Gretel’s Goldfish
Problem Statement
Hansel has goldfish that
quadruple, or become four times as many, every month. Gretel has goldfish
that increase by 20 every month. Right now, Hansel has 4 goldfish and
Gretel has 128 goldfish. In how many months will they have the same number
of goldfish? Show how you arrived at your answer.
Problem setup
I will need to look at the
different numbers of fishes for Hansel and for Gretel, for several
different months, and compare them until I find what month they will have
the same number of fish.
Plans to
Solve/Investigate the Problem
The first thing I will do is to
multiply Hansel’s 4 fish X 4 for 4 months; a nice round number. Then I will figure out Gretel’s
fish for 4 months and compare the two totals.
Investigation/Exploration
of the Problem
Month

Hansel

Gretel

1

16

148

2

64

168

3

256

188

4

1024

208

I noticed that between month 2
and 3, Hansel’s fish begin to grow much faster than Gretel’s. I did an Excel spreadsheet,
comparing week by week the numbers for Hansel and Gretel’s fish,
between Week 8 and Week 12.
Week

Hansel

Gretel

1

4

128

2



3



4

16

148

5


153

6


158

7


163

8

64

168

9

112

173

10

160

178

11

208

183

12

256

188

By doing this, I discovered
that between week 10 and week
11, Hansel and Gretel’s fish should be the same number. Probably about 2 ½ month; so
in the 3^{rd} month, they will have the same number of fish.
Extensions of the Problem
Now that I’ve learned how to do
Excel better, I can use it to help me figure out more hard to solve,
brainboggling problems.
Author & Contact
Meg Ramsey
mramsey@rockdale.k12.ga.us
Link(s) to resources, references, lesson plans, and/or other
materials
Link 1
Link 2
U
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