Lesson 8
Position, Speed, and Direction
Problem 1
A number line can represent positions that are north and south of a truck stop on a highway. Decide whether you want positive positions to be north or south of the truck stop. Then plot the following positions on a number line.
- The truck stop
- 5 miles north of the truck stop
-
3.5 miles south of the truck stop
Solution
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Problem 2
- How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words “east” and “west”?
- Four people are cycling. They each start at the same point. (0 represents their starting point.) Plot their finish points after five seconds of cycling on a number line
- Lin cycles at 5 meters per second
- Diego cycles at -4 meters per second
- Elena cycles at 3 meters per second
-
Noah cycles at -6 meters per second
Solution
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Problem 3
Find the value of each expression.
- \(16.2 + \text-8.4\)
- \(\frac25 - \frac35\)
- \(\text-9.2 + \text-7\)
- \(\text-4\frac38 - (\text-1\frac14)\)
Solution
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(From Unit 5, Lesson 6.)Problem 4
For each equation, write two more equations using the same numbers that express the same relationship in a different way.
- \(3 + 2 = 5\)
- \(7.1 + 3.4 = 10.5\)
- \(15 - 8 = 7\)
- \(\frac32 + \frac95 = \frac{33}{10}\)
Solution
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(From Unit 5, Lesson 5.)Problem 5
A shopper bought a watermelon, a pack of napkins, and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 5%. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?
Solution
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(From Unit 4, Lesson 10.)Problem 6
Which graphs could not represent a proportional relationship? Explain how you decided.
![Four graphs.](https://cms-im.s3.amazonaws.com/hFE6Dy2vJkEcRBhg2bKMBjYN?response-content-disposition=inline%3B%20filename%3D%227-7.2.E.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.E.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171431Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=15657cb8ceb68acad7845666c58a528b80a1fae538f668481751d3d9cb487700)
Solution
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(From Unit 2, Lesson 10.)