Intermath | Workshop Support

 Write-up

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 3rd 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, brain-boggling problems.

Author & Contact
Meg Ramsey
mramsey@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials