7 th Grade Math Unit 1: Operations with Rational Numbers

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1 MGSE7.NS.1 7 th Grade Math 1. The thermometer shows the temperature at the North Pole when Katelyn woke up this morning. The temperature rose 36 degrees by noon. What was the temperature at noon? MGSE7.NS.1a 2. In which of these situations would the answer to the question be 0? A. Ryan jumped into a pool from a diving board 12 feet above the water. He sank 12 feet and then swam straight up to the surface of the water. How many feet did Ryan swim? B. A trail begins at an elevation of -50 feet. The trail ends at an elevation of 50 feet. By how many feet does the elevation of the trail change from beginning to end? C. Henry left his house and walked 6 miles directly north. Then he walked 6 miles directly south. At this point, how many miles was Henry from his house? D. The high temperature one day was 3 0 Fahrenheit. The low temperature that day was -3 0 Fahrenheit. What is the difference between the low temperature and the high temperature that day? MGSE7.NS.1b 3. A volcano in the ocean rises approximately 14,000 feet above sea level. Its base is approximately 20,000 feet below sea level. What is the total height of the volcano? Show or explain your work and write your answer in the space provided. feet

2 MGSE7.NS.1c 4. Where would 10 on the number line? A. 10 units to the left of zero B. 10 units to the right of zero C. 10 units from zero D. 10 units to the left and right of zero = A. -9 B. -3 C. 3 D Adam buys 9 gift cards and gives 6 away. How many does he have left? MGSE7.NS.1d (-4) = (-7) = 9. A helicopter is 19 meters above the top of a canyon wall. It goes down 27 meters, passing into the canyon, and then goes up 5 meters. What is the new position of the helicopter relative to the top of the canyon wall?

3 MGSE7.NS.2 7 th Grade Math 10. Which rational numbers when multiplied by - 1 will result in a positive rational number 2 as the product? Why? A. Any negative rational number because the product of two negative rational numbers is a positive rational number. B. Any even rational number because the product of a rational number and an even rational number is a positive rational number. C. Any rational number greater than 1 because the product of two rational numbers 2 takes the sign of the greater rational number. D. Any rational number greater than 0 because the product of a negative rational number and a positive rational number is a positive rational number. MGSE7.NS.2a 11. What is the value of 4.2(46-65)? A B. 798 C D What is product? -8(7-3.2) A B C D A football team loses 7 yards for 4 consecutive plays. What signed number represents the team s total loss of yards on 4 plays? MGSE7.NS.2b 14. Jason and Kenzie are playing a game. Jason s score (J) and Kenzie s score (K) after round 1 are shown on the number line.

4 A. The sum of the absolute value of John s score and the absolute value of Kenzie s score. B. The sum of Jason s score and Kenzie score. C. The absolute value of the difference of Jason s score and Kamira s score. D. The difference between Jason s score and Kenzie s score. MGSE7.NS.2c 15. ( 2 5 )( 3 4 ) = A B. 5 9 C D = A. 3 B. 5 C. 6 D. 7 MGSE7.NS.2d 16. A telephone survey asked 240 people to rate their telephone service. The results are shown in the graph below. Express the fraction of people who answered excellent as a decimal. Show your work.

5 17. How are the numbers ,.05, and 1 ordered from greatest to least? 25 A. 0.05, , 1 25 B. 0.05, 1 25, C , 0.05, 1 25 D , 1 25, 0.05 MGSE7.NS Christa will use of her garden plot for vegetables, with of the vegetable section for tomatoes. What fraction of the whole garden plot will be used for tomatoes? A B. 1 2 C. 8 9 D Tara had 1 5 pounds of dried nuts. She ate 1 pound of dried nuts each day for 6 days. How 8 4 many pounds of dried nuts did Tara have left after 6 days? A. 1 8 B. 7 8 C D Ben wanted to run with his dad during a race. His dad was running a marathon, which has a distance of 26.2 miles. Ben's goal was to run with his dad for of the total distance. However, Ben only was able to run did Ben run? A. 9.3 miles B miles C miles D miles of his goal. How many miles, to the nearest tenth,

6 21. Humberto has toy cars in the following lengths. Which toy car has the GREATEST length? Roadstar SUV Sedan Coupe 4.5 in 4 3 in in 4 1 in 4 A. Roadstar B. SUV C. Sedan D. Coupe 22. During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week? A. $59 increase B. $691 increase C. $691 decrease D. $59 decrease Constructed Response: *Worth 4 points 23. Three pizzas of the same size were purchased for a party. After the guests finished eating pizza, of the first, of the second, and of the third pizzas were leftover. Part A If the leftover pieces are combined, what fraction of one whole pizza remains? Explain how you got your answer. Part B What fraction of all three of the pizzas purchased for the party was eaten? Explain how you got your answer. Part C Only six guests ate pizza at the party. If all of them ate the same amount, what fraction of one pizza did each person eat? Explain how you got your answer.