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Table of Contents Unit 1: Ratios, Rates, and Percents STAAR Reporting Categories 1 and 2 TEKS 6 4 C ♦, 6 4 D♦ Lesson 1 Ratios Lesson 2 Represent Ratios and Rates 12 6 5 A♦ Lesson 3 Making Predictions and Comparisons Using Ratios 22 6 4 B✶ Lesson 4 Ratios, Fractions, Decimals, and Percents 32 6 4 E♦, 6 4 F♦, 6 4 G✶, 6 5 C♦ Lesson 5 Solve Problems with Percent 42 6 5 B✶ 2 STAAR Practice 52 Unit 2: Number and Operations STAAR Reporting Categories 1 and 2 Lesson 6 Fractions as Division 54 6 2 E♦ Lesson 7 Understand Division with Unit Fractions 62 6 3 A♦ Lesson 8 Multiply and Divide Fractions 68 6 3 E✶, 6 3 B♦ Lesson 9 Multiply and Divide Decimals 80 6 3 E✶ 92 6 2 A♦ Lesson 10 Whole Numbers, Integers, and Rational Numbers Lesson 11 Understand Positive and Negative Numbers 100 6 2 B♦, 6 2 C ♦ Lesson 12 Absolute Value and Ordering Numbers 106 6 2 C ♦, 6 2 D✶ Lesson 13 The Coordinate Plane 116 6 11 A✶ Lesson 14 Add and Subtract Positive and Negative Integers 124 6 3 C ♦, 6 3 D✶ Lesson 15 Multiply and Divide Positive and Negative Integers 136 6 3 D✶ STAAR Practice 146 ✶ = STAAR Readiness Standard ♦ = STAAR Supporting Standard ©Curriculum Associates, LLC Copying is not permitted. iii Table of Contents TEKS Unit 3: Expressions and Equations STAAR Reporting Categories 1 and 2 Lesson 16 Numerical Expressions with Exponents 150 6 7 A✶ Lesson 17 Algebraic Expressions and Equations 162 6 7 B♦ Lesson 18 Equivalent Expressions 174 6 7 C ♦, 6 7 D✶ Lesson 19 Understand Solutions to Equations 186 6 9 A♦, 6 10 A✶, 6 10 B♦ Lesson 20 Solve Equations 192 6 9 A♦, 6 9 B♦, 6 9 C ♦, 6 10 A✶, 6 10 B♦ Lesson 21 Solve Inequalities 204 6 9 A♦, 6 9 B♦, 6 9 C ♦, 6 10 A✶, 6 10 B♦ Lesson 22 Dependent and Independent Variables 216 6 6 A♦, 6 6 B♦, 6 6 C✶ Lesson 23 Additive and Multiplicative Relationships 226 6 4 A♦ STAAR Practice 234 Unit 4: Geometry and Measurement STAAR Reporting Category 3 Lesson 24 Convert Measures 236 6 4 H✶ Lesson 25 Understand Conditions for Triangles 246 6 8 A♦ Lesson 26 Area of Polygons 252 6 8 B♦, 6 8 C ♦, 6 8 D✶ Lesson 27 Volume 262 6 8 C ♦, 6 8 D✶ STAAR Practice 272 ✶ = STAAR Readiness Standard ♦ = STAAR Supporting Standard iv ©Curriculum Associates, LLC Copying is not permitted. Table of Contents Unit 5: Data Analysis and Personal Financial Literacy STAAR Reporting Category 4 TEKS Lesson 28 Understand Statistical Questions 274 6 13 B♦ Lesson 29 Interpret Numeric Data 280 6 12 B♦, 6 12 C✶, 6 13 A✶ Lesson 30 Display Data on Dot Plots, Histograms, Box Plots, and Stem-and-Leaf Plots 290 6 12 A♦, 6 12 C✶ Lesson 31 Interpret Categorical Data 302 6 12 D✶ Lesson 32 Checking Accounts 314 6 14 A♦, 6 14 B♦, 6 14 C ♦ Lesson 33 Understand Credit Reports 324 6 14 E♦, 6 14 F♦ Lesson 34 Understand Paying for College 330 6 14 G♦ Lesson 35 Understand Annual Salaries 336 6 14 H♦ STAAR Practice 342 ✶ = STAAR Readiness Standard ♦ = STAAR Supporting Standard ©Curriculum Associates, LLC Copying is not permitted. v Focus on Math Concepts Lesson 11 Part 1: Introduction TEKS 6.2.B 6.2.C Understand Positive and Negative Numbers What are positive and negative numbers? Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative. Negative Zero 25 24 23 22 21 0 Positive 1 2 3 4 5 Positive and negative numbers are sometimes called signed numbers. Positive numbers can be written with or without a plus sign. Negative numbers are always written with a negative sign. When solving problems with positive and negative numbers, it important to think about how far from 0 the number is and in what direction. Think A thermometer shows positive and negative numbers. Temperatures above 0 are positive. Temperatures below 0 are negative. Look at the thermometer. F 120 50 100 40 80 20°F is 20 degrees above 0°F. 220°F is 20 degrees below 0°F. 230°C is 30 degrees below 0°C. 30°C is 30 degrees above 0°C. 100 C 60 40 20 Circle the negative numbers labeled on the thermometer. 30 20 10 0 210 0 220 220 230 240 240 L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 1: Introduction Lesson 11 Think Every positive and negative number has an opposite. Numbers that are the same distance from zero but in opposite directions are called opposite numbers. Every whole number, fraction, and decimal has an opposite. The opposite of 4 is 24. Both numbers are the same distance from 0. To plot a point at 4, count 4 units to the right of 0 and draw a point. To plot a point at 24, count 4 units to the left of 0 and draw a point. 28 27 26 25 24 23 22 21 0 1 2 3 4 Think about folding the number line in half so that the fold goes through 0. Numbers that line up are opposites. All the whole numbers and their opposites are called integers. All of the numbers labeled on the number line above are integers: 5 6 7 8 The number line shows that zero is its own opposite. 