##### Child pages
• Comparing Different Functions

# 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 Non-Linear Functions Production of Stories Production of Tables Small Group Work

### Activity Plan:

#### 1. Representing the Two Options as Patterns [Whole Class]

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]

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.

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.