For 14 15, use the coordinate plane shown. represents 1 kilometer. 10. Write the ordered pairs that represent the location of Sam and the theater.

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1 Name Class Date 12.1 Independent Practice CMMN CRE 6.NS.6, 6.NS.6b, 6.NS.6c, 6.NS.8 m.hrw.com Personal Math Trainer nline Assessment and Intervention For 10 13, use the coordinate plane shown. Each unit represents 1 kilometer. 10. Write the ordered pairs that represent the location of Sam and the theater. Theater 11. Describe Sam s location relative to the theater Sam Sam wants to meet his friend Beth at a restaurant before the go to the theater. The restaurant is 9 km south of the theater. Plot and label a point representing the restaurant. What are the coordinates of the point? -4 W N S E 13. Beth describes her current location: I m directl south of the theater, halfwa to the restaurant. Plot and label a point representing Beth s location. What are the coordinates of the point? For 14 15, use the coordinate plane shown. 14. Find the coordinates of points T, U, and V. 15. Points T, U, and V are the vertices of a rectangle. Point W is the fourth verte. Plot point W and give its coordinates. 16. Eplain the Error Janine tells her friend that ordered pairs that have an -coordinate of 0 lie on the -ais. She uses the origin as an eample. Describe Janine s error. Use a countereample to eplain wh Janine s statement is false. V U T Lesson

2 FCUS N HIGHER RDER THINKING Work Area 17. Critical Thinking Choose scales for the coordinate plane shown so that ou can graph the points J(2, 40), K(3, 10), L(3, -40), M(-4, 50), and N(-5, -50). Eplain wh ou chose the scale for each ais. 18. Communicate Mathematical Ideas Edgar wants to plot the ordered pair (1.8, -1.2) on a coordinate plane. n each ais, one grid square equals 0.1. Starting at the origin, how can Edgar find (1.8, -1.2)? 19. Represent Real-World Problems Zach graphs some ordered pairs in the coordinate plane. The -values of the ordered pairs represent the number of hours since noon, and the -values represent the temperature at that time. a. In which quadrants could Zach graph points? Eplain our thinking. b. In what part of the world and at what time of ear might Zach collect data so that the points he plots are in Quadrant IV? 336 Unit 5

3 Name Class Date 12.2 Independent Practice CMMN CRE 6.EE.9 6. The graph shows the relationship between the hours a soccer team practiced after the season started and their total practice time for the ear. a. How man hours did the soccer team practice before the season began? b. What are the two quantities in this situation? c. What are the dependent and independent variables? m.hrw.com Total practice time for ear (hours) Personal Math Trainer 10 nline Assessment and Intervention Practice time during the season (hours) d. Is the relationship between the variables additive or multiplicative? Eplain. e. Analze Relationships Describe the relationship between the quantities in words. 7. Multistep Teresa is buing glitter markers to put in gift bags. The table shows the relationship between the number of gift bags and the number of glitter markers she needs to bu. a. What is the dependent variable? b. What is the independent variable? c. Is the relationship additive or multiplicative? Eplain. Number of gift bags, Number of markers, d. Describe the relationship between the quantities in words. Lesson

4 8. T borrowed $500 from his parents. The graph shows how much he owes them each month if he pas back a certain amount each month. a. Describe the relationship between the number of months and the amount T owes. Identif an independent and dependent variable and eplain our thinking. Amount T owes (dollars) T s Loan Paments Months b. How long will it take T to pa back his parents? FCUS N HIGHER RDER THINKING Work Area 9. Error Analsis A discount store has a special: 8 cans of juice for a dollar. A shopper decides that since the number of cans purchased is 8 times the number of dollars spent, the cost is the independent variable and the number of cans is the dependent variable. Do ou agree? Eplain. 10. Analze Relationships Provide an eample of a real-world relationship where there is no clear independent or dependent variable. Eplain. 344 Unit 5

