Arrays, Multiplication and Factors

The Magical Minds have a pretty good understanding of what multiplication is.  They know it has to do with groups of the same number.  It is adding the same number over and over again.  It is skip counting.

A 3x4 array of picture books

Building arrays is another way we explore multiplication.  An array is a set of objects placed in rows and columns. Because we know the brain remembers connections, this is one more way we help our brain learn and remember multiplication facts.  This manipulation of objects helps the visual, kinesthetic and naturalistic learners understand multiplication on a deeper and more meaningful level.

How Many Different Arrays Will Make 36?

Arrays also help us understand factors and division.  Our class hasn’t gotten to the division discussion, but we are digging deep into the idea of factoring.  Last week I used a lesson form NCTM‘s site, Illuminations where the third graders created factor posters.  They first built and drew the arrays, and then used a “factor rainbow” to figure out all the numbers we can skip count to get to our product.

An Array Built From a Variety of Classroom Objects

This study of arrays will also come in handy when we begin our measurement unit.  Arrays are simply width and length.

The Different Arrays You Can Build to Make 12

What kinds of arrays do you see in your life?

Do you see arrays in your home, at the store, on the road?


2 responses to “Arrays, Multiplication and Factors

  1. Mathematics at 10:45 p.m. on a Friday night. Let’s see… my schedule is an array. I follow it in order. Does that count? My refrig has arrays. I know where things go accordingly. Oh, the store – definitely. I see it in my mind, so when they change the layout, it drives me crazy. 🙂

  2. I love all you’re done with arrays. How motivated your students appear to be. Congratulations!

    I am retired now but taught for many years. I have some multiplication models I used in my combined first and second grades, but they could be for any age. Each blog gives 4 ways to fully understand the multiplication processes:
    Read more about my math program, including models of addition and subtraction in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success. Included is a web site where programs and activities can be downloaded for use in a classroom. Also, see 7 reviews on

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