Lesson 5
Using Negative Numbers to Make Sense of Contexts
Problem 1
Write a positive or negative number to represent each change in the high temperature.
- Tuesday’s high temperature was 4 degrees less than Monday’s high temperature.
- Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature.
- Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
- Friday’s high temperature was 2 degrees less than Thursday’s high temperature.
Solution
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Problem 2
Decide which of the following quantities can be represented by a positive number and which can be represented by a negative number. Give an example of a quantity with the opposite sign in the same situation.
- Tyler’s puppy gained 5 pounds.
- The aquarium leaked 2 gallons of water.
- Andre received a gift of $10.
- Kiran gave a gift of $10.
- A climber descended 550 feet.
Solution
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Problem 3
Make up a situation where a quantity is changing.
- Explain what it means to have a negative change.
- Explain what it means to have a positive change.
- Give an example of each.
Solution
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Problem 4
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On the number line, label the points that are 4 units away from 0.
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If you fold the number line so that a vertical crease goes through 0, the points you label would match up. Explain why this happens.
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On the number line, label the points that are \(\frac52\) units from 0. What is the distance between these points?
Solution
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(From Unit 7, Lesson 2.)Problem 5
Evaluate each expression.
- \(2^3 \boldcdot 3\)
- \(\frac{4^2}{2}\)
- \(3^1\)
- \(6^2 \div 4\)
- \({2^3}-{2}\)
- \({10^2}+{5^2}\)
Solution
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(From Unit 6, Lesson 12.)