# Lesson 1ET on the RunDevelop Understanding

## Learning Focus

Model patterns with functions.

Compare and contrast linear and quadratic functions.

How can I use representations to model a growing pattern?

What kind of function is the sum of a linear and quadratic function?

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

DeShawn is designing an old-school style video game featuring extraterrestrials invading the earth. He has created the following set of images for his program:

### 1.

Assuming the pattern continues to grow in the same way, use a table, graph, and equation to model the number of unshaded blocks that make up the eyes, arms, and legs in each image.

### 2.

Is the model you made in problem 1 a function? Why or why not?

### 3.

If the model you made in problem 1 is a function, what type of function is it? Explain.

### 4.

For a given image, model the number of blocks in the shaded area that make up the body of the space creature using a table, graph, and equation.

### 5.

What type of function is your model for the number of blocks in the body? How do you know?

### 6.

Now, model the total number of blocks in the given image with a table, graph, and equation.

### 7.

Which representation did you find first, and how did you use your previous work to find it?

### 8.

What type of function is the model for the total number of blocks? How do you know?

### 9.

Examine the equations for each of the three models you have created. What relationships do you see?

### 10.

Examine the graphs for each of the three models you have created. What relationship do you see?

Find a second way to annotate the diagram and write an equation. Then, verify that your new equation is equivalent to your original equation

Linear

Diagram

Equation

Table

Rate of change

Graph

## Lesson Summary

In this lesson, we modeled a quadratic and a linear function and compared representations. We combined a linear function and a quadratic function to examine the representations of the combined function. We noticed that when two functions are added, their corresponding outputs are added to make the new function.

## Retrieval

Draw an area model to represent each set of factors. Then. multiply each set of factors and provide the equivalent expression in standard form.

Standard Form:

### 2.

Standard Form:

Identify the functions in the tables as linear, exponential, quadratic, or neither.