Relating Number Sequences to Graphs

October 26, 2007Ms. Manaktola

Meet Homer Simpson

• Homer’s neighbour’s name is Ned Flanders.

• Ned is going to

Florida for a week, and he has hired Homer to water his plants.

The Options

• Homer has a choice. He can:– Receive $10 each day for

payment, OR

– Receive $5 on the first day, $10 on the second day, $15 on the third day, and so on.

Which option will give Homer the greatest total earnings?

Comparing the Options

•Let’s use tables to compare the two options:–OPTION 1: $10 each day

Day Number

Payment on This Day

Total Earnings

1 $10 $10

2 $10 $20

3 $10 $30

• Can you describe the pattern using words or an algebraic expression?

Comparing the Options

–OPTION 2: $5 on the 1st day, $10 on the 2nd day, $15 on the 3rd day, and so on.

Day Number

Payment on This Day

Total Earnings

1 $5 $5

2 $10 $15

3 $15 $30

• Can you describe the pattern using words or an algebraic expression?

How Can We Compare the Two Options Easily?

Total Earnings For Two Payment Options

$0

$20

$40

$60

$80

$100

$120

$140

0 1 2 3 4 5 6 7

Day Number

To

tal E

arn

ing

s

Option 1 Option 2

Try It Yourself!

• Your task:– In your groups, you will be given a

problem.You must: •Use a table to organize the information•Describe the pattern using words and

algebraic expressions•Graph the patterns using a scatter plot

Group Roles

• Assign roles for each of the group members:– Recorder(s) for

•Table•Algebraic Expression•Graph

– Presenter– Facilitator/Timer