5 Name Class Date 12.3 Independent Practice CMMN CRE 6.EE.9 m.hrw.com Personal Math Trainer nline Assessment and Intervention 7. Vocabular What does it mean for an equation to epress in terms of? 8. The length of a rectangle is 2 inches more than twice its width. Write an equation relating the length l of the rectangle to its width w. 9. Look for a Pattern Compare the -values in the table to the corresponding -values. What pattern do ou see? How is this pattern used to write an equation that represents the relationship between the - and -values? Eplain the Error A student modeled the relationship in the table with the equation = 4. Eplain the student s error. Write an equation that correctl models the relationship Multistep Marvin earns $8.25 per hour at his summer job. He wants to bu a video game sstem that costs $ a. Write an equation to model the relationship between number of hours worked h and amount earned e. b. Solve our equation to find the number of hours Marvin needs to work in order to afford the video game sstem. Lesson

6 12. Communicate Mathematical Ideas For ever hour that Noah studies, his test score goes up 3 points. Eplain which is the independent variable and which is the dependent variable. Write an equation modeling the relationship between hours studied h and the increase in Noah s test score s. FCUS N HIGHER RDER THINKING Work Area 13. Make a Conjecture Compare the -values in the table to the corresponding -values. Determine whether there is an additive relationship or a multiplicative relationship between and. If possible, write an equation modeling the relationship. If, not eplain wh Represent Real-World Problems Describe a real-world situation in which there is an additive or multiplicative relationship between two quantities. Make a table that includes at least three pairs of values. Then write an equation that models the relationship between the quantities. 15. Critical Thinking Georgia knows that there is either an additive or multiplicative relationship between and. She onl knows a single pair of data values. Eplain whether Georgia has enough information to write an equation that models the relationship between and. 350 Unit 5

7 Name Class Date 12.4 Independent Practice CMMN CRE 6.EE.9 m.hrw.com Personal Math Trainer nline Assessment and Intervention Students at Mills Middle School are required to work a certain number of communit service hours. The table shows the numbers of additional hours several students worked beond their required hours, as well as the total numbers of hours worked. 5. Read the ordered pairs from the graph to make a table. Additional hours Total hours 6. Write an equation that epresses the total hours in terms of the additional hours. Total (h) Additional (h) 7. Analze Relationships How man communit service hours are students required to work? Eplain. Beth is using a map. Let represent a distance in centimeters on the map. To find an actual distance in kilometers, Beth uses the equation = Make a table comparing a distance on the map to the actual distance. Map distance (cm) Actual distance (km) 9. Make a graph that compares the map distance to the actual distance. Label the aes of the graph. 10. Critical Thinking The actual distance between Town A and Town B is 64 kilometers. What is the distance on Beth s map? Did ou use the graph or the equation to find the answer? Wh? Lesson

8 11. Multistep The equation = 9 represents the total cost for movie tickets. Label the aes of the graph. a. Make a table and a graph to represent the relationship between and. Number of tickets, 50 Total cost ($), b. Critical Thinking In this situation, which quantit is dependent and which is independent? Justif our answer c. Multiple Representations Eight friends want to go see a movie. Would ou prefer to use an equation, a table, or a graph to find the cost of 8 movie tickets? Eplain how ou would use our chosen method to find the cost. FCUS N HIGHER RDER THINKING Work Area 12. Critical Thinking Suppose ou graph = 5 and = on the same coordinate plane. Which line will be steeper? Wh? 13. Persevere in Problem Solving Marcus plotted the points (0, 0), (6, 2), (18, 6), and (21, 7) on a graph. He wrote an equation for the relationship. Find another ordered pair that could be a solution of Marcus s equation. Justif our answer. 14. Error Analsis The cost of a personal pizza is $4. A drink costs $1. Anna wrote the equation = to represent the relationship between total cost of buing meals that include one personal pizza and one drink. Describe Anna s error and write the correct equation. 356 Unit 5

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