Printable multiplication arrays
Four pictures, each set out in equal rows. The child writes how many rows there are, how many are in each row, and the multiplication fact those two numbers make. Print a clean PDF in seconds.
Array size
Up to 12 prints the largest pictures and suits a child meeting arrays for the first time. Up to 24 uses taller and wider arrangements. The two sheets share no array, so a child can work both.
Orientation
Rows and arrays
Each picture is set out in equal rows. Write how many rows there are, how many are in each row, and the multiplication fact.
Quick Math Sheets
How to use it
Look at one picture and count down the side first: that is the number of rows. Then count along a single row, not the whole picture, to get how many are in each row. Those two numbers go straight into the multiplication fact underneath, and the answer is how many objects there are altogether. A child who counts every object one by one will get the right total, but the point of the sheet is to notice that the rows make counting them unnecessary.
Why rows matter
An array is what multiplication actually means. Three rows of four is not a fact to memorize before it is a picture to see, and once a child has seen it, the times table stops being an arbitrary list. This is also where the commutative property becomes obvious rather than abstract: turn the page ninety degrees and three rows of four becomes four rows of three, with not a single object added or taken away.
No square arrays
None of the pictures is a square, and that is deliberate. On a four by four arrangement a child can write four in both blanks and be correct without ever having worked out which number came from the rows and which came from the columns. Keeping every array a different shape in each direction forces the reading that the sheet is actually teaching.
Practice the facts
Once arrays make sense, the facts they produce are worth having nearby. The printable multiplication chart is the reference for looking one up, and fact family triangles take the same three numbers and turn them into the matching division facts. For written practice, multiplication worksheets cover facts through multi-digit work, or browse all printables.
A simple routine