Comparing Different Functions
Summary 
The students will discuss, represent, and solve a verbal problem involving the choice between two functions. 
Goals 
1. Use diverse representations to solve a problem. 
Materials 
Overheads, White Board or Chart Paper, Handouts 
Keywords 
Compare/Contrast Functions Contextualized Situations Equivalences Full Class Discussion Interpretation of Stories Interpretation of Tables Linear Functions NonLinear Functions Production of Stories Production of Tables Small Group Work 
Activity Plan:
1. Representing the Two Options as Patterns [Whole Class]
Show the problem using the overhead on Page 1 and ask the children to read it.
Ask the children to state what they would prefer.
Ask the children to show on the board which deal is better.
[Since large quantities are involved, it turns out that dots do not provide a convenient representation for the problem. Therefore children should work on numbers to represent the amounts.]
2. Representing the Two Options on a Table [Group Work]
Distribute the handout (Page 2) and display the corresponding overhead (also Page 2) and ask children to complete the two tables and to state, in writing, what they would prefer.
3. Discussion of Handout: Comparing the Two Functions [Whole Class]
Ask a few volunteers to present and discuss their answers. Ask questions such as:
Is one option better than the other? Always?
When is option 1 better than option 2?
When is option 2 better than option 1?
Are there days when the two options will give you the same amount of money gained on that day?
Is there a day when the two options will give you the same total amount of money?
4. Homework (Page 3)
They will solve a problem similar to the one they discussed in class. Note that there is a “take away” condition in Deal F. The problem here is to recognize that Deal F eventually loses to deal H.
Overhead: The Problem
(Page 1)
Your grandmother offers to give you, for the whole year:
 Deal A : 5 cents on each day

Deal B
:
 She gives 0 cents on day 0
 She gives 1 cent on day 1,
 She gives 2 cents on day 2,
 She gives 3 cents on day 3, and so forth.
Which deal would you accept, Deal A or Deal B ? Show that the deal you chose is better than the other one.
Overhead and Handout: Representing the Problem
(Page 2)
Name: _________________________________ Date: ____________
Which deal is better? Explain.
Overhead and Homework
(Page 3)
Name: _________________________________ Date: ____________
Franklin takes Deal F . Explain how his deal works.

Hannah takes Deal H . Explain how her deal works.

Whose Deal is better after 3 days? Explain.

Will Franklin and Hannah ever have exactly the same amount of money? Explain.
