Lesson 3 Growing, Growing Dots Develop Understanding

Jump Start

Which One Doesn’t Belong?

$5 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$

$5 (2^{5})$

$5 \cdot 128 {(\frac{1}{2})}^{2}$

$16 (10)$

$20 (2 \cdot 2 \cdot 2)$

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?

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 $5$ 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 $t$ minutes.

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.

Retrieval

1.

Use the table to find the indicated values.

$x$	$f (x)$
$- 2$	$8$
$- 1$	$1$
$0$	$- 6$
$1$	$- 13$
$2$	$- 20$

a.

Find $f (1)$

b.

Find $f (- 2)$

c.

Find $x$ for $f (x) = 1$

d.

If $x = 2$ then what is $f (x - 1)$ ?

2.

Fill in the table for the given explicit function.

$g (x) = {(- 4)}^{x}$

$x$	$g (x)$
$0$
$1$
$2$
$3$
$4$