Square Mural Problem


Credit Where Credit is Due:

Thanks, Mr. Brian Errey, for all your help trouble-shooting and putting this problem together.


Number Sense 8m15 Determine common factors and common multiples using the prime factorization of numbers

Measurement 7m1 Report on research into real-life applications of area measurements (This is a grade 7 overall expectation)

Act I

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1. What are the dimensions of the smallest square mural you can create using copies of the original rectangle?

2. Will the mural fit in the wall space provided?

Act II

3. What information do you need to get an answer?

Only provide the following information to a student if s/he asks for it.

Information 1

Information 2

Information 3

Information 4


4. Here's one possible solution.


5. If you answered yes: How many sheets (not squares, but the big red, green, beige, pink and yellow sheets that you cut into the smaller squares) will you need, in order to make the entire mural?

6. If you answered no: Think of the dimensions of the individual squares used to create this entire mural. What size of little squares gives you the biggest square mural you can fit?

It isn't enough just to say yes or no. Students must be able to convince others of how they know.