The tables below show the number of jumping jacks completed after a given period of time in minutes.

Question

Kimberly

Time (min) # Jumping Jacks
3 28
8 58
12 82
16 106
Katrina

Time (min) # Jumping Jacks
2 16
5 40
12 96
20 160


(3 points)
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The person that did the most jumping jacks initially before the time started
The person doing the most jumping jacks per minute
The person showing a proportional relationship between time and # of jumping jacks

Answer 1

To evaluate the data provided, let's analyze both Kimberly's and Katrina's performance in terms of the criteria given.

1. The person that did the most jumping jacks initially before the time started:

   • In the given data, we don't have an "initial" count before the time started for either person. However, looking at the earliest time provided for each:
     • Kimberly does 28 jumping jacks at 3 minutes.
     • Katrina does 16 jumping jacks at 2 minutes.
   • Answer: Kimberly (28 jumping jacks at 3 minutes is higher than Katrina's 16 at 2 minutes)

2. The person doing the most jumping jacks per minute:

   • Let's calculate the jumping jacks per minute for both:
     • Kimberly:
       • From 3 to 8 minutes: (58 - 28) / (8 - 3) = 30 / 5 = 6
       • From 8 to 12 minutes: (82 - 58) / (12 - 8) = 24 / 4 = 6
       • From 12 to 16 minutes: (106 - 82) / (16 - 12) = 24 / 4 = 6
       • Kimberly has a consistent rate of 6 jumping jacks per minute.
     • Katrina:
       • From 2 to 5 minutes: (40 - 16) / (5 - 2) = 24 / 3 = 8
       • From 5 to 12 minutes: (96 - 40) / (12 - 5) = 56 / 7 = 8
       • From 12 to 20 minutes: (160 - 96) / (20 - 12) = 64 / 8 = 8
       • Katrina has a consistent rate of 8 jumping jacks per minute.
   • Answer: Katrina (8 jumping jacks per minute is higher than Kimberly's 6)

3. The person showing a proportional relationship between time and # of jumping jacks:

   • A proportional relationship means that as time increases, the number of jumping jacks increases at a consistent rate (i.e., a constant ratio).
   • Both individuals show a linear relationship, but we can check if they have constant rates:
     • Kimberly has different rates but they are consistent (6 jumping jacks/min).
     • Katrina has constant rates of 8 jumping jacks/min.
   • To determine if one is more proportional, we can consider factors like whether doubling time results in doubling jumping jacks:
     • For Kimberly:
       • There’s no simple direct proportionality; the total jumping jacks do not double consistently as time doubles.
     • For Katrina:
       • At 2 minutes (16 jumping jacks) vs. 4 minutes (32 jumping jacks), it doubles,
       • At 5 minutes (40 jumping jacks) vs. 10 minutes (80 jumping jacks), it doubles
       • At 12 minutes (96 jumping jacks) vs. 24 minutes (192 jumping jacks), it doubles.
   • Answer: Katrina (She demonstrates a consistent proportional relationship as shown in the analysis above)

In summary:

1. Kimberly (most jumping jacks initially)
2. Katrina (most jumping jacks per minute)
3. Katrina (shows a proportional relationship)