JPS Grade 7 Math Benchmark 1 (2022-23) PDF

Version: 2022-23 SY JPS Grade 7 Math Benchmark 1 IM Student Version Section One (Non-Calculator) Instructions: You will now complete Section One of the benchmark assessment. During this section, you may NOT USE A CALCULATOR. In...

Version: 2022-23 SY JPS Grade 7 Math Benchmark 1 IM Student Version Section One (Non-Calculator) Instructions: You will now complete Section One of the benchmark assessment. During this section, you may NOT USE A CALCULATOR. In this section, each question is worth 1 point. 1. Which table demonstrates a proportional relationship between 𝑥 and 𝑦? 𝒙 𝒚 2 9 4 11 6 13 8 15 𝒙 𝒚 3 6 6 12 9 18 12 24 𝒙 𝒚 2 12 3 13 4 14 5 15 𝒙 𝒚 1 1 3 9 5 25 7 49 1  Version: 2022-23 SY 2. During the summer, Tram often babysits a child who lives in her neighborhood. She charges a constant rate per hour to babysit. When she babysits 8 hours, she charges $128. Which equation represents the amount in dollars that Tram charges, 𝑐, to babysit ℎ hours? 1 𝑐= ℎ 16 𝑐 = 8ℎ 𝑐 = 16ℎ 𝑐 = 120ℎ 3. Yesterday, Naveen went on a bike ride. During the ride, Naveen tracked how long it took him, in minutes, to bike different distances, in miles. The table shows his results. Naveen’s Bike Ride Distance (Miles) Number of Minutes 2 22 5 50 12 138 Is the number of minutes that Naveen biked proportional to the distance, in miles, that he biked? Complete the statement by selecting a phrase from the provided list. The number of minutes that Naveen biked _________________________ to the distance, in miles, that he biked. is proportional is not proportional 2  Version: 2022-23 SY 4. While planning a family reunion at a state park, the Ortiz family is determining the total cost for the family members to enter the park. The table shows a proportional relationship between the number of family members attending the reunion and the total cost to enter the state park. Ortiz Family Reunion Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 3 9 5 15 8 24 ? ? In the last row of the table, the values are missing. Which number of family members attending the reunion and total cost to enter the state park can represent the missing values so that the table continues to show a proportional relationship? Select all the correct responses. Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 15 36 Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 16 40 Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 22 66 Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 24 120 Number of Family Members Total Cost to Enter State Park Attending the Reunion (Dollars) 30 90 3  Version: 2022-23 SY 5. The table below provides the cost of purchasing different numbers of books at a used bookstore. Books Purchased at Used Bookstore Number of Books Cost of Books (dollars) Purchased 2 8 4 16 5 20 8 32 The cost of the books is proportional to the number of books purchased. What is the cost, in dollars, per book? Enter your answer in the box. $ 4  Version: 2022-23 SY 6. Franklin’s office got a new copy machine. The copy machine prints at a constant rate. The number of pages printed by the copy machine after 𝑚 minutes of printing is shown in the table. Pages Printed on Copy Machine Minutes Printing Pages Printed 𝑚 𝑝 2 84 4 168 6 252 8 336 Which equation represents the number of pages printed, 𝑝, by the new copy machine in 𝑚 minutes? 𝑝 = 84𝑚 𝑝 = 42𝑚 1 𝑝= 𝑚 42 1 𝑝= 𝑚 84 5  Version: 2022-23 SY Use the following information to answer questions 7-8. Jadyn works on a horse farm. Each evening, he is in charge of feeding hay to the horses. The table shows the amount of hay, ℎ, in pounds consumed by each horse over 𝑑 days. Hay Consumed by Each Horse Number of Days (𝒅) Hay Consumed in Pounds (𝒉) 2 30 4 60 6 90 The relationship between the number of days and the amount of hay consumed by each horse is proportional. 7. A row is added to the bottom of the table to represent the amount of hay consumed by each horse over 7 days. What amount of hay consumed, in pounds, can be input in the new row when the number of days is 7 so that the table remains proportional? Enter your answer in the box. 6  Version: 2022-23 SY 8. Which equation best represents the amount of hay, ℎ, in pounds that each horse consumes over 𝑑 days? 1 ℎ= 𝑑 15 ℎ = 2𝑑 ℎ = 15𝑑 ℎ = 30𝑑 9. Which relationships have a constant of proportionality that is equal to 14? Select the three correct relationships. 𝑦 = 14𝑥 𝑦 = 𝑥 + 14 Cost of Theater Tickets Coffee Shop Pay Number of Number of Cost (𝑐) Tickets (𝑡) Hours Pay (𝑝) 1 $12.50 Worked (ℎ) 3 $37.50 2 $28.00 5 $62.50 4 $56.00 5 $70.00 Regena walks at a constant A copy machine is printing rate per mile. It takes her workbooks at a constant 42 minutes to walk 3 miles. rate. The machine prints 30 workbooks every two minutes. 