Frustrated that Students Don't Know The Multiplication Facts?

Have you've encountered the student who doesn't study the multiplication facts? Or the student who learns one multiplication table and then seemingly forgets most of the facts? Or the student who studies but has a hard time recalling the facts?


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I'm sure you have!  Multiplication is introduced in second grade as counting groups by a certain number (2, 5 and 10).  It is not until third grade that most students are formally introduced to the concept of multiplication through equal groups, arrays, area model, etc.  And for the most part, most students "get" multiplication as a concept.

But there eventually comes a time when the math will get more complicated (and maybe harder).  So as a mathematician, you want to be more efficient.  Learning by memory all the multiplication facts will make you a more efficient mathematician when the math does get more complicated.


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So now we are back to the students and memorizing the multiplication tables.  There are lots of tips and tricks and strategies for memorizing the multiplication facts.  I've even developed resources for my students that give them tips and strategies for remembering the tables.

But the problem with memory is that it needs to be recalled easily if it is to be useful.  So beyond teaching memorization tips and strategies for the multiplication tables, what else can we do so that students learn those facts to be more efficient if they can NOT recall from memory?


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Teach them strategies for fluency!  Let me show you some mental math strategies that you can teach your students to use with memory is not enough!  But first, what exactly is "fluency?"

WHAT IS MULTIPLICATION FLUENCY?


The Common core DOES specify that memorization of the multiplication tables is an expectation.  But that does not mean that meaningless memorization is the route to go.  We want students to understand multiplication conceptually as well as recalling facts.  In the Common Core, there are various terms used:  know from memory, be fluent in, demonstrate fluency, etc.  It even states that "by the end of Grade 3, know from memory all the products of two one-digit numbers."

Now, let us clear up some terms.  To know from memory means to recall from memory a fact.  It is remembering.


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Fluency is more complicated. Fluency is NOT the instant spouting of memorized facts.  Fluency is the combination of recalling from memory OR using patterns and strategies when memory is not enough which then leads the student to use mental math strategies for multiplication.


WHAT STRATEGIES SHOULD I TEACH THEN FOR FLUENCY?


The mental math strategies used to teach multiplication fluency can be grouped into two categories:  Foundational Strategies and Derivative Strategies.

The Foundation Strategies are the first strategies to teach and use the reliable mental math strategies of counting by a number (also known as skip counting), knowing the square numbers, and knowing the Zero and Identity Properties of Multiplication.

The Derivative Strategies build on the Foundation Strategies and teach halving and doubling, adding or subtracting a group, using a nearby square, the patterns for the nines multiplication table, and the Commutative and Distributive Properties of Multiplication.


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The strategies are similar in use to the addition strategies you would teach students learning to add: decomposing a number, doubles, doubles plus one, adding one more, etc.  They are mental math strategies that are explicitly taught and practiced with pencil and paper first before becoming part of the mental math repertoire for adding.  The same applies to these multiplication strategies.  They are explicitly taught and practiced with pencil and paper until the student can use the strategy in mental math.


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In Part 2 of this 3 part blog series, come back to learn more about how to teach the Foundation Strategies.  In Part 3, we'll take a look at the Derivative Strategies.

In the meantime, check out the latest resource in my Teachers Pay Teachers store!  Made explicitly for teaching multiplication fluency strategies!


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