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Table of Contents
TEKS
Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Test-Taking Checklist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
TEKS Student Expectations Correlation Chart . . . . . . . . . . . . . . . . . . . 7
Chapter 1
Numbers, Operations, and Quantitative Reasoning . . . 11
Lesson 1
Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . 12
8.1A, 8.1E
Lesson 2
Comparing and Ordering Rational Numbers . . 17
8.1A, 8.1E
Lesson 3
Scientific Notation . . . . . . . . . . . . . . . . . . . . . . 22
8.1D
Lesson 4
Irrational Numbers . . . . . . . . . . . . . . . . . . . . . . 26
8.1C
Lesson 5
Proportional Relationships . . . . . . . . . . . . . . . . 30
8.1B, 8.2D, 8.3A, 8.3B
Lesson 6
Problem Solving with Rational Numbers . . . . . 36
8.2A, 8.2B
Lesson 7
Reasonable Solutions to Problems . . . . . . . . . 42
8.2C,8.14D
Lesson 8
Problem Solving with Reporting Category 1 . . 47
8.14A
Chapter 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 2
Patterns, Relationships, and Algebraic Reasoning . . . 55
Lesson 9
Proportional and Non-Proportional Linear
Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . 56
8.3A
Lesson 10 Applications of Percents. . . . . . . . . . . . . . . . . . 62
8.3B
Lesson 11 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.3B, 8.14D
Lesson 12 Representing Data in Different Forms . . . . . . . 74
8.4A
Lesson 13 Arithmetic Sequences . . . . . . . . . . . . . . . . . . . 80
8.5B
Lesson 14 Solving Problems using Tables, Graphs,
and Equations. . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.5A
Lesson 15 Problem Solving with Reporting Category 2 . . 91
8.14B, 8.14C
Chapter 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 3
Geometry and Spatial Reasoning. . . . . . . . . . . . . . . . . 101
Lesson 16 Viewing Solids . . . . . . . . . . . . . . . . . . . . . . . . 102
8.7A, 8.7B
Lesson 17 Ordered Pairs on the Coordinate Plane . . . . . 107
8.7D
Lesson 18 Dilations, Reflections, and Translations . . . . . 112
8.6B
Lesson 19 Pythagorean Theorem . . . . . . . . . . . . . . . . . . 118
8.7B, 8.7C, 8.9A
Lesson 20 Problem Solving with Reporting Category 3 . . 124
8.15A
Chapter 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Duplicating any part of this book is prohibited by law.
3
Chapter 4
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Lesson 21 Proportional Relationships in
Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . 136
8.6A, 8.9B
Lesson 22 Surface Area and Volume of Solids . . . . . . . . 141
8.8A, 8.8B, 8.8C
Lesson 23 Effects of Changing Dimensions . . . . . . . . . . 148
8.10A, 8.10B
Lesson 24 Problem Solving with Reporting Category 4 . 153
8.7B, 8.14C
Chapter 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Chapter 5
Probability and Statistics . . . . . . . . . . . . . . . . . . . . . . . 163
Lesson 25 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.11A, 8.11B
Lesson 26 Mean, Median, Mode, and Range . . . . . . . . . 171
8.12A
Lesson 27 Line Graphs and Scatterplots. . . . . . . . . . . . . 176
8.12B
Lesson 28 Bar Graphs and Histograms . . . . . . . . . . . . . . 184
8.12C
Lesson 29 Line Plots and Venn Diagrams . . . . . . . . . . . . 189
8.12C
Lesson 30 Circle Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.12C
Lesson 31 Box-and-Whisker Plots and
Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . 199
8.12A, 8.12C
Lesson 32 Misleading Representations . . . . . . . . . . . . . . 206
8.13B
Lesson 33 Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.13A
Lesson 34 Problem Solving with Reporting Category 5 . . 217
8.14C, 8.15A
Chapter 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Chapter 6
Underlying Processes and Mathematical Tools . . . . . 227
Lesson 35 Planning and Solving Everyday
Math Problems . . . . . . . . . . . . . . . . . . . . . . . . 228
8.2A, 8.14A, 8.14B,
8.14D
Lesson 36 Modeling a Problem . . . . . . . . . . . . . . . . . . . . 232
8.14B, 8.14C
Lesson 37 Using Mathematical Rules . . . . . . . . . . . . . . . 236
8.14A, 8.14D, 8.15A,
8.16B
Lesson 38 Sets of Examples and Nonexamples . . . . . . . 241
8.16A
Lesson 39 Validating Your Answer . . . . . . . . . . . . . . . . . . 246
8.2A, 8.14B, 8.16B
Chapter 6 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Mathematics Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
4
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1
Rational Numbers
TEKS: 8.1A, 8.1E
Getting the Idea
Whole numbers include all of the natural numbers (counting numbers) and 0. Integers
are natural numbers and their opposites and 0.
a
, where a and b are
Rational numbers are numbers that can be expressed in the form __
b
integers and b 0. Rational numbers include positive and negative fractions, mixed
numbers, improper fractions, terminating decimals, and repeating decimals.
