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.


Balanced hanger, left side, 7 blue squares, right side, 2 red circles, 3 blue squares.

Problem 2

For the hanger below:

  1. Write an equation to represent the hanger.
  2. Draw more hangers to show each step you would take to find \(x\). Explain your reasoning.
  3. 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.

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.


  1. What value for \(x\) can be found using the diagram?
  2. Show how to fix Clare’s diagram to correctly match the equation. 
  3. Use the new diagram to find a correct value for \(x\).
  4. Explain the mistake Clare made when she drew her diagram.
(From Unit 3, Lesson 3.)