7  Version: 2022-23 SY 10. Paola sends her dog to doggie daycare during the week while she is at work. The amount Paola pays to send her dog to doggie daycare is proportional to the number of days that the dog attends. Last week, Paola paid $125 to send her dog to doggie daycare for five days. Which equation models the amount that Paola pays, 𝑝, in dollars for her dog to attend doggie daycare for 𝑑 days? Complete the statement by selecting an equation from the provided list. The equation _____________ models the amount that Paola pays, 𝑝, in 𝑑 = 25𝑝 𝑝 = 25𝑑 dollars for her dog to attend doggie daycare for 𝑑 days. 8  Version: 2022-23 SY Section Two (Calculator) Instructions: You will now complete Section Two of the benchmark assessment. During this section, you ARE ALLOWED TO USE A CALCULATOR. Questions 1-6 are worth 1 point each. Questions 7-9 are open-response questions. Questions 7-8 are worth 2 points each and question 9 is worth 3 points. 1. Minh creates a scale drawing of a park located in her neighborhood. The scale drawing, which is shown below, is 18 cm long and 12 cm wide. 18 cm 12 cm The actual park in Minh’s neighborhood is 108 meters wide. What is the area of the actual park in square meters? 162 216 1,944 17,496 9  Version: 2022-23 SY 2. Serina is filling a fish tank with water. The water flows into the tank at a constant rate. It takes 20 minutes to fill the tank with 30 gallons of water. What is the unit rate in gallons per minute? Complete the statement by selecting a number from the provided list. The unit rate is ________ gallons per minute. 0.67 1.5 2 3 3. Maryam is at an amusement park. She receives a map of the park when she enters. The scale of the map says that 3 cm represents 60 feet. On the map, the distance from the park entrance to the most popular roller coaster is 22 cm. What is the actual distance, in feet, from the park entrance to the most popular roller coaster? Enter your answer in the box. feet 10  Version: 2022-23 SY 4. The table shows the costs of purchasing honeycrisp apples from a food store. Cost of Honeycrisp Apples Number of Pounds Total Cost 3 $7.47 4 $9.96 5 $12.45 At this rate, what is the cost, in dollars, per pound of honeycrisp apples purchased? 0.40 2.49 3.00 4.47 5. A photographer took a photo of an oak tree with Mardi Gras beads on it. She sells prints of the photo. The original print has a length of 72 inches and a width of 54 inches. The photographer also offers two additional print sizes. 2 Print A is a scaled copy of the original print using a scale factor of 3. 3 Print B is a scaled copy of Print A using a scale factor of 4. What is the length, in inches, of Print B? Complete the statement by selecting a number from the provided list. The length of Print B is ________ inches. 54 48 36 14 11  Version: 2022-23 SY 6. Figure 𝐵 is a scale copy of figure 𝐴. Figure 𝑨 Figure 𝑩 16 units 4 units 3 units 12 units What is the scale factor from figure 𝐴 to figure 𝐵? 1 4 3 4 1 1 3 4 12  Version: 2022-23 SY Use the following information to answer questions 7-8. Akio and Beth are using different recipes to make homemade lemonade. The tables show the total number of servings compared to the amount of lemon juice included in the lemonade in each recipe. Akio’s Lemonade Recipe Beth’s Lemonade Recipe Cups of Total Servings Cups of Total Servings Lemon Juice of Lemonade Lemon Juice of Lemonade 2 7 2 8 5 17.5 3 11 10 35 7 23 The total servings of lemonade that Akio makes is proportional to the cups of lemon juice used to make the lemonade. The total servings of lemonade that Beth makes is not proportional to the cups of lemon juice used to make the lemonade. 13  Version: 2022-23 SY 7. Justify why Akio’s table models a proportional relationship and justify why Beth’s table does not model a proportional relationship between the total servings of lemonade made to the cups of lemon juice used to make the lemonade. Enter your justifications in the box provided. 8. Akio’s table models a proportional relationship between the total servings of lemonade that Akio makes and the cups of lemon juice used to make the lemonade. Determine the constant of proportionality. Create an equation that represents the total servings of lemonade that Akio makes, 𝑠, when using 𝑐 cups of lemon juice in the lemonade. Enter your answer and equation in the box provided. 14  Version: 2022-23 SY 9. Maurice is building a rectangular workshop. He provided the same actual dimensions of the workshop to two different architects. Both architects provided blueprints, which are scale drawings of the same-sized actual workshop. The blueprint from Architect A is shown. 30 in 20 in Workshop The scale on Architect A’s blueprint is 4 inches equals 8 feet. Architect B’s blueprint is not shown. The scale on Architect B’s blueprint is 2 inches equals 5 feet. Assume the longest side of the workshop is the length of the building. How many inches long is the length of the workshop on Architect B’s blueprint? Show work or explain your thinking. Enter your answer and your work or explanation in the box provided. 15