To locate rational numbers on a number line, you may need to convert one form into
another form. To convert a fraction to a decimal, divide the numerator by the denominator.
To convert a decimal to a fraction, write the digits in the decimal as the numerator and
the value of the smallest decimal place as the denominator. Then write the fraction in
8
4.
__
simplest form. For example, 0.8 ___
5
10
EXAMPLE 1
Plot each point on a number line.
8
3
7
__
, __
, 1.25, __
4
1
2
STRATEGY
STEP 1
Write the numbers in an equivalent form.
8
Write __
as a whole number.
STEP 2
4
8
__
842
4
3
Write __
as an integer.
1
3
3
__
1
STEP 3
Write 1.25 as a mixed number with a fraction.
25
1.25 1___
STEP 4
12
100
1
1__
4
7
__
Write as a mixed number.
2
7
1
__
3__
2
2
Duplicating any part of this book is prohibited by law.
Lesson 1: Rational Numbers
STEP 5
Locate each number on the number line.
Positive numbers are located to the right of 0.
Negative numbers are located to the left of 0.
SOLUTION
–4
–3
–2
–1
0
1
2
3
4
EXAMPLE 2
Show that 3.75 is a rational number.
STRATEGY
Convert the decimal to an improper fraction.
Write 3.75 as a mixed number in simplest form.
STEP 1
75
3.75 3___
100
3
__
3
4
3
a
Write 3__
as an improper fraction or in the form __
.
STEP 2
b
4
3
15
__
3 ___
4
4
15
___
ⴚ3.75 ⴝ ⴚ 4
SOLUTION
EXAMPLE 3
5
Write ___
as a decimal.
11
STRATEGY
STEP 1
Divide the numerator by the denominator.
5
___
5 11
11
0.4545…
_______
11冄5.0000
44
60
55
50
44
60
55
5
STEP 2
Write 0.4545… as a repeating decimal.
___
0.4545… 0.45
SOLUTION
___
5
___
ⴝ 0. 45
11
Duplicating any part of this book is prohibited by law.
13
You can also use a calculator to convert a fraction to a decimal.
EXAMPLE 4
7 as a decimal.
Write ___
32
STRATEGY
Use a calculator.
Enter 7 32 into your calculator and press .
The screen shows that the answer is 0.21875.
SOLUTION
7
___
ⴝ 0.21875
32
COACHED EXAMPLE
Show that each of the following is a rational number.
28, ⴚ9, 0, ⴚ1.7, and 5_1
3
THINKING IT THROUGH
Write each number in the form _a .
b
Write the whole number as an improper fraction with a denominator of _____.
28 ⴝ _______
Use the integer as the numerator and write a denominator of _____.
ⴚ9 ⴝ _______
Write _____ in the numerator and write any nonzero whole number in the denominator.
0 ⴝ ________
Convert the decimal to a fraction. Write an __________________ fraction.
Write the negative sign in the _________________.
7 ⴝ ________
ⴚ1.7 ⴝ ⴚ1__
10
Write the mixed number as an __________________ fraction.
5_1 ⴝ ________
3
The numbers in the form _a are ___________________________________________.
b
14
Duplicating any part of this book is prohibited by law.
Lesson 1: Rational Numbers
Lesson Practice
Choose the correct answer.
1.
Which point on the number line best
represents _62 ?
Q
–8
A.
B.
C.
D.
2.
RS
–4
3.
A. 8.5
T
0
4
B. 1_23
8
point Q
point R
point S
point T
A pole is 3.8 meters long. Which shows
that 3.8 is a rational number?
Which number is an integer?
4.
C.
12
__
6
D.
4.1
Which point on the number line best
represents 1_23?
J
–3
8
A. 3__
10
B. 3_4
5
38
C. __
5
19
D. __
5
Duplicating any part of this book is prohibited by law.
A.
B.
C.
D.
K
–2
L M
–1
0
1
2
3
point J
point K
point L
point M
15
5.
Which shows 0.28 as a fraction in
simplest form?
1
_
4
_
B. 28
14
C. __
50
7
D. __
25
8.
9.
Which shows that 2.65 is a
rational number?
265
A. ___
20
213
B. ___
20
53
C. __
20
2
D. __
65
7.
4.56
_
4.56
__
4.83
_
4.83
Drew lives _3 mile from the park. What is _3
4
4
as a decimal?
0
0
0
0
0
0
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
9
3?
Which decimal is equivalent to __
64
A.
B.
C.
D.
16
6
A.
B.
C.
D.
A.
6.
Which decimal is equivalent to 4_5 ?
0.046875
0.058675
0.06875
0.088925
Duplicating any part of this book is prohibited by law.