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The Language of Multiplication

Multiplication (2 groups of 3)Recently, my kindergartener, Lilly,  came home and declared, “I’m bad at times.”  Let me clarify a couple of things.  First, when she said that, she didn’t mean that she was occasionally evil.  She meant she was bad at multiplication.  Second, we don’t do, “I’m bad at ___.” in our house.  We work pretty hard to send the message that we’re all capable of most things if we only apply ourselves.  Lilly knows this, but as the youngest kid in her class, and likely her entire grade district-wide, she’s constantly comparing herself to classmates who are much older and wiser.  She’ll tell you all day long, “You just have to practice, practice, practice.”  And at times, she actually believes this.  Over spring break she was determined to skip a bar on the monkey bars and by jove, she did it.  Other times, she needs some convincing.

So your first thought at a kindergartener declaring her deficiency in multiplication might be, “Why are they doing multiplication in kindergarten?”  I assure you, they’re not (at least not formally).  This statement came from a classmate, whose older brother just went through third grade.  Third grade is the year students are supposed to know from memory (and by the end of the year) the product of all single digit numbers.  Needless to say, her classmate spent a year listening to his brother complete math homework and picked up a little – perhaps a lot – here and there.

My first thought was, “You’re not bad at times.  You’re using the wrong language.”  Most of us learned our multiplication facts from drill and practice.  We learned tricks to remember the nines and were always stumbling over the sevens and eights.  No one bothered to explain the meaning behind multiplication until after we’d memorized our facts.  Turns out, if we do the reverse, understand before we practice, memorization comes a whole lot faster.  And better.  Part of understanding is knowing what “times” means.  I sat my daughter down and explained that “times” just meant “groups of”.  We practiced this way:

Me: “2 times 3 just means 2 groups of 3.”Multiplication (4 groups of 2)

Lilly: “Oh, I know that!  That’s just 3+3.  It’s 6!”

Me: “Let’s try another one.  4 times 2.”

Lilly: “4 times 2 . . . so that’s four groups of 2.  So 2, 4, 6, 8!”

When multiplication language is understood, especially the language of operations, competency and fluency increases.  Learning multiplication requires an understanding of the language (times, factor, product, etc.) and an ability to think flexibly about numbers.  Most kids are comfortable multiplying by 1, 2, 5, and 10.  That’s because they all have had practice skip counting in these number patterns.  If they’ve had good instruction, they understand that counting by 2s is just adding 2 each time.  This connects to student understanding of multiplication as repeated addition.  The other facts anchor around knowing these facts and are based on students being able to decompose (break) numbers into parts.  There are classroom appropriate posters that are useful for parents to use as references for helping their children at home too.

Practice with multiplication strategies and work with word problems allows third graders to develop an understanding of multiplication, which in turn supports recall of “basic facts”.  Because kids have had so much practice developing a foundation of multiplication in K-2 in looking for patterns, working with repeated addition and arrays, they are able to more quickly develop fluency for multiplication.

If your little one isn’t yet learning multiplication, don’t hesitate to pose questions that support multiplicative thinking.  As I was writing this post, I took a break to put my daughter to bed.  We finished reading The Lion the Witch and the Wardrobe earlier in the day.  At bedtime, Lilly asked how many pages we’d read.  I wasn’t sure, and since I was in the middle of writing this post, I couldn’t help but respond, “I’m not sure how many pages but, if we read 4 chapters and each chapter was about 9 pages, how many pages do you think?”  She said, “So 9+9+9+9 . . .”  She understood the situation and was thinking multiplicatively.  I’m assuming, with more conversations like this, she’ll be ready to go when she gets some formal instruction in multiplication in three years!

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