# Lesson 2Growing DotsDevelop Understanding

## Learning Focus

Describe a growing pattern with tables, graphs, and equations.

How does the pattern change from one figure to the next?

How can I use a mathematical representation to show how I see a pattern?

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

### 1.

Mark the way you see the pattern growing in the sequence of figures given.

### 2.

Assuming the pattern continues in the same way, how many dots are there at minutes?

### 3.

How many dots are there at minutes?

### 4.

How many dots are there at ? Model the pattern using a table, a graph, and an equation. Your model should indicate how many dots will be in the pattern at , , and . Be sure to show how your solution relates to the picture and how you arrived at your solution.

Table:

Equation:

Create a pattern of dots that increases by each minute, starting with . Write an equation that models your pattern.

## Takeaways

Representations of an arithmetic sequence:

Table:

Graph:

Explicit equation:

Recursive equation:

## Adding Notation, Vocabulary, and Conventions

Arithmetic sequence:

Recursive thinking:

Recursive equation:

Explicit thinking:

Explicit equation:

## Lesson Summary

In this lesson, we modeled a pattern using tables, graphs, equations, and diagrams. We found that this type of relationship is called an arithmetic sequence. We used recursive and explicit ways of thinking about functions, and learned to describe the relationship between inputs and outputs using function notation.

## Retrieval

Identify the pattern in the table and fill in the missing values.

### 1.

 Term Value $1\text{st}$ $2\text{nd}$ $3\text{rd}$ $4\text{th}$ $5\text{th}$ $6\text{th}$ $28$ $37$ $46$

### 2.

 Term Value $1\text{st}$ $2\text{nd}$ $3\text{rd}$ $4\text{th}$ $5\text{th}$ $6\text{th}$ $128$ $64$ $32$

### 3.

Use the given equation to find the -values needed to complete each coordinate pair.