Have you’ve encountered the student who doesn’t study the multiplication facts? What about the student who learns one multiplication table and then seemingly forgets most of the facts? Then there is the student who studies but has a hard time recalling the facts?
I’m sure you have! We introduce multiplication in second grade as counting groups by a certain number (2, 5 and 10). In third grade, we formally introduce the concept of multiplication through equal groups, arrays, the area model, etc. And for the most part, most students “get” multiplication as a concept.
Eventually, there comes a time when math will get more complicated. Consequently, as a mathematician, you want efficiency. One way is to memorize the multiplication facts.
Should Students Just Memorize the Multiplication Facts?
So now we are back to the students and memorizing the multiplication facts. 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 multiplication facts.
But the problem with memory is that for it to be useful, you should be able to recall easily. So beyond teaching memorization tips for the multiplication tables, what else can we do? How can we ensure students learn those facts when they can NOT recall from memory?
The answer is to teach them fluency strategies! Let me show you some mental math strategies that you can teach your students to use when memory is not enough! But first, what exactly is “fluency?”
What is Fluency with the Multiplication Facts?
The Common Core DOES specify that memorization of the multiplication tables is an expectation. However, that does not mean meaningless memorization is the route to go. 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.”
But with the rigor of the Common Core, we want students to link their understanding of multiplication with knowing the facts. Foremost, fact fluency flows from conceptual understanding.
Now, let us clear up some terms. To know from the memory means to recall from memory a fact. It is remembering.
As I will detail in the next part, fluency is more complicated. For now, just know it does involve accuracy and recall. The idea of recall is connected to retrieving from memory.
But memory can fail because the stress of producing or performing can lead to a mental block or shutdown. As you will see, fluency is also about using strategies. Why? Because strategies plug the gap when recalling or “knowing from memory” fails.
What Are the Strategies to Teach for Multiplication Fluency?
These mental math strategies used to teach multiplication fluency are grouped into two categories: Foundational Strategies and Derivative Strategies.
The Foundation Strategies are the first strategies to teach and use. They are the mental math strategies of counting by a number (also known as skip counting), knowing the product of square numbers, and knowing the Zero and Identity Properties of Multiplication. These are the basic or base multiplication facts.
The Derivative Strategies build on the Foundation Strategies. They 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.
Mental Math for the Multiplication Facts
The strategies are similar in use to the addition strategies you would teach students learning to add. When learning addition, they include decomposing a number, doubles, doubles plus one, adding one more, etc.
These are mental math strategies that are explicitly taught and practiced with pencil and paper first. After that, they become 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.
Are you eager to see the rest? Then download the FREE Guide to Achieving Multiplication Fluency!
It’s a 15-page guide that explains all the strategies. It has some suggestions for teaching these strategies and how to assess strategy use. It’s a comprehensive guide to boost student fluency with the multiplication facts. It is not a miracle cure and does not guarantee instant fluency. What it does is give your students strategies for achieving that fluency by the end of a school year.
It’s FREE and you can get it by subscribing to my newsletter.
Don’t forget to read Parts 2 and 3 of This 3 Part Series!
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.
Here’s the link to PART 2: Foundation Strategies.
Here’s the link to PART 3: Derivative Strategies
Time Saver for the Strategies!
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