# Reasoning about Solving Equations (Part 2)

Warmup

How fast can you solve one-step equations? Beat the record here on 10 questions!

Activity #1

Solve Equations Using Diagrams.

Clare drew this diagram to match the equation 2x + 16 = 50, but she got the wrong solution as a result of using this diagram. • Study the diagram and then answer the following questions.

(a.) What value for x can be found using the diagram?

(b.) Show how to fix Clare’s diagram to correctly match the equation.

(c.) Use the new diagram to find a correct value for x.

(d.) Explain the mistake Clare made when she drew her diagram.

Activity #2

Solve Equations Using Diagrams.

Here is a balanced hanger. Each piece is labeled with its weight. • Study the system and answer the questions that follow.

(a.) Assign one of these equations to the hanger:

(b.) Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.

Here is a balanced hanger. Each piece is labeled with its weight.

(a.) Assign one of these equations to the hanger:

(b.) Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.

In this balanced system of hangers, each piece is labeled with its weight.

(a.) Assign one of these equations to the hanger:

(b.) Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.

Activity #3

 Match Equations to the Solution Step. • Match each equation below to a step that will help to find the value of .

Challenge #1

Explain how each part of the equation 9 = 3( + 2) is represented in the hanger below. (i.) (ii.) 9

(iii.) 3

(iv.) + 2

(vi.) 3( + 2)

(vi.) The equation sign.

Challenge #2

Here below is a hanger. (1.) Write an equation to represent the hanger.

(2.) Solve the equation by reasoning about the equation or the hanger. Explain your reasoning.

Challenge #3

Select the word from the following list that best describes each situation.

Quiz Time