Lesson 2 Growing Dots Develop 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.

At the beginning there is one dot. At one minute four dots are shown around the beginning dot. At two minutes four additional dots are shown around the group of previous dots At the beginningAt one minuteAt two minutes

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:

a blank 17 by 17 grid

Ready for More?

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:

Function of t equals 4 times t plus 1 written with symbols. Function of t is circled and labeled as the output. OutputInput

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

2.

Term

Value

3.

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