Inquiry Lab: Unit Rates
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1 Work with a partner to solve. 1. Travis drove 129 miles in 3 hours. He drove at a constant speed. How many miles did he drive in 1 hour? Step 1 The bar diagram represents 129 miles. Divide the bar diagram into 3 equal sections to represent 3 hours. Step 2 Label the first section "1 hour." Determine the number of miles Travis drove in 1 hour. Since = 43, Travis drove 43 miles in 1 hour. esolutions Manual - Powered by Cognero Page 1
2 2. Six oranges cost $5.34. How much does 1 orange cost? Step 1 The bar diagram represents $5.34. Label the entire bar diagram "$5.34." Divide the bar diagram into 6 equal sections to represent 6 oranges. Step 2 Label the first section "1 orange." Determine the cost for 1 orange. Since $ = $0.89, the cost of 1 orange is $0.89. esolutions Manual - Powered by Cognero Page 2
3 3. Doug read 231 pages in 7 hours. He read the same number of pages each hour. How many pages did he read in 1 hour? Step 1 The bar diagram represents 231 pages. Label the entire bar diagram "231 pages." Divide the bar diagram into 7 equal sections to represent 7 hours. Step 2 Label the first section "1 hour." Determine the number of pages read in 1 hour. Since = 33, Doug read 33 pages in 1 hour. esolutions Manual - Powered by Cognero Page 3
4 4. Mariah has 72 flowers in 4 vases. She put the same number of flowers in each vase. How many flowers are in 1 vase? Step 1 The bar diagram represents 72 flowers. Label the entire bar diagram "72 flowers." Divide the bar diagram into 4 equal sections to represent 4 vases. Step 2 Label the first section "1 vase." Determine the number of flowers in 1 vase. Since 72 4 = 18, there are 18 flowers in 1 vase. esolutions Manual - Powered by Cognero Page 4
5 Work with a partner to complete the problem. 5. In the bakery, a container of cookies is $4.55 and contains 13 servings. The coins below equal $4.55. Divide the coins into 13 equal groups to determine the cost per serving. Circle each group. Divide the coins in 13 equal groups. There are 13 quarters and 13 dimes. Each group should contain 1 dime and 1 quarter. Circle each group. The cost per serving is $ $0.10, or $ Reason Inductively How does dividing the coins into equal groups help solve the problem? Circling the equal groups gives the cost per serving and counting the 13 circled groups checks my work. esolutions Manual - Powered by Cognero Page 5
6 7. Justify Conclusions The comparison of miles to hours in Activity 1 is 14:2, which can be reduced to 7:1. How is simplifying the ratio similar to division? Simplify the ratio 14:2. Write the ratio as a fraction. Divide by the greatest common factor, which is 2. The simplified ratio is 7:1. Sample answer: When simplifying a ratio, you could divide common factors. Since 14 2 = 7 and 2 2 = 1, the ratio can be simplified to 7:1. 8. Identify Repeated Reasoning Write a rule for how to compare two quantities so that the second quantity has a value of 1 without using a diagram. Sample answer: When the second number is a factor of the first number, divide the first number by the second number. 9. Model with Mathematics Write a real-world word problem in which the unit rate is 6 miles per hour. Sample answer: Robert inline skated 12 miles in 2 hours. He skated at a constant speed. How many miles did he inline skate in 1 hour? 6 miles 10. HOW can you use bar diagrams to compare quantities in real-world situations? Sample Answer: You can use bar diagrams to compare the total number of miles driven on a three-hour trip to the number of miles driven in one hour. esolutions Manual - Powered by Cognero Page 6
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