Lesson 6
Per Each
Problem 1
A scooter travels 30 feet in 2 seconds at a constant speed.
![Double number line. Distance, feet. Time, seconds.](https://cms-im.s3.amazonaws.com/zaoMAu7son8Eb5yGxr9rz6Yr?response-content-disposition=inline%3B%20filename%3D%226-6.2.C4.PP.Image.Rev.0101.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C4.PP.Image.Rev.0101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033056Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=709dec2c077ba7b1019da2b182406d03859d48db4c17718942449c764d5e3090)
- What is the speed of the scooter in feet per second?
- Complete the double number line to show the distance the scooter travels after 1, 3, 4, and 5 seconds.
- A skateboard travels 55 feet in 4 seconds. Is the skateboard going faster, slower, or the same speed as the scooter?
Solution
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Problem 2
The double number line shows that 4 pounds of tomatoes cost \$14. Draw tick marks and write labels to show the prices of 1, 2, and 3 pounds of tomatoes.
![Double number line. Top number line labeled “pounds of tomatoes.” The bottom number line labeled “cost in dollars.”](https://cms-im.s3.amazonaws.com/qcLDEPQfFvupLH4985UNc6eG?response-content-disposition=inline%3B%20filename%3D%226-6.2.C.PP_Image_13.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C.PP_Image_13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033056Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4f665616420ab42b0cae7c6fc0ddad8f8b985c619ad3fa4595f8cf30d2dacf52)
Solution
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Problem 3
4 movie tickets cost $48. At this rate, what is the cost of:
- 5 movie tickets?
- 11 movie tickets?
Solution
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Problem 4
Priya bought these items at the grocery store. Find each unit price.
- 12 eggs for $3. How much is the cost per egg?
- 3 pounds of peanuts for $7.50. How much is the cost per pound?
- 4 rolls of toilet paper for $2. How much is the cost per roll?
-
10 apples for $3.50. How much is the cost per apple?
Solution
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Problem 5
Han ran 10 meters in 2.7 seconds. Priya ran 10 meters in 2.4 seconds.
- Who ran faster? Explain how you know.
- At this rate, how long would it take each person to run 50 meters? Explain or show your reasoning.
Solution
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Problem 6
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice.
- Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
- How should Kiran change the quantities that he used so that his smoothie tastes just like Clare's?
Solution
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(From Unit 2, Lesson 2.)Problem 7
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios.
- \(5:1\) and \(15:3\)
- \(25:5\) and \(10:2\)
- \(198:1,\!287\) and \(2:13\)
Solution
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(From Unit 2, Lesson 3.)