28, 27, 26, 25, 24, 23, 22, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8 Reflect 1 Think about the numbers 210 and 10. How could you describe these numbers? What is the same and what is different about these numbers? L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. 101 Part 2: Guided Instruction Lesson 11 Explore It A number line can help you understand positive and negative numbers. Jana and a friend are playing a game that shows a number line from 27 to 7. The game is played with 15 cards numbered with the integers from 27 to 7. Players draw a card from a pile. They earn points for correctly locating the number on the card on the number line and then identifying its opposite. 27 0 24 3 6 7 2 Finish labeling the number line. 3 Suppose Jana draws a card that shows 23. Draw a point at 23 on the number line. 4 What number is the opposite of 23? . Explain your reasoning. 5 Jana’s friend draws a card that shows a 0. Draw a point at 0. What is the opposite of 0? Explain. 6 The next card drawn is 26. How far from 0 is 26? In which direction? Draw a point at 26. 7 What number is the same distance from 0 as 26 but in the other direction? 8 Two numbers that are the same distance from 0 but on different sides of zero are called numbers. Now try this problem. 9 Graph each integer and its opposite on the number line below. 5 21 4 22 28 27 26 25 24 23 22 21 102 0 1 2 3 4 5 6 7 8 L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 2: Guided Instruction Lesson 11 Talk About It Solve the problems below as a group. 10 Look at the number lines on the previous page. There are numbers between the numbers you graphed. Just as whole numbers can be positive or negative, fractions and decimals can also be positive and negative. The number 1.5 is between 1 and 2. The number 21.5 is between 22 and 21. Draw a point at 1.5 and a point at 21.5 on the number line below. Label each point with its value. 24 23 22 21 0 1 2 3 4 11 How is locating 21.5 on a number line the same as locating 1.5 on a number line? How is it different? 12 Use the number line below to graph the following numbers. Label each point with its value. Then graph and label the opposite of each number. 11 211 2 ·· 4 ·· 22 1 2 ··2 21 0 1 2 Try It Another Way Work with your group to explore writing positive and negative numbers to represent a situation. 13 Write a positive or a negative number to represent each situation. A you owe $25 B a team has a gain of 20 yards in a football game C two floors below ground level D 15 degrees above 0°C E a stock price fell 4.26 points L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. 103 Part 3: Guided Practice Lesson 11 Connect It Talk through these problems as a class, then write your answers below. 14 Conclude: What number is the opposite of the opposite of 5? What can you say about the opposite of the opposite of a number? 15 Interpret: Positive and negative numbers can show an amount above or below zero. They can also be used to show an amount above or below a certain point. Students at Taft Middle School have a goal of collecting 1,000 pounds of recycling materials each month. The following table shows their results over a 6-month time period. Complete the table. The first month is done for you. Month January Pounds Collected 985 February March April May June 1,010 995 1,050 975 980 Compared to 1,000 215 ←15 less than 1,000 16 Analyze: Look at the number line below. The letters a, b, c, and d all represent integers. a c 0 b A Which letters represent negative integers? B Which letters represent positive integers? d How do you know? How do you know? C If b and c are the same distance from 0, how can you describe them? 104 L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 4 : Performance Task Lesson 11 Put It Together 17 Use what you have learned to complete this task. Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero. A Write your problem. B Graph the numbers you used in your problem on a number line. 0 C Explain what zero means in this situation. D What can you say about the sum of a number and its opposite? L11: Understand Positive and Negative Numbers ©Curriculum Associates, LLC Copying is not permitted. 