Math CentralQuandaries & Queries


Question from Vickie, a parent:


I am not sure how to help my son figure out one of his math journal problems.
He is in third grade and this just seems a bit much for him.
They have only been working on multiplication for about 3 weeks
and just went back to school from Christmas break.
Their other homework has been about arrays,
so I guess his teacher wants this answered in some sort of array.
Unfortunately I'm not sure.

The problem states: If you have 24 chairs find the total number
of ways the chairs can be arranged.

Thank you in advance for your help.


Hi Vickie,

The (perhaps unwritten) assumption is that they will be arranged in a rectangular array, N equal rows of M chairs. So for six chairs the answer would be

1 x 6    1x6


2 x 3    2x3


3 x 2    3x2

6 x 1    6x1

-that is, four ways. At this level a certain amount of experiment [can we put them in rows of five? Let's try...] is encouraged. Informal looking for patterns is also good.

You should be able to see how this ties in with factoring, equal division of candies, etc.

Good Hunting!



I would have your son experiment, as RD says, with physical objects. Perhaps 24 pennies or candies or Cheerios. The task is then to arrange them in rows so that each row has the same number of "chairs". When you find an arrangement (array) record it by writing it as RD did, (the number of rows) x (the number of columns).



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