Common Core Coach Mathematics 8 First Edition
Contents Domain 1 The Number System...4 Lesson 1 Understanding Rational and Irrational Numbers...6 Lesson 2 Estimating the Value of Irrational Expressions... 12 Common Core State Standards 8.NS.1 8.NS.2 Domain 1 Review... 16 Domain 2 Expressions and Equations...20 Lesson Applying Properties of Exponents...22 Lesson 4 Understanding Square and Cube Roots...26 Lesson 5 Scientific Notation...0 Lesson 6 Using Scientific Notation...4 8.EE.1 8.EE.2 8.EE. 8.EE.4 Lesson 7 Lesson 8 Representing and Interpreting Proportional Relationships...40 Relating Slope and y-intercept to Linear Equations...46 8.EE.5 8.EE.6 Lesson 9 Solving Linear Equations in One Variable....52 8.EE.7.a, 8.EE.7.b Lesson 10 Lesson 11 Solving Systems of Two Linear Equations Graphically...56 Solving Systems of Two Linear Equations Algebraically...62 8.EE.8.a 8.EE.8.b Lesson 12 Problem Solving: Using Systems of Equations...... 68 8.EE.8.c Domain 2 Review...72 Domain Functions...76 Lesson 1 Introducing Functions....78 8.F.1 Lesson 14 Comparing Functions Represented in Different Ways...82 Lesson 15 Linear and Nonlinear Functions....86 Lesson 16 Using Functions to Model Relationships....90 Lesson 17 Describing Functional Relationships from Graphs....94 Domain Review...98 8.F.2 8.F. 8.F.4 8.F.5 2 Problem Solving Performance Task
Common Core State Standards Domain 4 Geometry...102 Lesson 18 Lesson 19 Properties of Rotations, Reflections, and Translations...104 Understanding Congruence of Two-Dimensional Figures (Using Rigid Motions).... 110 8.G.1.a, 8.G.1.b, 8.G.1.c 8.G.2 Lesson 20 Rigid Motion on the Coordinate Plane.... 114 Lesson 21 Dilations on the Coordinate Plane....120 8.G. 8.G. Lesson 22 Understanding Similarity of Two-Dimensional Figures (Using Transformations)....124 8.G.4 Lesson 2 Extending Understanding of Angle Relationships....128 Lesson 24 Angles in Triangles...12 Lesson 25 Explaining the Pythagorean Theorem....16 8.G.5 8.G.5 8.G.6 Lesson 26 Lesson 27 Applying the Pythagorean Theorem in Two and Three Dimensions...142 Applying the Pythagorean Theorem on the Coordinate Plane...146 8.G.7 8.G.8 Lesson 28 Problem Solving: Volume....150 8.G.9 Domain 4 Review...156 Domain 5 Statistics and Probability...160 Lesson 29 Constructing and Interpreting Scatter Plots....162 8.SP.1 Lesson 0 Modeling Relationships in Scatter Plots with Straight Lines...166 8.SP.2 Lesson 1 Using Linear Models to Interpret Data....170 8.SP. Lesson 2 Investigating Patterns of Association in Categorical Data... 174 Domain 5 Review...178 Glossary...182 Math Tools...185 8.SP.4
1 LESSON Understanding Rational and Irrational Numbers UNDERSTAND All numbers can be written with a For example, you can rewrite 2 and 5 with decimal points without changing their values. 2 2.0 or 2.00 or 2.000, and so on 5 5.0 or 5.00 or 5.000, and so on You can expand the decimal places of a number that already has digits to the right of the 2.2 2.20 or 2.200, and so on 5. _ 1 5.1 _ 1 or 5.11 _ 1, and so on Each of the numbers above has a decimal expansion that ends either in zeros or in a repeating digit. Any number with a decimal expansion that ends in 0s or in repeating decimal digits is a rational number. UNDERSTAND Some numbers, like the ones below, do not end in 0s or in repeating decimal digits. The three dots, called an ellipsis, mean that digits continue, but not in a repeating pattern. 2 1.41421 5 2.2606 10.16227 Any number with a decimal expansion that does not end in 0s or in repeating decimal digits is an irrational number. You have previously worked with a very important number, pi, which is represented by the symbol..14159 The decimal expansion of does not end in 0s or in repeating decimal digits. It is an irrational number. Every real number belongs either to the set of rational numbers or to the set of irrational numbers. Set of all Real Numbers Rational Numbers 2 2.2 5 5.1 Irrational Numbers 2 5 6 Domain 1: The Number System
