# Reasoning about Solving Equations (Part 1)

Warmup

Activity #1

` Analyze a System in Equilibrium.`

• Study the system below and answer the questions.

(1.) Write a statement about one thing that must be true

(2.) Write a statement about one thing that could be true

(3.) For the same diagram, write a statement about one thing that cannot possibly be true.

In this diagram below, all the squares weigh the same.

(a.) Write a statement about one thing that must be true

(b.) Write a statement about one thing that could be true

(c.) For the same diagram, write a statement about one thing that cannot possibly be true.

Activity #2

` Graphical Interpretation.`

• Study the graphs below and answer the questions that follow.

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.

(1.) What is the constant of proportionality in this relationship?

(2.) In this situation, what is the meaning of the constant of proportionality in this relationship?

(3.) Add at least three more points to the graph below, and label with their coordinates.

(4.) 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.

Activity #3

` Balance a System of Hangers.`

• Study the system of hangers below and answer the questions that follow.

(3.) Find the solution to the equation.

(4.) Use the hanger to explain what the solution means.

(3.) Find the solution to the equation.

(4.) Use the hanger to explain what the solution means.

(3.) Find the solution to the equation.

(4.) Use the hanger to explain what the solution means.

Challenge #1

Here is a balanced hanger where each piece is labeled with its weight.

Here is a balanced hanger where each piece is labeled with its weight.

(1.) Write an equation for the system.

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

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

Challenge #2

Explain how the parts of the balanced hanger compare to the parts of the equation 7 = 2 + 3.

Challenge #3

On each balanced hanger, figures with the same letter have the same weight.

Quiz Time