105 Develop Skills and Strategies Lesson 12 Part 1: Introduction TEKS 6.2.C 6.2.D Absolute Value and Ordering Numbers In Lesson 11, you learned how to locate positive and negative numbers on a number line. In this lesson you will learn how to compare the numbers and find their absolute value. Take a look at this problem. The elevation of an object tells you its distance above or below sea level. Negative numbers are used to represent objects below sea level. Positive numbers are used to represent objects above sea level. The table below shows the elevations of four objects. Graph their locations on a number line. Describe the distances of the objects above or below sea level. Object Elevation (in km) Mountain 2 Elevation Ocean Fish 21 Sunken Ship 24 Airplane 4 Explore It Use the math you already know to solve the problem. Sea level is marked and labeled on the number line. Mark and label the elevation of the objects listed in the table above on the number line. How far above sea level is the mountain? How far below sea level is the school of fish? Is the airplane above or below sea level? 0 Sea level What two objects are the same distance from sea level? Explain how you know. Explain how you could find the distances of the objects from sea level. 106 L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 1: Introduction Lesson 12 Find Out More When you answered how far each object is from sea level, you found the absolute value of a number. The absolute value of a number is its distance from 0 on the number line. |24| means the absolute value of 24. 24 is 4 units from 0. |24| 5 4 The absolute value of 24 is 4 because 24 is 4 units from 0 on the number line. 24 23 22 21 0 1 2 3 4 4 units from 0 Absolute value represents distance, so its value is always greater than or equal to 0. The absolute value of 0 is 0, or |0| 5 0. The farther a number is from 0, the greater the number’s absolute value. In real-world situations, the absolute value of a number is often used to describe the situation. The elevation of the fish is 21 km, but you could also say that the fish is 1 km below sea level. The elevation of the sunken ship is 24 km, but you could also say that the sunken ship is 4 km below sea level. Reflect 1 Look at your number line on the previous page. Which pair of numbers have the same absolute value? How are the numbers related? Explain. L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. 107 Part 2: Modeled Instruction Lesson 12 Read the problem below. Then explore how to use a number line to compare positive and negative numbers. One morning it was 29°F in Columbus, Ohio and 27°F in Pittsburgh, Pennsylvania. Was it warmer in Columbus or Pittsburgh? Picture It You can graph the numbers on a number line. 29 28 27 26 25 24 23 22 21 0 1 2 3 4 5 6 7 Model It You can use the number line to write an inequality to compare the numbers. 29 is to the left of 27 on the number line. This means that 29 is less than 27. You can use symbols to compare the numbers. The symbol , means is less than. 29 , 27 Model It You can use the number line to write a second inequality to compare the numbers. 27 is to the right of 29 on the number line. This means that 27 is greater than 29. You can use symbols to compare the numbers. The symbol . means is greater than. 27 . 29 108 L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 2: Guided Instruction Lesson 12 Connect It Now use the number line and the comparison statements to solve the problem. 2 Look at the number line in Picture It. Where is 29 located? Where is 27 located? 3 From left to right, does the number line show numbers from least to greatest or greatest to least? 4 Which is the warmer temperature, 29°F or 27°F? Which city was warmer? 5 Model It shows that you can write two inequalities to compare 29 and 27. Write two inequalities to compare 26 and 5. Tell how you decided. 6 Explain how you can use a number line to compare any two numbers. Try It Use what you just learned to compare the numbers below. Use the number line to help if needed. 210 29 28 27 26 25 24 23 22 21 0 1 2 3 4 5 6 7 8 9 10 7 Write two inequalities to compare 25 and 23. 8 Write two inequalities to compare 9 and 29. L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. 109 Part 3: Modeled Instruction Lesson 12 Read the problem below. Then explore how to use a number line to order positive and negative numbers. Five friends played a game where you earn positive and negative points. Their final scores were 23.5, 2, 23, 21, 1.5. What was the highest score? What was the lowest score? Picture It You can graph the numbers on a number line. 1.5 23.5 24 23 22 21 0 1 2 3 4 Model It You can compare the positions of the numbers on the number line. 23.5 is to the left of 23. 23 is to the left of 21. 21 is to the left of 1.5. 1.5 is to the left of 2. Model It You can compare the positions of the numbers on the number line in another way. 2 is to the right of 1.5. 1.5 is to the right of 21. 21 is to the right of 23. 23 is to the right of 23.5. 110 L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 3: Guided Instruction Lesson 12 Connect It Now use the number line to order the numbers and solve the problem. 9 Look at the first Model It. Order the numbers from least to greatest. 10 Look at the second Model It. Order the numbers from greatest to least. 