Piggy Bank Patterns: Saving Week by Week

Make two patterns from rules, form ordered pairs, and graph them.

Part 1: Two savings patterns

Ava and Ben both start with empty piggy banks. Each week, Ava adds $3 to her bank and Ben adds $9 to his.

Ava's rule: start at 0, add 3. Ben's rule: start at 0, add 9. Write the next two terms of each pattern.

Ava: 0, 3, 6, ,
Ben: 0, 9, 18, ,

Make ordered pairs from the matching terms: (Ava's total, Ben's total). Fill in the missing numbers.

(0, 0), (3, 9), (6, ), (, 27), (12, )

Compare each of Ben's terms with the matching term in Ava's pattern. Which sentence is true for every ordered pair?

A. Ben's total is always $6 more than Ava's total.B. Ben's total is always 9 times Ava's total.C. Ben's total is always 3 times Ava's total.D. Ben's total is always $3 more than Ava's total.

Ava and Ben keep saving the same way every week.

When Ava has saved $24, how many dollars has Ben saved? $
When Ben has saved $45, how many dollars has Ava saved? $

Part 2: Read the graph

Cora already has $6 in her piggy bank. Dev's bank is empty. Each week, both of them add $2.

Cora's rule: start at 6, add 2. Dev's rule: start at 0, add 2. The graph shows the ordered pairs (Dev's total, Cora's total) for the first 5 terms.

What does point A at (0, 6) show?

A. Dev has $6 and Cora has $0.B. Both Dev and Cora have $6.C. Cora adds $6 each week.D. Dev has $0 and Cora has $6.

Which point shows the week when Dev has $6? Write its letter.
How many dollars does Cora have that same week? $

Look at every point on the graph. How does Cora's total compare with Dev's total?

A. Cora's total is always $6 more than Dev's total.B. Cora's total is always 2 times Dev's total.C. Cora's total is always $2 more than Dev's total.D. Cora's total is always $6 less than Dev's total.

The patterns keep going. Circle every ordered pair (Dev's total, Cora's total) that belongs to the patterns.

Part 3: Make your own graph

Eli adds $4 to his piggy bank each week. Fay adds $2 to hers each week. Both start with $0.

Eli's rule: start at 0, add 4. Fay's rule: start at 0, add 2. Fill in the missing numbers in the ordered pairs (Eli's total, Fay's total).

(0, 0), (4, 2), (8, ), (, 6), (16, )

10.

Plot the 5 ordered pairs (Eli's total, Fay's total) from your list on the graph.

11.

Which sentence is true for every ordered pair (Eli's total, Fay's total)?

A. Fay's total is 2 times Eli's total.B. Eli's total is always $2 more than Fay's total.C. Eli's total is always $4 more than Fay's total.D. Eli's total is 2 times Fay's total.

12.

Gabe says that Ben from Part 1 will have exactly $40 in his piggy bank one week. Is Gabe right? Use Ben's pattern to explain.