IM 7.2.8 Lesson: Comparing Relationships with Equations

Do you see a pattern? What predictions can you make about future rectangles in the set if your pattern continues?

Is the relationship between temperature () and temperature () a proportional relationship? Explain why or why not.

Is the relationship between length (in) to length (cm) a proportional relationship? Explain why or why not.

Complete the table. Then explain how the total edge length of any cube is found.

Explain how the surface area of any cube is found.

Explain how the volume of any cube is found.

Which of these relationships is proportional? Refer back to the tables you completed if you need help.

Explain how you know that relationship is proportional.

Write equations for the total edge length , total surface area , and volume  of a cube with side length .

A rectangular solid has a square base with side length ℓ, height 8, and volume . Is the relationship between  and  a proportional relationship?

A different rectangular solid has length , width 10, height 5, and volume . Is the relationship between  and  a proportional relationship?

Why is the relationship between the side length and the volume proportional in one situation and not the other?

Here are six different equations. Select all of the equations that you predict will represent a proportional relationship.

Do the results in each of the tables change your prediction from the first question? Explain your reasoning.

What do the equations of the proportional relationships have in common?