Mathematics Grade 8 CROSSWalk for the Co on Core State Standards
Table of Contents Common Core State Standards Correlation Chart... 6 Domain 1 The Number System.... Domain 1: Diagnostic Assessment for Lessons 1 4...12 Lesson 1 Rational Numbers...14 Lesson 2 Irrational Numbers...20 Lesson 3 Compare and Order Rational and Irrational Numbers....26 Lesson 4 Estimate the Value of Expressions....31 Domain 1: Cumulative Assessment for Lessons 1 4...36 Domain 2 Expressions and Equations...39 Domain 2: Diagnostic Assessment for Lessons 18...40 Lesson Exponents....43 Lesson 6 Square Roots and Cube Roots...49 Lesson 7 Scientific Notation...4 Lesson 8 Solve Problems Using Scientific Notation....62 Lesson 9 Linear Equations in One Variable...67 Lesson 10 Use One-Variable Linear Equations to Solve Problems....7 Lesson Slope....80 Lesson 12 Slopes and y-intercepts...88 Lesson 13 Proportional Relationships...9 Lesson 14 Direct Proportions....101 Common Core State Standards 8.NS.1 8.NS.1, 8.NS.2, 8.EE.2 8.NS.1, 8.NS.2 8.NS.2 8.EE.1 8.EE.2 8.EE.4 8.EE.3, 8.EE.4 8.EE.7.a, 8.EE.7.b 8.EE.7.a, 8.EE.7.b 8.EE.6 8.EE., 8.EE.6 8.EE. 8.EE. Lesson 1 Pairs of Linear Equations...107 Lesson 16 Solve Systems of Equations Graphically...... 3 Lesson 17 Solve Systems of Equations Algebraically...120 Lesson 18 Use Systems of Equations to Solve Problems.. 128 Domain 2: Cumulative Assessment for Lessons 18...133 Domain 3 Functions...137 Domain 3: Diagnostic Assessment for Lessons 19 23...138 Lesson 19 Introduction to Functions...141 Lesson 20 Work with Linear Functions...149 8.EE.8 8.EE.8.a, 8.EE.8.b 8.EE.8.a, 8.EE.8.b, 8.EE.8.c 8.EE.8.c 8.F.1, 8.F.3 8.F.3, 8.F.4 4
Lesson 21 Use Functions to Solve Problems....1 8.F.4 Common Core State Standards Lesson 22 Use Graphs to Describe Relationships...163 Lesson 23 Compare Relationships Represented in Different Ways...169 Domain 3: Cumulative Assessment for Lessons 19 23..... 176 Domain 4 Geometry...179 Domain 4: Diagnostic Assessment for Lessons 24 32....180 Lesson 24 Congruence Transformations...183 Lesson 2 Dilations...190 Lesson 26 Similar Triangles...196 Lesson 27 Interior and Exterior Angles of Triangles...20 Lesson 28 Parallel Lines and Transversals...2 Lesson 29 The Pythagorean Theorem...218 Lesson 30 Distance....224 Lesson 31 Apply the Pythagorean Theorem....230 Lesson 32 Volume....236 8.F. 8.EE., 8.F.2 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.2, 8.G.3 8.G.3, 8.G.4 8.G.4, 8.G. 8.G. 8.G. 8.G.6, 8.G.7 8.G.8 8.G.7, 8.G.8 8.G.9 Domain 4: Cumulative Assessment for Lessons 24 32..... 242 Domain Statistics and Probability...24 Domain : Diagnostic Assessment for Lessons 33 36....246 Lesson 33 Scatter Plots...249 Lesson 34 Trend Lines...27 Lesson 3 Interpret Linear Models...263 Lesson 36 Patterns in Data...269 Domain : Cumulative Assessment for Lessons 33 36..... 277 Glossary...280 Summative Assessment: Domains 1................. 28 Math Tools...30 8.SP.1 8.SP.1, 8.SP.2 8.SP.3 8.SP.4
Domain 1 Lesson 1 Rational Numbers Common Core State Standard: 8.NS.1 Getting the Idea Integers include the set of whole numbers (0, 1, 2, 3, ) and their opposites (21, 22, 23, ). The number line below shows integers from 2 to. Notice that positive numbers are located to the right of zero, and negative numbers are located to the left of zero. negative numbers positive numbers 4 3 2 1 0 1 2 3 4 A rational number is any real number that can be expressed as the ratio of two integers a b, where b is not equal to zero. Some examples of rational numbers are shown below. 26, 2 3, 2 7, 16%, 4, 0. 7, 0.79 9 Any rational number can be expanded to form a decimal with digits that either terminate or repeat. To convert a fraction to a repeating decimal, use long division and divide the numerator by the denominator. Example 1 Is a rational number? If so, write it as a decimal. Strategy Decide if is rational. Then divide to write it as a decimal. Step 1 Is a rational number? and are both integers. So, shows the ratio of two integers. It is rational. Step 2 Divide the numerator,, by the denominator,. Insert zeros after the decimal point in as needed to perform the long division. 0.44 q.0000 2 4 4 60 2 0 2 44 60 2 14
