Problem Solving

Question

Here the question on my daughter's 4th grade homework assignment:

Sarah is decorating a mosaic board it is 12 inches wide and 16 inches long. Sarah is using square tiles all the same size. What size tiles should Sarah use?

Answer 1

Assuming she has to use tiles with integer sides, there are three solutions: $1\times 1, 2\times 2, 4\times 4$. Most likely the teacher is looking for $4\times 4$.

Answer 2

Although I wouldn't want to overanalyze a 4th grade homework question, I have to say this is a little ambiguous. I assume the tiles are of integer sides, and that you're supposed to fill the board completely without leaving any gaps, in which case there's one obvious solution: use squares of side length $1$ inch. Maybe they're looking for the biggest possible size?

You might encourage your daughter to look for all square sizes that would work (there's only three). Note that for a side length to work, it has to divide both $12$ and $16$, so you're looking for common divisors of $12$ and $16$. It might be instructive for her to look for all of the common divisors of $12$ and $16$. This shouldn't be hard for her: just write down the numbers between $1$ and $12$ and test each one in turn.

Answer 3

Any common divider of 12 and 16 would do.

Common dividers are 1, 2 & 4.

I'd go with 4. This sounds like heading towards GCD concepts.