Lesson 6

Changing Temperatures

Let's add signed numbers.

Problem 1

Draw a diagram to represent each of these situations. Then write an addition expression that represents the final temperature.

  1. The temperature was \(80 ^\circ \text{F}\) and then fell \(20 ^\circ \text{F}\).
  2. The temperature was \(\text-13 ^\circ \text{F}\) and then rose \(9 ^\circ \text{F}\).
  3. The temperature was \(\text-5 ^\circ \text{F}\) and then fell \(8 ^\circ \text{F}\).

Problem 2

  1. The temperature is -2\(^\circ \text{C}\). If the temperature rises by 15\(^\circ \text{C}\), what is the new temperature?
  2. At midnight the temperature is -6\(^\circ \text{C}\). At midday the temperature is 9\(^\circ \text{C}\). By how much did the temperature rise?

Problem 3

Complete each statement with a number that makes the statement true.

  1.  _____ < \(7^\circ \text{C}\)
  2.  _____ < \(\text- 3^\circ \text{C}\)
  3.  \(\text- 0.8^\circ \text{C}\) < _____ < \(\text- 0.1^\circ \text{C}\)
  4.  _____ > \(\text- 2^\circ \text{C}\)
(From Unit 7, Lesson 1.)

Problem 4

Match the statements written in English with the mathematical statements. All of these statements are true.

A:

The number -15 is further away from 0 than the number -12 on the number line.

B:

The number -12 is a distance of 12 units away from 0 on the number line.

C:

The distance between -12 and 0 on the number line is greater than -15.

D:

The numbers 12 and -12 are the same distance away from 0 on the number line.

E:

The number -15 is less than the number -12.

F:

The number 12 is greater than the number -12.

1:

\(|\text-12| > \text-15\)

2:

\(\text-15 < \text-12\)

3:

\(|\text-15| > |\text-12|\)

4:

\(|\text-12| = 12\)

5:

\(12 > \text-12\)

6:

\(|12| = |\text-12|\)

(From Unit 7, Lesson 5.)

Problem 5

Evaluate each expression.

  • \(2^3 \boldcdot 3\)
  • \(\frac{4^2}{2}\)
  • \(3^1\)
  • \(6^2 \div 4\)
  • \({2^3}-{2}\)
  • \({10^2}+{5^2}\)
(From Unit 4, Lesson 13.)

Problem 6

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality?

  1. The number of wheels on a group of buses.

    number of buses number of wheels wheels per bus
    5 30
    8 48
    10 60
    15 90

  2. The number of wheels on a train.

    number of train cars number of wheels wheels per train car
    20 184
    30 264
    40 344
    50 424
(From Unit 5, Lesson 4.)