Frustrated That Students Don't Know the Multiplication Facts? Part 2 The Foundational Strategies

In the first part of this post, I wrote that we need to teach mental math strategies for multiplication just as we do for addition and subtraction.   But first, students need to learn about the concept of multiplication through arrays, equal groups, and repeated addition.  Then it is time to start memorizing the multiplication facts.

What usually happens is that some students are good at memorizing and can recall them on demand.  But most will learn a multiplication table and then start forgetting it soon thereafter.  Yes, there are ways to improve memorization skills and I do teach my students those tips.  Memorization is part of being fluent in the facts.  As we probably already know, we will have many students who will battle with memorizing all the multiplication facts.

But what if there was a different way to address multiplication fluency?  How? By teaching students multiplication mental math strategies that will help them arrive at the product more efficiently WHEN or IF memory recall fails.

These mental math strategies are first practiced with paper and pencil, but eventually (just like the addition strategies) they begin to use them mentally with more efficiency.  There are two categories of strategies:  Foundational Strategies and Derivative Strategies.

In part 2, let's explore the Foundation Strategies.


The Foundation Strategies must be taught first as they are the foundation for the later Derivative Strategies.

The Foundation Strategies involve basic mental math skills such as skip counting, finding a pattern, knowing the Identity and Zero Properties of Multiplication and learning by memory the all-important square numbers.  Here's a chart comparing the Foundation Strategies for both Addition and Multiplication.

If a student uses these strategies, the student will know about 50 facts on a multiplication chart.  That is a great start to eventually learning the rest and being fluent in the computation of multiplication facts.  The student must have these skills under control in order to advance to the next level of strategies, the Derivative Strategies.

Let's take a look at how the Foundation Strategies can be taught.


Skip counting is one of those mental math skills that begins early in kindergarten.  By second grade children should be able to count by 2s, 5s, and 10s.  Counting by 2s, 5s, and 10s will enable students to quickly learn the multiplication facts for those tables.

Skip counting can be done with songs ( are a great way to motivate kids and keep them engaged while learning.  Counting dimes and nickels is another way to motivate students to learn to count by 5s and 10s.  A game for learning to count by 2s is thinking of things that come in pairs.  How many pairs of eyes are in our class? How many shoes?  There are lots of possibilities!  Games, flash cards, multiples strips, and bookmarks also help with learning to count by 2s, 5s, and 10s.

Teaching and learning the Properties of Multiplication lay the foundation later for Algebra and more advanced math.  So it is important that we explicitly teach these building block properties.  Start with the Identity Property and the Zero Property,

I like to teach these two properties in a fun way by making Zero a Hero and One a Bum.  Zero can obliterate any factor to produce a product of zero while One is a bum because he's lazy and produces a product equivalent to the factor.

Finally, the products of squares (2 x 2, 3 x 3, 4 x 4, etc.) should be learned and memorized.  The square numbers run diagonally along a multiplication chart.  The resulting line of squares produces a mirror image of the other products (3 x 4 = 12 and 4 x 3 = 12). That is why it's important to memorize these square number products.  It reduces the number of facts to learn!

To teach the square numbers is to make cards with all the square factors (1 x 1, 2 x 2, 3 x 3, etc) on one card.  Then on other cards write all the products of those squares.  Then hand out one card to each student.  On a signal, they are to quietly get up and find their partner to match the square factors to the square product.  When they've found their match, the pair stands back to back.  You can practice this multiple times in a 5 - 10 minute period by giving students a different card each time.  You can even time the class to see how fast all the pairs can partner up.

Students should practice the Foundation Strategies until they are proficient because they will be needed later to develop the Derivative Strategies.

In Part 3, we'll take a look at the Derivative Strategies including video of strategy use in action!

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