Question

grade 8 unit 2 georgias k - 12 mathematics standards
name:__ date:__
proportional vs nonproportional
diagnostic assessment
the two tables below show how much money terry and shanice have in their piggy banks at the end of each week. they have been saving money for the past 7 weeks. answer the questions that follow about the money they have in their piggy banks.
terrys piggy bank

week number	week 1	week 2	week 3	week 4	week 5	week 6	week 7

shanices piggy bank

week number	week 1	week 2	week 3	week 4	week 5	week 6	week 7

1. is the relationship between weeks and total amount saved proportional for terry and shanice? explain.
2. how much are they saving each week?

a. terry?
b. shanice?

1. the tables show how much money each person has in total at the end of each week. how much money did they have before they started saving each week?

a. terry?
b. shanice?
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Explanation:

Step1: Check proportionality for Terry

For a proportional relationship, the ratio of total saved to week number should be constant. For Terry, in week 1, ratio is $\frac{12}{1}=12$, in week 2, $\frac{20}{2} = 10$. Since ratios are not constant, Terry's relationship is non - proportional.

Step2: Check proportionality for Shanice

For Shanice, in week 1, ratio is $\frac{9}{1}=9$, in week 2, $\frac{18}{2}=9$, and so on. Since the ratio of total saved to week number is always 9, Shanice's relationship is proportional.

Step3: Calculate Terry's weekly savings

Terry's savings from week 1 to week 2 increase by $20 - 12=8$. Savings from week 2 to week 3 increase by $28 - 20 = 8$. So Terry saves $8$ per week.

Step4: Calculate Shanice's weekly savings

Since Shanice has a proportional relationship with a ratio of 9, she saves $9$ per week.

Step5: Find Terry's initial money

Let the initial money be $b$ and the weekly savings be $m$. For Terry, using the equation $y=mx + b$ with $x = 1,y = 12,m = 8$, we have $12=8\times1 + b$. Solving for $b$, we get $b=12 - 8=4$.

Step6: Find Shanice's initial money

Since Shanice has a proportional relationship $y = mx$ (passes through the origin), her initial money is $0$.

Answer:

1. Terry: No, because the ratio of total saved to week number is not constant. Shanice: Yes, because the ratio of total saved to week number is 9 for each week.
2. a. Terry: $8

b. Shanice: $9

1. a. Terry: $4

b. Shanice: $0