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Transcript
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 Duplicating any part of this book is prohibited by law. 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.