Lesson 3 Growing, Growing Dots Develop Understanding

Jump Start

Which One Doesn’t Belong?

A.

B.

C.

D.

E.

Reason:

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?

Open Up the Math: Launch, Explore, Discuss

pattern of growing dots over four minutes At the beginningAt one minuteAt two minutesAt three minutesAt four minutes

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 minutes?

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 minutes.

Table:

Recursive equation:

Explicit equation:

a blank 17 by 17 grid

Ready for More?

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

pattern of dots growing over 3 minutes At 1 minuteAt 2 minutesAt 3 minutes

Takeaways

Geometric sequence:

Table:

Explicit equation:

Recursive equation:

Graph:

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.

Retrieval

1.

Use the table to find the indicated values.

a.

Find

b.

Find

c.

Find for

d.

If then what is ?

2.

Fill in the table for the given explicit function.