Connect Is 0.07 rational or irrational? Examine the digits to the right of the 0.07 0.070 or 0.0700, and so on 0.07 is rational because its decimal expansion ends in 0s. Is. 45 rational or irrational? Examine the digits to the right of the. 45.45 45 or.4545 45, and so on. 45 is rational because its decimal expansion repeats. Is 10.049846 rational or irrational? Examine the digits to the right of the 10.049846 10.049846 is irrational because its decimal expansion does not end in 0s or in repeating decimal digits. Is 8 rational or irrational? Use a calculator to find the decimal form. 8 2.828427125 Examine the digits to the right of the 8 is irrational because its decimal expansion does not end in 0s or in repeating decimal digits. DISCUSS How could you show that 4.95271 is a rational number using methods shown above? Lesson 1: Understanding Rational and Irrational Numbers 7
EXAMPLE A Write each of the following rational numbers in fraction form., 0.9,.0 1 Express each number as a fraction of the form a b where a and b are integers and b 0. Use the place value of the rightmost digit to determine the value of the denominator. The rightmost digit in is in the ones place, so 1. The rightmost digit in 0.9 is in the tenths place, so 0.9 9 10. The rightmost digit in.0 is in the hundredths place, so.0 0 100. 2 1 0.9 9 10.0 0 100 EXAMPLE B Convert the rational number 0. to a fraction. 1 Use algebra. Set the number, 0., equal to n. n 0. There is one repeating digit, so multiply n by the first power of 10, or 10. 10n. 2 Subtract the number, n, from 10n. 10n. n 0. 9n Solve the equation and simplify the result. 9n 9 9 n 9 1 0. 1 CHECK How can you work backward from 1 to check the answer? 8 Domain 1: The Number System
1 EXAMPLE C Convert 0. 45 to a fraction. Use algebra. Set the number, 0. 45, equal to n. n 0. 45 There are two repeating digits, so multiply n by the second power of 10, or 100. 100n 45. 45 2 Subtract the number, n, from 100n. 100n 45. 45 n 0. 45 99n 45 Solve the equation and simplify the result. 99n 45 99 99 n 45 99 5 11 0. 45 5 11 DISCUSS What steps could you use to express the decimal 0.8 as a fraction? Lesson 1: Understanding Rational and Irrational Numbers 9
Practice Identify whether the number is rational or irrational. Then explain why it is rational or irrational. 1. 101 2. 8 17. 21.192 4. 7 5. 9 6. HINT If a square root has an integer value, is it rational? 7. 50 8. 9. 81 Write three equivalent decimal forms for each number. 9. 19 10. 21.5 11. 44.045 12. 1. _ 1 REMEMBER Adding zeros to the end of a decimal does not change its value. 10 Domain 1: The Number System
Complete each sentence. 1. 11. is rational because. 14. 19 is irrational because. 15. 0.08 is rational because. 16. 2.17198 is irrational because. Convert the repeating decimal to a fraction. 17. 0. 6 18. 1. _ 1 19. 4. 4 20. 9. 09 21. 2. 90 22. 4. 54 Choose the best answer. 2. Which is an irrational number? A.. 4 B. 1 C. 20 D. 11.2092 24. Which number is not equivalent to 1.02? A. 1.002 B. 1.020 C. 1.0200 D. 1.020000 Solve. 25. WRITE MATH Convert.1 6 to a fraction. Explain your strategy or show the steps you used to convert the number. 26. DESCRIBE Describe two real-life applications of irrational numbers. Lesson 1: Understanding Rational and Irrational Numbers 11