Illustrative Mathematics Grade 7, Unit 5, Lesson 3: Changing Elevation

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Illustrative Math
Grade 7

Let’s solve problems about adding signed numbers.

The following diagram shows how to add positive and negative numbers in general.
Add Signed Numbers

Draw arrows on a number line to represent these situations:
a. The temperature was -5 degrees. Then the temperature rose 5 degrees.
b. A climber was 30 feet above sea level. Then she descended 30 feet.
What’s the opposite?
a. Running 150 feet east.
b. Jumping down 10 steps.
c. Pouring 8 gallons into a fish tank.

Explore the applet and then answer the questions.
Open Applet

A mountaineer is climbing on a cliff. She is 200 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
a. Complete the table.
b. Select three rows from the table and draw a number line diagram for each. Include the starting elevation, change, and final elevation on each diagram.
A spelunker is down in a cave next to the cliff. If she climbs down deeper into the cave, this will be a negative change. If she climbs up, whether inside the cave or out of the cave and up the cliff, this will be a positive change.
a. Complete the table.
b. Select three rows from the table and draw a number line diagram for each. Include the starting elevation, change, and final elevation on each diagram.
Complete the table and draw a number line diagram to represent each row in this table.

Find the sums.

Find the sum without a calculator.
10 + 21 + 32 + 43 + 54 + (-54) + (-43) + (-32) + (-21) + (-10)

Your teacher will give you a long strip of paper.
Follow these instructions to create a number line.

Fold the paper in half along its length and along its width.
Unfold the paper and draw a line along each crease.
Label the line in the middle of the paper 0. Label the right end of the paper + and the left end of the paper -.
Select two objects of different lengths, for example a pen and a gluestick. The length of the longer object is a and the length of the shorter object is b.
Use the objects to measure and label each of the following points on your number line.
Complete each statement using <, >, or =. Use your number line to explain your reasoning.

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality?
a. Annie’s Attic is giving away $5 off coupons.
b. Bettie’s Boutique is having a 20% off sale.
What is the final elevation if
a. A bird starts at 20 m and changes 16 m?
b. A butterfly starts at 20 m and changes -16 m?
c. A diver starts at 5 m and changes -16 m?
d. A whale starts at -9 m and changes 11 m?
e. A fish starts at -9 meters and changes -11 meters?
One of the particles in an atom is called an electron. It has a charge of -1. Another particle in an atom is a proton. It has charge of +1. The charge of an atom is the sum of the charges of the electrons and the protons. A carbon atom has an overall charge of 0, because it has 6 electrons and 6 protons and -6 + 6 = 0. Find the overall charge for the rest of the elements on the list.
Last week, the price, in dollars, of a gallon of gasoline was . This week, the price of gasoline per gallon increased by 5%. Which expressions represent this week’s price, in dollars, of a gallon of gasoline? Select all that apply.
Add.

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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