Lesson 1: Rational Numbers Step 3 Solution Write 0.44 using a bar to show the repeating digits. 0.44 0. 4 is rational. It can be expressed as the repeating decimal 0. 4. Some rational numbers can be expanded to form finite decimals. The digits of a finite decimal terminate and do not repeat. If you perform long division and the digit 0 keeps repeating, the decimal is finite and the zeros can be dropped. Example 2 Is 22 3 a rational number? If so, write it as a decimal. Strategy Decide if 2 3 is rational. Then divide to write it as a decimal. Step 1 Is 22 3 a rational number? Convert 22 3 to an improper fraction. 22 3 2 (2? ) 1 3 10 1 3 13 2 2 213 Since 213 is the ratio of two integers, 22 3 is rational. Step 2 Divide the numerator, 213, by the denominator,. Since you are dividing a negative integer by a positive integer, the quotient will be negative. For now, drop the negative sign. 2.600 q13.000 2 10 3 0 2 3 0 00 2 00 00 2 00 0 The actual quotient is 22.600 Step 3 Solution Write 22.600 as a finite decimal. Since 22.600 ends in a sequence of zeros, the zeros can be dropped. The quotient can be written as 22.6. 2 3 is rational. It can be expressed as the finite decimal 2.6. 1
All rational numbers can be represented on a number line. To plot rational numbers on a number line, it is helpful to convert them to the same form. You already know that you can convert a fraction to a decimal using long division. You can also convert a percent to a decimal by dividing the percent by 100 and dropping the percent sign. This is the same as moving the decimal point in the percent two places to the left. Some square roots are also rational. Any number that has a whole-number square root is a perfect square, such as the ones below. 1, 4, 9, 16, 2, 36, 49, 64, 81, 100, 121, 144, 169, 196, 22 If the number under a square root symbol (œw) is a perfect square, its value is an integer and it is a rational number. For example, 9 is rational because it is equal to the integer 3. Example 3 Plot and label a point for each rational number below on a number line. 2 2 2, 1 1, 20.2, 72.%, 4 2 Strategy Write the numbers in an equivalent form. Step 1 Step 2 Rewrite each number as a decimal or integer. 2 2 2 22 4 2 21 1 1 4 2 0., so 1 1 1 1 0. 1.. 2 2 20.2 is already in decimal form. 72.% 72.% 4 100% x 72. 0.72 4 2, because 2 2 4. Plot and label each number on a number line. Draw a number line from 21 to 2 and divide it into tenths. 2 Plot a point at 21 and label it 2 2. Plot a point for 1. at the tick mark halfway between 1.4 and 1.6 and label it 1 1 2. Plot a point halfway between 20.2 and 20.3 and label it 20.2. Plot a point for 0.72 closer to 0.7 than to 0.8 and label it 72.%. Plot a point at 2 and label it 4. 2 2 0.2 72.% 1 1 2 4 1 0.8 0.4 0 0.4 0.8 1 1.4 1.8 2 Solution The number line with the rational numbers labeled is shown in Step 2. 16 Domain 1: The Number System
Lesson 1: Rational Numbers Coached Example What decimal is represented by point P on the number line below? 0 1 2 The number line is divided into sixths. Starting at the tick mark for 1, you count tick marks from 1 to point P. So, point P represents the mixed number. Instead of converting the mixed number to an improper fraction, just convert the fractional part,, to a decimal. Divide the numerator,, by the denominator,. P 6 q.0000 If the decimal repeats, write it with a bar over the repeating digit: Add 1 to the decimal: 1 1 1 6 The decimal represented by point P is. 17
Lesson Practice Choose the correct answer. 1. Which point on the number line best 6_ represents 22? Q R S T 4. Which point on the number line below best represents 42%? A B C D 8 4 0 4 8 0 0.2 0.4 0.6 0.8 1 A. point Q B. point R C. point S D. point T A. point A B. point B C. point C D. point D 2. Which is the decimal expansion of 3? A. 0. 34 B. 0.3434 C. 0. 27 D. 0.02727 3. Which shows how 22.6 can be written as the ratio of two integers? 26 A. 2 20 B. 2 213 20 C. 2 3 20 D. 2 2 2. Which fraction is equivalent to 0.3? A. 1_ 7 B. 20 C. 20 D. 3_ 6. Which point on the number line best represents 22 2_ 3? J K L M 3 2 1 0 1 2 3 A. point J B. point K C. point L D. point M 18 Domain 1: The Number System
Lesson 1: Rational Numbers 7. A gymnast is 4 feet tall. Which 12 decimal is equivalent to 4 12? A. 4.416 B. 4.41 _ 6 C. 4.12 D. 4.1 _ 2 8. The metal composition of a penny is 97.% zinc and only 2.% copper. How would 2.% be written as a decimal? A. 2.00 B. 2.0 C. 0.2 D. 0.02 9. Consider the number line below. 1 0 1 A. Write 6% as a decimal. Show your work. Then plot and label a point for it on the number line. 2_ B. Write 29 as a decimal. Show your work. Then plot and label a point for it on the number line. 19