11 What was the lowest score? How do you know? 12 What was the highest score? How do you know? 13 Explain how to use a number line to order numbers. Try It Use what you just learned about ordering numbers to solve these problems. Use a number line to help if needed. 14 Order the numbers from least to greatest. A 28, 26, 25, 27 B 28.2, 6, 23.5, 8.2, 25 15 Order the numbers from greatest to least. 3 A 2··4, 21, 5, 2 B 20.5, 1.5, 0, 25, 1.25 4 ·· L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. 111 Part 4: Guided Practice Lesson 12 Study the student model below. Then solve problems 16–18. Student Model The student graphed the numbers on a number line to order them from least to greatest. A 6th grade class is studying transportation in New York City. They collected this data about the heights above ground and depths below ground of different structures. Write the names of these structures in order from lowest elevation to highest elevation. Verrazano Narrows Bridge 70 m Holland Tunnel 225 m George Washington Bridge 60 m Lincoln Tunnel 230 m 230 225 Pair/Share Are positive numbers always greater than negative numbers? Will graphing the numbers on a number line help? 0 60 70 Solution: Lincoln Tunnel, Holland Tunnel, George Washington Bridge, Verrazano Narrows Bridge 16 Eyeglass prescriptions use positive and negative numbers to describe vision. In general, the farther away from zero the number on a prescription is, the more vision correction you need. Negative numbers mean you are nearsighted, positive numbers mean you are farsighted. The table below shows prescription numbers for five patients. Patient Prescription A 22.25 B 1.00 C 21.50 D 3.25 E 23.00 Which patients are nearsighted? Which patients are farsighted? Which patient is the most nearsighted? Which patient is the most farsighted? Pair/Share Solution: How do you compare negative numbers? 112 L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 4: Guided Practice Lesson 12 17 Which number is greater, 27 or 6? Which number has the greater absolute value, 27 or 6? Explain your thinking. Use comparison symbols and absolute value symbols when you write your answer. What does absolute value mean? Solution: Pair/Share Can a negative number have a greater absolute value than a positive number? 18 The table below shows elevations of different locations in the world. List the elevations in order from greatest to least. Circle the letter of the correct answer. Location Elevation (in ft) Caspian Sea 298 A 252, 298, 75, 92, 230 B 298, 252, 75, 92, 230 C 230, 92, 75, 252, 298 Mekong Delta 230 Lake Eyre 252 Senegal River 75 Are negative numbers always less than positive numbers? Iron Gate 92 D 230, 92, 75, 298, 252 Randy chose B as the correct answer. How did he get that answer? Pair/Share How can you tell that Randy’s answer can’t be correct by looking at one number’s position in his answer? L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. 113 Part 5: TEKS Practice Lesson 12 Solve the problems. 1 The lowest temperatures ever recorded in five of Earth’s continents are shown in the table below. Continent Temperature (in °C) South America North America Antarctica 239 266.1 289.2 Europe 258.1 Asia 268 Which continent has a lower recorded temperature than Asia? A South America B North America C Europe D Antarctica 2 On February 17, 1936, the following temperatures were recorded: City McIntosh, SD Duluth, MN Miami, FL Temperature 258°F 226°F 78°F Choose True or False for each statement. A The temperature difference between McIntosh, SD, and Duluth, MN, was 84°F. True False B Duluth, MN, was 32°F warmer than McIntosh, SD. True False C The temperature difference between Miami, FL, and Duluth, MN, was 52°F. True False The temperature difference between the highest and lowest temperatures was 136°F. True False D 114 L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 5: TEKS Practice Lesson 12 3 From the list on the left, write in the correct temperature along the thermometer. 0° Celsius [not drawn to scale] 278° 4° 276.8° 25° °Celsius 4 A tour group is going sea diving. Sea level is 0 feet. The ocean floor is 218 feet. One diver is already at 211 feet. The tour guide is keeping watch on the deck at 5 feet above sea level directly above the diver. What is the distance from the tour guide to the diver? Draw and label a number line to justify your answer. feet Answer 5 Look at the number line below. The letters a, b, c, and d all represent integers. a b 0 c d A Write two inequalities to compare a and b. How do you know? B Write two inequalities to compare b and 0. How do you know? C If |a| 5 |d |, what can you say about a and d? L12: Absolute Value and Ordering Numbers ©Curriculum Associates, LLC Copying is not permitted. 115