What's the Deal with Multiplication Arrays?

Let’s talk multiplication. I’ve seen people losing their minds over seeing children using the multiplication array on the bottom, and there is no reason.

If we go back to the early grades multiplication is often introduced through grouping. Children concretely group things to multiply. “How many marbles are there if we have four groups of three marbles?” Eventually we want to move to more representational and abstract approaches, and like with subtraction, we want to build off of the heavy place value emphasis from Kindergarten and First Grade. That’s where that multiplication array comes in. Children know that 47 is 40 + 7 and that 23 is 20 + 3. Multiplying each of the pieces is much easier since they have worked with single digit “times tables” and multiplying by 10s is also easy. And the four numbers can be easily added. 40 x 20 = 800, 40 x 3 = 120, 7 x 20 = 140, 7 x 3 = 21, 800 + 120 + 140 + 21 = 1,081. Comparing to the standard algorithm at the top, the square array is the same approach, but it is easier for the children to see what is actually happening. It’s a conceptual stepping stone to the standard algorithm so they can make sense of multi-digit multiplication using place value.

The arrays also help build mental math, which as I said before, is an important goal. With a problem like 25 x 12, starting with the array allows them to get to point of doing something like “25 x 12 is 25 x 10 and 25 x 2. 25 x 10 = 250 and 25 x 2 = 50. 250 + 50 = 300.” Again, looks like a lot written, but takes bit a few second in your head. The array visual helps improve mental multiplication.

Lastly, progression in math is important. Eventually students get to algebra and “more abstract” math in later grades. Arrays are used to multiply polynomials, for example, as in the last pic. Having already seen and used arrays for multiplication allows the student to make a conceptual connection to the algebra. They see multiplication is the same in all facets. We’re building coherence.

These arrays are not new math or a new way to multiply. They are a tool for understanding and visualizing the concept of multiplying and for building mental math. (And they’ve actually been around a long time.)