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Child's hands writing multiplication tables

3 Steps to Memorizing Multiplication Tables

Jean Boylan
Jean Boylan

January 30, 2020 6 min read

Basic supplies:

Students need to master multiplication by 4th grade! This is a pivotal stepping stone to higher math. It's nearly impossible to understand fractions, geometry and even money without knowing how to multiply. More reason to memorize those facts!

By “master”, I mean 2 things -

  1. They need to intuitively understand what multiplication is and how it applies to their world.  Memorizing the facts is not enough. Many smart kids memorize their facts quickly and early, and ultimately get stumped with higher level math because they fail to understand what multiplication can really do for them.
  2. They need a pathway to the correct answer. Memorization can be very difficult. Imagine if you were learning Chinese using a time test of a couple of hundred random flashcards! They need a way to reliably get to the correct answer - even if it is slow at first.

Finally, they need to get fast so that they are not bogged down and feeling defeated. So, how do we help them get there? I'll show you in a few fun simple steps. Before you get started you must shift your paradigm to understand that every student (and parent) needs the right framework for success. 

The Right Framework

Stop the negative talk. Right now! Kids must believe that they can do it. They pick up on your vibes and maybe even your words - stop telling yourself that you were bad at math or that math was never your strong suit.  Stop believing that you cannot help them because you never memorized your own multiplication facts. (Trust me, even professional engineers can be stumped with how to support a struggling mathematician.)

They need a system to access to the correct answers! Remember how you felt when your brain was frozen and you thought, “I don’t know the answer”, “I will never know the answer”, “It is simply not floating up from my memory banks?”  Well, we can fix that for your child. We'll give them a path to all correct answers. This will help them believe that they can achieve success! It will be slow at first, but we can build speed after that.

The kids must own the process and the outcomes. Your role is to support and coach, but they must manage and own the process and the outcomes.

Alert! Before you start working with your child, remember that this process must be fun, positive and empowering. Don't get stern, stressed or forceful because you will sabotage your efforts – let the candy counters do the talking. 

I'm going to show you two ways to always get the correct answer. These methods aren't tricks – they're visual examples of multiplication. They are SLOW, but they work to cement the concept and to get the correct answer. Follow along …!

Step One – Building the Problems

Tools for Step One:  paper, pencil, counters

This is a tactic to truly understanding what multiplication is and how it works. With time, they can see that there are patterns and that these patterns will lead to the correct answers every time! Keep your focus simple. Don't stray into other examples and ways of doing things.  

Build the Problems:

Using your counters, build a simple multiplication problem.

2 x 3 =   o o

            o o  

            o o = 6

How many are there? Count them!

(Remind the student that this is “two, three times”.  Say the words slowly so that they have time to sink in.)

Count the answer and write it down.

You are looking for 2 sets of three. Their sets should be lined up in rows like the image. Remind them that neatness matters in math. It's too easy to make a mistake if the work is messy.

Repeat this process as many times as necessary to gain confidence in the process and to repeatedly visualize what multiplication is. It's a way of counting fast! It is a way of grouping numbers to save time.

Give them a series of 4-6 problems at a time to work using this method.

  • 3 x 5 =        
  • 7 x 3 =
  • 6 x 4 =      
  • 9 x 7 =
  • 8 x 4 =

Include problems that they have not yet memorized. Let them experience that they can get to the correct answer every time. It'ss slow, but accurate! This is one way to get to an answer, but you need to have counters with you at all times.  What if you're at school with only a paper and pencil?

STEP TWO -  A “Trick”

Tools for Step Two: paper, pencil

This is a faster way to build the problems. 

The next step is a way to get a correct answer without the use of counters. Instead of placing the candies, what if you drew lines to represent the numbers in the problem and you crossed them with the second number in the equation?  

Click here for a video tutorial on this method! How to Multiply Numbers by Drawing Lines

Can you see where the counters would be in this drawing? Instead of counting the counters we count where they lines cross – this is where the counters would be if we were using them!

You can do any problem you want simply by drawing the lines and counting where they cross. This will give you the correct answer every time.

Give the child a few problems that they may not know, and allow them to try the system. Remind them that neatness counts! You may also need to coach them to make their lines long enough.

Another helpful hint is to write the count down at the end of each row in case they get confused.

Try it a few times with simple problems to see that it works. It can be done with a million times a trillion if you had enough time and paper!

They now know how to get the answer every time. It's time to get faster! The children will continue to use Step One and Step Two as they move into Step Three.

Step Three - To Build Speed

Tools for Step 3: your multiplication flashcards, stopwatch or timer, paper and pencil 

Your student now knows two ways to always get the correct answer.

  1. To build the problem with counters and count the answer and
  2. To draw crosshatches and count the intersections

They can use these methods to continue to get correct answers while they build their memory and speed. In order to empower them and instill confidence and self-direction, this next phase should all happen at their own pace and control. 

  1. By themselves, with no conversation, the student sorts all the flashcards into two piles – what they know fast and what they don’t know fast. If they are counting to themselves or using other similar tricks, gently encourage them to put the card in the "don’t know" pile.
  2. Put away the cards they know! Don't stress about them anymore!
  3. The student chooses 5 cards at a time. They'll work with these cards for 5 days, for 1 week. At the end of the week, they'll choose 5 new cards.
  4. With the help of a partner/buddy/parent, quiz the student by showing them the flashcards one at a time. The student can use any technique they want to get to the correct answer - including the techniques from Steps One and Two. The partner is only a helper and provides NO COACHING. (Coaching produces stress.) The helper can only respond with, "Yes" or, "No, the correct answer is ..."
  5. The student goes through the cards 1 at a time. If they choose to go through the flashcards more than 1 at a time, it's the student's choice, but 1 time is all that's required.
  6. In addition to the quiz with a partner, the student should write the same 5 problems across a piece of paper. Using the timer, the student will time themselves to see how long it takes to get the correct answer. Again, the student may use any of the techniques they have learned to get to the correct answer. No coaching! Your child may choose to use Step Two drawing multiple times. Say nothing! Let them figure it out! They'll eventually remember that they've drawn that same problem multiple times before, and refer to their scratch paper to reach the correct answer.
  7. Repeat this activity 5 days per week. Your student will soon realize that the entire flashcard quiz, and self timing, can happen in a matter of minutes once they get going!
  8. At the end of the week, the student chooses the 5 cards for the next week. They may use the same cards or start fresh. It's their call! It's their math! They're in charge!

Bonus:  Fun Games to Support Multiplication Include:

  • Math Dice
  • Equate
  • Zoom
  • Multiplication Mosaics

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