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MathBait™ Multiplication

Fluency without Memorization

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How to build fluency without multiplication? In this planning document we explain the pedagogy behind MathBait™ Multiplication.


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MathBait™ Multiplication has been wildly successful in teaching children as young as 6 to become fluent without ever memorizing a product. How? Here we summarize the problem with memorization and why the MathBait™ method is so powerful.

A world leader was once asked in an interview to calculate 8×7. He fumbled around, turning a silly ice breaker into international news. How is it possible that our leaders cannot complete basic multiplication?

Well, it's the same idea we have been emphasizing throughout this series. He probably learned through memorization. You stare at the table, you repeat it again and again, you take timed tests in order to cement these facts in your head.

And then, you lose them.

You lose them because memorization doesn't stick, it doesn't have anything to hold on to. In order to build lasting knowledge we must scaffold learning into manageable pieces and connect each piece to prior understanding. At MathBait™ we use storytelling because it has the ability to connect daily life, things we understand from simply being human, to mathematical concepts, automatically setting up students to better understand (and thus remember) as it is connected, anchored, to existing knowledge.

As everyone rushed to gossip on the leader's blunder, a particular commenter stuck out among the noise. He explained that rather than guessing or trying to rattle through his memory on the spot to pull out that one little square from this sacred table, it would have been much more impressive if he said, "Ooh, that's a tough one, but I know 7×4=28 and so I can double that to get 56."

As teachers, we often forget the long term. Our job is to make sure our students know the content in front of us, so that becomes the focus. However, if we expand our focus to consider why students need to know this (and it's not because the district or state or leadership have told us so!) we can not only help our students with this year's content, but set them up for long term success.

Multiplication is the foundation for many advanced topics. In the second book of our Marco the Great series, students will be introduced to factoring quadratics and simplifying radicals. These tasks rely on a solid understanding of numbers and multiplication. However, we often work backwards. That is, to determine the roots of a quadratic we undo multiplication, we factor, to identify what values could multiply to 24.

It is a much stronger skill for students to have the ability to problem-solve rather than spout out facts. Our Multiplication series started with skip counting and showing students we only need a small handful of facts to derive the remainder of the table. This is a great time to circle back to this idea and not allow students to get too caught up in remembering each product. In fact, in higher math they will need to decompose values and it is often counterproductive to multiply everything out as we end up needing to rip it back apart to solve.

The activities in this lesson fit well into an analogy:

We have built a multiplication store in our brain. There, we store all the multiplication facts we can. Note, if we memorize these facts, the store will quickly go out of business as soon as we stop shopping there regularly!

Next, we have carved out many different ways to get to our store. Just like in real life, a store needs a lot of traffic to be successful, it needs multiple ways to access it. We haven't directly practiced products much at this point, because this is only one route and we want to have many.

Finally, until our store is popular, people will need a map to get there. In MathBait™ Multiplication Part 3, we are working on traveling to the store (lots and lots!) and taking many different paths to get there. The more we visit the store on different routes, the easier it will be for us to quickly run to the store and grab a product without much thinking. Just like driving to familiar places becomes almost automatic.

The moral of our tale is that although students will practice their facts a lot in Part 3, we still want to avoid memorization. We want to practice facts from many different routes and perspectives. This will not only solidify fact fluency and faster recall, but will also support students much more in the long term and help build the skills they will need through high school and even college math! Figuring out 8×7 is much more impressive and impactful than trying to keep it memorized throughout life. 

The material on this page is copyrighted by MathBait™. Please use and enjoy it! MathBait™ provides a temporary license for Non-Commercial purposes. You are not permitted to copy, distribute, sell, or make derivative work without written permission from MathBait™. 

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