Lesson 7: Practice Problems

Problem 1 From Unit 2 Lesson 11

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 coordinate plane with the origin labeled “O”. The horizontal axis is labeled “mass in grams” and the numbers 0 through 22, in increments of 2, are indicated. The vertical axis is labeled “volume in liters” and the numbers 0 through 180, in increments of 10, are indicated. The point with coordinates 5 comma 28 is indicated.

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

  2. In this situation, what is the meaning of the number you found in part a?

  3. Add at least three more points to the graph above, 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 for mass and for volume.

Problem 2

Explain how the parts of the balanced hanger compare to the parts of the equation.

A balanced hanger diagram with 7 squares on the left and 2 circles and 3 squares on the right with the equation 7 = 2x + 3

Problem 3

Here is a hanger:

Hanger has 5 circles and rectangle labeled 2 on the left, rectangle labeled 17 on the right

  1. Write an equation to represent the hanger.

  2. Draw more hangers to show each step you would take to find . Explain your reasoning.

  3. Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.