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.
Problem 1
Explain how the parts of the balanced hanger compare to the parts of the equation.
\(7=2x+3\)
![Balanced hanger, left side, 7 blue squares, right side, 2 red circles, 3 blue squares.](https://cms-im.s3.amazonaws.com/inMChNH4d532hq7vWJYqCSYf?response-content-disposition=inline%3B%20filename%3D%227-7.6.B1.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.B1.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2f19e1efaab95cf207ad4f6b44576c8129bc59faa6acbbe1f2569c9742ed08a8)
Problem 2
For the hanger below:
- Write an equation to represent the hanger.
- Draw more hangers to show each step you would take to find \(x\). Explain your reasoning.
- Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.
![Balanced hanger, left side, 5 circles labeled x, 1 square labeled 2, right side, rectangle labeled 17.](https://cms-im.s3.amazonaws.com/JLQRDzvTPpAjLUa1j7Jo33pS?response-content-disposition=inline%3B%20filename%3D%227-7.6.B1.newPP.04.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.B1.newPP.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8dfdd2362e3b2ca0840c11f9a8188cff4267cbc928df5aa3fda6677c5ae9098d)
Problem 3
Clare drew this diagram to match the equation \(2x+16=50\), but she got the wrong solution as a result of using this diagram.
![A tape diagram partitioned into three different sized rectangles, labeled 2, x and 16. The total length of the bar is labeled 50.](https://cms-im.s3.amazonaws.com/56WU7UHC7TvuswRthhztpiBy?response-content-disposition=inline%3B%20filename%3D%227-7.6.B.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.B.PP.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f4408d3cc0fb6a03e4d94d45e758a2d7904923016b04cd8fd08043fe4f0f857e)
- What value for \(x\) can be found using the diagram?
- Show how to fix Clare’s diagram to correctly match the equation.
- Use the new diagram to find a correct value for \(x\).
- Explain the mistake Clare made when she drew her diagram.