Lesson 4 Scott’s Workout Solidify Understanding

Learning Focus

Model a sequence using a table, graph, and explicit and recursive equations.

How do I see the change between figures in each representation?

How can I tell if a sequence is arithmetic, geometric, or neither?

How are explicit equations different than recursive equations?

What are the advantages of using an explicit equation versus a recursive equation?

Open Up the Math: Launch, Explore, Discuss

Scott has decided to add push-ups to his daily exercise routine. He is keeping track of the number of push-ups he completes each day in the given bar graph, with day 1 showing he completed push-ups.

After four days, Scott is certain he can continue this pattern of increasing the number of push-ups he completes each day.

Day 1 depicts a stack of 3 unit blocks. Day 2 a stack of 5 unit blocks. Day 3 a stack of 7 unit blocks. Day 4 a stack of 9 unit blocks. 1234

1.

How many push-ups will Scott do on day ?

2.

Model the number of push-ups Scott will complete on any given day. Include a table, a graph, and both recursive and explicit equations.

Table:

Recursive equation:

Explicit equation:

a blank 17 by 17 grid

3.

What type of sequence is your model for the number of push-ups that Scott did? How do you know?

Ready for More?

Aly is also including push-ups in her workout and says she does more push-ups than Scott because she does fifteen push-ups every day. Is she correct? Explain.

Takeaways

Finding the common difference in each representation of an arithmetic sequence:

Table:

Explicit equation:

Recursive equation:

Graph:

Adding Notation, Vocabulary, and Conventions

Recursive notation:

Vocabulary

Lesson Summary

In this lesson, we modeled a real-world situation with a table, graph, and equations, both explicit and recursive. We learned the mathematical notation for writing recursive equations and how to identify the common difference in each of the representations.

Retrieval

Use the explicit function equations below to find the indicated values.

1.

a.

b.

2.

a.

b.

For problems 3–5, use the graph to answer the questions. The graph is a sketch that was created to represent the distance traveled by a biker over time.

coordinate plane where x is labeled time in hours and y axis is labeled distance in miles. There are 3 connected line segments with positive slopes. Time (hours)0.20.20.20.40.40.40.60.60.6Distance (mi)555101010151515000

3.

How far away are they at ?

4.

How long does it take them to reach away?

5.

Which of the variables is represented by ?

Time or distance?

A.

Time

B.

Distance

Find the slope for each representation given.

6.

7.

,

8.