . . . . . . . . . . . . . . . 147
8.13a
Lesson 21
Scatterplots . . . . . . . . . . . . . . . . . . . . . . . 154
8.13b
Lesson 19
Chapter 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Chapter 6 Patterns, Functions, and Algebra
Lesson 22 Represent Relations. . . . . . . . . . . . . . . . . 166
8.14
Lesson 23
Represent Functions . . . . . . . . . . . . . . . . 172
8.14, 8.17
Lesson 24
Solve Linear Equations . . . . . . . . . . . . . . 178
8.15a, 8.15c
Lesson 25
Solve Linear Inequalities . . . . . . . . . . . . . 185
8.15b
Lesson 26
Graph Linear Equations . . . . . . . . . . . . . . 191
8.16, 8.17
Chapter 6 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Duplicating any part of this book is prohibited by law.
Grade 8 Mathematics Formula Sheet . . . . . . . . . . . . 253
5
Chapter 1 t -FTTPO
Standards of Learning: 8.1a
Use the Order of Operations to
Simplify Numerical Expressions
Getting the Idea
You can simplify a numerical expression that contains more than one operation by using
the order of operations. The order of operations tells you the order in which to perform the
operations in an expression.
Order of Operations
1. Perform operations within grouping symbols, such as parentheses,
brackets, or braces.
2. Perform calculations involving exponents or square roots.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
Example 1
1.
Simplify the expression 8 2 __
8
Strategy
Step 1
Follow the order of operations.
There are no grouping symbols or exponents.
Perform multiplication and division from left to right.
Multiply.
1
8 2 __
Step 2
Perform addition and subtraction from left to right.
Subtract.
1
8 __
Solution
10
4
3
__
7
4
3
1 ⴝ 7__
8 ⴚ 2 ⴛ __
4
8
Duplicating any part of this book is prohibited by law.
8
2
8 __
8
__
81
4
Example 2
Simplify: [(5 2) 10] 4
2
Strategy
Step 1
Follow the order of operations.
There are two grouping symbols: parentheses and brackets.
First, apply the order of operations inside the parentheses.
Clear the exponent. Then divide.
2
[(5 2) 10] 4
[(25 2) 10] 4
[12.5 10] 4
Step 2
Perform the operation within the brackets.
Subtract.
[12.5 10] 4
2.5 4
Step 3
Multiply and divide from left to right.
Multiply.
2.5 4 10
Solution
[(52 ⴜ 2) ⴚ 10] ⴛ 4 ⴝ 10
In addition to parentheses, brackets, and braces, the absolute value symbol, fraction bar,
and square root sign are also treated as grouping symbols.
Duplicating any part of this book is prohibited by law.
11
Example 3
8
______
Simplify: 22
6 10
5
Strategy
Step 1
Follow the order of operations.
Remember that the fraction bar is a grouping symbol.
Simplify the numerator of the fraction.
22
8
______
6 10
5
30
___
6 10
5
Step 2
Multiply and divide from left to right.
30
___
6 10
5
6 6 10
6 60
Step 3
Add and subtract from left to right.
Add.
6 60 66
Solution
22
ⴙ8
______
ⴙ 6 ⴛ 10 ⴝ 66
5
Coached Example
Simplify the expression 72 ⴚ 3(25 ⴚ 6).
Follow the order of operations.
2
Evaluate. 7 3(25 6) ___________
What is the second step?
Evaluate. ___________
What is the third step?
Evaluate. ___________
What is the fourth step?
Evaluate. ___________
2
7 ⴚ 3(25 ⴚ 6) ⴝ ___________
t $IBQUFSNumber and Number Sense
Duplicating any part of this book is prohibited by law.
What is the first step?
Lesson 1: Use the Order of Operations to Simplify Numerical Expressions
Lesson Practice
Choose the correct answer.
1.
5.
Simplify the following expression.
92 (12 8)
__________
30
10
2
12_12 2 21
A. 14
B.
29
2.
C. 128
D. 604
Simplify the following expression.
6.
45 23
______
3(5 8)
10
A. 17.2
B. 3.7
3.
7.
C. 10.5
D. 15
D. 40_1
5
Simplify the following expression.
C. 49
D. 62
Simplify the following expression.
A. 135
B. 71
8.
6217
Duplicating any part of this book is prohibited by law.
9.
7
B. 37__
10
42 11 5
Simplify the following expression.
C.
39
D. 25
Simplify the following expression.
(29 14) 3
2
A. 1_17
C. 6_27
4_37
D. 8_17
B.
C. 39
A. 11
B. 37
9 12 _12
4.
1
A. 36__
10
24 (12 31) 18 (3)
C. 5.7
D. 36.8
Simplify the following expression.
A. 3
B. 1.5
Simplify the following expression.
A. 75
C.
B. 16_23
D. 55_23
15
Fran is simplifying the following expression: _1 52 (7 4 2).
5
A. According to the order of operations, what operation should be performed first to
simplify the expression?
B. Simplify the expression. Show your work.
Answer:
13