# Lesson 5 Getting Your Share of the Pie Develop Understanding

## Learning Focus

Identify and create inverse variation functions, tables, and graphs to model real-world situations.

How do I model situations where some fixed amount has to be shared equally among more and more people, such as sharing my birthday cake with more and more of my family and friends?

## Open Up the Math: Launch, Explore, Discuss

Tehani, Taska, and Trevor are planning a picnic to celebrate the completion of their engineering project. Tehani plans to bring three

Tehani, Taska, and Trevor each think there will be too much food for just the three of them, so unbeknown to the others, they have each invited some of their friends.

This picnic scenario contains at least four important questions that can be explored:

**Question 1:** How many inches of submarine sandwich will each person get, depending upon the number of people that attend the picnic? Include the possibility that Tehani shows up with the subs, but no one else, not even Taska and Trevor, make it to the picnic.

**Question 2:** How many ounces of beverage will each person get, depending upon the number of people that attend the picnic? Include the possibility that Taska shows up with the drinks, but no one else, not even Tehani and Trevor, make it to the picnic.

**Question 3:** How much of a whole pie will each person get, depending upon the number of people that attend the picnic? Include the possibility that Trevor shows up with the pies, but no one else, not even Taska and Tehani, make it to the picnic.

**Question 4:** What is the average speed that each of the three friends who live

### 1.

Analyze two or more of these questions using various representations, including tables, graphs, and equations.

### 2.

Based on your explorations, what do all of the four contexts described in the questions have in common?

### 3.

What would be similar in the tables representing each of these four contexts? What would be different?

### 4.

What would be similar in the graphs representing each of these four contexts? What would be different?

### 5.

What would be similar in the equations representing each of these four contexts? What would be different?

### 6.

Each of these contexts describes an inverse variation. What are the defining features of an inverse variation function?

## Ready for More?

Because the scenarios in the task didn’t make sense for input values between

## Takeaways

Key features of inverse variation functions:

## Vocabulary

- inverse variation
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned about inverse variations, functions in which the quantities are said to vary inversely because doubling one quantity cuts the other in half, tripling the quantity cuts the other quantity in thirds, etc.

### 1.

Given:

Find the length of

Begin by proving the relationship between

Show your work.

### 2.

Solve.