Lesson 5

Using Negative Numbers to Make Sense of Contexts

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Problem 1

Write a positive or negative number to represent each change in the high temperature.

  1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature.
  2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature.
  3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
  4. 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.

  1. Tyler’s puppy gained 5 pounds.
  2. The aquarium leaked 2 gallons of water.
  3. Andre received a gift of $10.
  4. Kiran gave a gift of $10.
  5. A climber descended 550 feet.

Solution

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Problem 3

Make up a situation where a quantity is changing.

  1. Explain what it means to have a negative change.
  2. Explain what it means to have a positive change.
  3. Give an example of each.

Solution

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Problem 4

  1. On the number line, label the points that are 4 units away from 0.

    A number line with 11 evenly spaced tick marks, the numbers negative 5 through 5 indicated.

  2. 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.

  3. 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.)