Illustrative Mathematics Grade 7, Unit 5, Lesson 1: Interpreting Negative Numbers

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Illustrative Math
Grade 7

Lesson 1: Interpreting Negative Numbers

Let’s review what we know about signed numbers.

Illustrative Math Unit 7.5, Lesson 1 (printable worksheets)

Lesson 1 Summary

The following diagram shows how to use positive and negative numbers to describe temperature and elevation.

Lesson 1.1 Using the Thermometer

Here is a weather thermometer. Three of the numbers have been left off.

1. What numbers go in the boxes?
2. What temperature does the thermometer show?

• See Video for Whole Lesson

Lesson 1.2 Fractions of a Degree

1. What temperature is shown on each thermometer?
2. Which thermometer shows the highest temperature?
3. Which thermometer shows the lowest temperature?
4. Suppose the temperature outside is -4°C. Is that colder or warmer than the coldest temperature shown? How do you know?

Lesson 1.3 Seagulls Soar, Sharks Swim

Here is a picture of some sea animals. The number line on the left shows the vertical position of each animal above or below sea level, in meters.

1. How far above or below sea level is each animal? Measure to their eye level.
2. A mobula ray is 3 meters above the surface of the ocean. How does its distance from the surface of the ocean compare to the vertical distance from the eyes of:
   The jumping dolphin?
   The flying seagull?
   The octopus?
   
3. An albatross is 5 meters above the surface of the ocean. How does its distance from the surface compare to the vertical distance from the eyes of:
   The jumping dolphin?
   The flying seagull?
   The octopus?
   
4. A clownfish is 2 meters below the surface of the ocean. How does its distance from the surface compare to the vertical distance from the eyes of:
   The jumping dolphin?
   The flying seagull?
   The octopus?
   
5. The vertical distance of a new dolphin from the dolphin in the picture is 3 meters. What is its distance from the surface of the ocean?

Are you ready for more?

The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of the earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?

• Show Answer

  The distance from the sea floor below the north pole to the center of the earth is 3,949 - 2.7 = 3,946.3 miles.
  The distance from the elevation of the south pole to the center of the earth is 3,949 + 1.7 = 3,950.7 miles.
  The distance from a person standing on the south pole from a submarine at the sea floor below the north pole is 3,946.3 + 3,950.7 = 7897 miles.

Lesson 1 Practice Problems

1. It was -5°C in Copenhagen and -12°C in Oslo. Which city was colder?
   
2. a. A fish is 12 meters below the surface of the ocean. What is its elevation?
   b. A sea bird is 28 meters above the surface of the ocean. What is its elevation?
   c. If the bird is directly above the fish, how far apart are they?
   
3. Compare using >, =, or <.
   a. 3 _____ -3
   b. 12 _____ 24
   c. -12 _____ -24
   d. 5 _____ -(-5)
   e. 7.2 _____ 7
   f. -7.2 _____ -7
   g. -1.5 _____ -3/2
   h. -4/5 _____ -5/4
   i. -3/5 _____ -6/10
   j. -2/3 _____ 1/3
   
4. Han wants to buy a $30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold the day of the game, with a markup of 200%. How much should Han expect to pay for the ticket if he buys it the day of the game?
   
5. A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
   a. Find a mixture that will make the same shade of green but a smaller amount.
   b. Find a mixture that will make the same shade of green but a larger amount.
   c. Find a mixture that will make the different shade of green that is bluer.
   d. Find a mixture that will make the different shade of green that is more yellow.
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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