Lesson 7: Reasoning about Solving Equations (Part 1)
Let’s see how a balanced hanger is like an equation and how moving its weights is like solving the equation.
Illustrative Math Unit 7.6, Lesson 7 (printable worksheets)
Lesson 7 Summary
The following diagram shows how a balanced hanger is like an equation and how moving its weights is like solving the equation.
Lesson 7.1 Hanger Diagrams
In the two diagrams, all the triangles weigh the same and all the squares weigh the same.
For each diagram, come up with . . .
- One thing that must be true
- One thing that could be true
- One thing that cannot possibly be true
Lesson 7.2 Hanger and Equation Matching
On each balanced hanger, figures with the same letter have the same weight.
- Match each hanger to an equation. Complete the equation by writing x, y, z, or w in the empty box.
- Find the solution to each equation. Use the hanger to explain what the solution means.
Lesson 7.3 Use Hangers to Understand Equation Solving
Here are some balanced hangers where each piece is labeled with its weight. For each diagram:
- Write an equation.
- Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
- Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Are you ready for more?
When you have the time, visit the site https://solveme.edc.org/Mobiles.html to solve some trickier puzzles that use hanger diagrams like the ones in this lesson. You can even build new ones. (If you want to do this during class, check with your teacher first!)
Lesson 7 Practice Problems
- There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. If the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below.
a. What is the constant of proportionality in this relationship?
b. In this situation, what is the meaning of the number you found in part a?
c. Add at least three more points to the graph above, and label with their coordinates.
d. Write an equation that shows the relationship between the mass of a sample of helium and its volume. Use m for mass and v for volume.
- Explain how the parts of the balanced hanger compare to the parts of the equation.
7 = 2x + 3
- Here is a hanger:
a. Write an equation to represent the hanger.
b. Draw more hangers to show each step you would take to find . Explain your reasoning.
c. Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.
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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