Lesson 1 Something to Talk About Develop Understanding

Jump Start

Which One Doesn’t Belong?” Five functions are given below. Determine which function is different than the others and be prepared to justify your answer.

A.

B.

C.
a pattern of shapes made up of squares Figure 1:Figure 2:Figure 3:Figure 4:
D.

E.

Learning Focus

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

Analyze the type of growth exhibited by a pattern.

What do different representations tell us about a pattern?

Open Up the Math: Launch, Explore, Discuss

Let’s start with a little “Notice and Wonder.” Given the pattern below, what do you notice? What do you wonder?

a pattern of shapes made up of squares Figure 1Figure 2Figure 3Figure 4

Cell phones often indicate the strength of the phone’s signal with a series of bars. The image shows how this might look for various levels of service.

a pattern of shapes made up of squares Figure 1Figure 2Figure 3Figure 4

1.

Assuming the pattern continues, draw the next figure in the sequence.

2.

How many blocks will be in Figure 10?

3.

Examine the sequence of figures and find a rule or formula for the number of tiles in any figure number.

a blank 17 by 17 grid

Ready for More?

Using the same sequence of figures, model the relationship between the perimeter of a figure and the figure number with a table, an explicit equation, and a recursive equation.

Table:

Explicit Equation:

Recursive Equation:

Takeaways

Quadratic Function

Table:

Graph:

Recursive equation:

Next:

Explicit Equation:

Vocabulary

Lesson Summary

In this lesson we investigated a new kind of function called a quadratic function. We modeled a sequence of figures with tables, graphs, and explicit and recursive equations to identify features of quadratic functions and how they appear in each representation.

Retrieval

Rewrite the following expressions using the distributive property.

1.

2.

3.

Identify the rate of change in each representation of a linear function.

4.

5.

Graph of a line passing through (0, 3) and (2, -1) x–5–5–5555y–5–5–5555000