Unit 5, Lesson 1
Interpreting Negative Numbers
Grade 7
1.1
Warm-up
Four vertical thermometers measured in degrees Celsius. There are 16 evenly spaced tick marks and starting from the bottom of the thermometer, negative 5 is on the first tick mark, zero on the sixth, 5 on the eleventh, and 10 on the sixteenth. The first thermometer is shaded starting from the bottom of the thermometer to the tenth tickmark. The second thermometer is shaded starting from the bottom of the thermometer to the third tickmark. The third thermometer is shaded starting from the bottom of the thermometer to between the eleventh and twelfth tickmark. The fourth thermometer is shaded starting from the bottom of the thermometer to between the fourth and fifth tickmark.
1.2
Activity
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What temperature is shown on each thermometer?
Four vertical thermometers measured in degrees Celsius. There are 16 evenly spaced tick marks and starting from the bottom of the thermometer, negative 5 is on the first tick mark, zero on the sixth, 5 on the eleventh, and 10 on the sixteenth. The first thermometer is shaded starting from the bottom of the thermometer to the tenth tickmark. The second thermometer is shaded starting from the bottom of the thermometer to the third tickmark. The third thermometer is shaded starting from the bottom of the thermometer to between the eleventh and twelfth tickmark. The fourth thermometer is shaded starting from the bottom of the thermometer to between the fourth and fifth tickmark. - Which thermometer shows the highest temperature?
- Which thermometer shows the lowest temperature?
- Suppose the temperature outside is . Is that colder or warmer than the coldest temperature shown? Explain your reasoning.
1.3
Activity
Here is a picture of some sea animals. The number line on the left shows the vertical position, in meters, of each animal above or below sea level.
- How far above or below sea level is each animal? Measure to their eye level.
- A mobula ray is 3 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:
- An albatross is 5 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:
- A clownfish is 2 meters below the surface of the ocean. How does its vertical position compare to the height or depth of:
- The vertical distance between a new dolphin and the dolphin in the picture is 3 meters. What is the new dolphin’s distance from the surface of the ocean?
A graph. Vertical axis is labeled vertical position, in meters. 5 tick marks. Scale from negative 15 to 15, by 5s. Horizontal axis has no label or scale. Seagull is at 10. Dolphin is at 3. Penguin is at 0. Shark is at negative 3. Fish is at negative 7. Octopus is at negative 10.
The jumping dolphin?
The flying seagull?
The octopus?
The jumping dolphin?
The flying seagull?
The octopus?
The jumping dolphin?
The flying seagull?
The octopus?
Student Lesson Summary
We can use positive numbers and negative numbers to represent temperature and elevation.
When numbers represent temperatures, positive numbers indicate temperatures that are warmer than zero and negative numbers indicate temperatures that are colder than zero. This thermometer shows a temperature of -1 degree Celsius, which we write .
A thermometer positioned horizontally and with the bottom of the thermometer on the left, is labeled “degrees Celsius.” There are 4 evenly spaced large tick marks. Starting on the left, the large tick marks are labeled negative 5, 0, 5, and 10. Between each large tick mark, there are 4 evenly spaced small tick marks. The thermometer is shaded, starting from the left, up to negative 1.
When numbers represent elevations, positive numbers indicate positions above sea level and negative numbers indicate positions below sea level.
We can see the order of signed numbers on a number line.
A number is always less than a number to its right. So .
We use absolute value to describe how far a number is from 0. The numbers 15 and -15 are both 15 units from 0, so and . We call 15 and -15 opposites. They are on opposite sides of 0 on the number line but the same distance from 0.
A negative number is a number that is less than 0.
A positive number is a number that is greater than 0.