# Lesson 3 Growing, Growing Dots Develop Understanding

## Jump Start

Which One Doesn’t Belong?

## Learning Focus

Model a sequence of figures using tables, graphs, and equations.

How can I label the diagram to show how I see the pattern?

How can I use mathematical representations to show how I see the pattern changing?

Technology guidance for today’s lesson:

- Basic Calculations — Exponents: Casio ClassPad Casio fx-9750GIII

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

### 1.

Describe and label the pattern of change you see in the given sequence of figures.

### 2.

Assuming the sequence continues in the same way, how many dots are there at

### 3.

Model the sequence of figures using a table, graph, and recursive and explicit equations to show how many dots are in the pattern at

Table:

Recursive equation:

Explicit equation:

## Ready for More?

Write the recursive and explicit equations to model the pattern if the diagram were relabeled this way:

## Takeaways

Geometric sequence:

Table:

Explicit equation:

Recursive equation:

Graph:

## Vocabulary

## Lesson Summary

In this lesson, we modeled a growing pattern using tables, graphs, and equations. We learned about a new type of function, a geometric sequence that has a common ratio between terms.

### 1.

Use the table to find the indicated values.

#### a.

Find

#### b.

Find

#### c.

Find

#### d.

If

### 2.

Fill in the table for the given explicit function.