### Unlocking the "Secret Code" of Multiplication Memorization

Multiplication is so important for third grade.  It is imperative that students know the facts so that they can focus on higher level math tasks in fourth grade and beyond.

We've already discussed some of the key ways to ensure that students understand how multiplication works (see the post and get a freebie HERE).  Now the question is... how do we get them to memorize 8 x 7 = 56?  See how I used the word memorize?  Some educators will tell you that this is the wrong word.  They like to use fluency instead, or maybe automaticity.  Memorization connotes, to some, a type of rote learning that the Common Core State Standards are trying to move us away from.  But here is what the standards say:

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. (3.OA.7)

If the understanding comes first, as it should, then memorizing is what the students need to do, so that they can become fluent, and have automaticity.  There.  See how they can all come together?  I particularly like this definition from the online psychology dictionary:

Think about riding a bike.  It took work to learn how, and a lot of practice to do it well.  You had to think about balance, and steering straight, and moving your feet on the pedals.  Those training wheels really helped!  And when you finally got everything working together, it took practice to get to the point where it no longer required conscious effort.  (And it was wonderful!)  This is what we want to do with multiplication facts.

So what does this mean for the classroom?  It means that students must be given time, in class, to practice their multiplication facts.  In more than one way!  They should also be practicing at home.  And then we need a way to assess their _______________ (insert your favorite word here: fluency, automaticity, or memorization).  But let's give them some training wheels (scaffolds) - like the "Secret Code" to begin with.  Finally, let's give them an incentive, something that keeps them engaged and excited in the learning process.

Step 1: Tell students about the "Secret Codes" that will help them learn their facts.  Eight-year-olds love secrets!  (Some of them will know that it's only skip-counting... but they'll still have fun with it.)  Study them closely, decipher them, and look for patterns together.  Then practice them!  Write them down, say them together, get in a circle and have each person say a number in order (We play a game called "Sparkle" with them).  Write them in a multiplication chart, so students can see how many they already know.  You can even sing them... but that's another post.

Step 2: Practice, Practice, Practice!  Practice the multiplication facts in many different ways.  We use regular flash cards, which they take home to practice every night.  There are tons of computer games, iPad apps, card games, multiplication charts, dice games, free worksheet generators, etc.  Find the ones you like.  Here are a few of my favorites:

 These can be purchased on Amazon.

These are fabulous cards for practicing and understanding fact families!  Cover the top number for multiplication practice, and one of the bottom numbers for division.  (I bought these from Amazon.com)

 Click the picture to try this computer game!
Math Magician Games - put a link on your student computers.  Click on multiplication or division to practice any set of facts from ones to tens.  Students try to answer 20 questions in one minute.  (My students love this one, and it's free!)  They can print a certificate when they pass.

Show a video!  Here's a student explaining multiplication memorization, and why it's not so hard (3:49)

 Click on the picture to see this paid product on TpT

The following pages are from my Multiplication Memorization Tool Kit.  Click on any picture to see the kit in my Teachers Pay Teachers Store.  It has over 100 pages of multiplication memorization magic!  (There is a cost for this product, since it took me eight years to make...)

Ice Cream Cone Fluency Practice
My students love to practice with dry erase markers.  We put these ice cream cones into page protectors, and they use them at a math station.  These can be differentiated by having students work with different factors in the middle.  One version has the factors in order, the other has them mixed up.

Secret Code Mazes
My students love these!  They have to follow the code (x1 to x10) four times in a row to get to the end.

Partner Dice Games
This is one of the games in my Multiplication kit.  They use two dice and go up to 6x6.  These make a great math center when placed inside a plastic page protector and played with dry erase markers or game tokens.

Multiplication Homework
I have three different pages of practice that are easily differentiated.  Perfect for students who need extra practice or have not quite mastered certain multiplication facts.
Step 3: Assess with scaffoldsMake sure
students have a strategy for the facts you are testing! Van de Walle states that a drill without an efficient strategy is a waste of time, but an effective drill strengthens memory and retrieval capabilities.  Let them take a practice timed test, but have them write the "Secret Code" down the side.  Set the timer to count up from zero, and have them write the time it took to finish.  When they do it again the next day, they can try to beat their previous time.  (I use the online timer HERE)

Step 4:  Finally, assess with a timed test.  By this time the hope is that they will have memorized the set of facts you are working on.  I use my own timed tests from my Multiplication Tool Kit, because they have a built in review section at the bottom of the page.  (What good is remembering the fours if you have forgotten all of the threes?)  There are also many that you can find for free, on TpT or using a Google search.

I give my students a week to memorize each set of facts (we have already been working on understanding multiplication for at least a month by the time we start this process).  I keep track of the class on a word document that shows when they have passed the test and the regular flash cards.

 Click on the picture to see my Ice Cream Incentive Program on TpT
Step 5: Whew!  If you've made it this far, thanks!  Now comes the reward.  When students pass the timed test and the flash cards, they earn a part of their ice cream sundae.  I have the pieces copied onto colored construction paper, and they cut it out and glue it onto their sundae on the wall.  They LOVE to glue each part on - and to show it to their parents at conference time!

When the ten (or more) weeks of multiplication memorization are completed, we have a huge party.  I invite parents to provide the goodies, and to help scoop ice cream, squirt syrup, sprinkle sprinkles, spray whipped cream, etc.  I work in a high poverty district, but we have always had parents willing to help their children celebrate this milestone.

My teaching partner and I have had considerable success with variations on this process for the last eight years.  I'm sure there are many other (and maybe better) ways to lead students to multiplication fluency, automaticity, and memorization... but this has worked well for us.  Plus, we get ice cream!

p.s. 8x7 used to be difficult for me to remember, until I thought about the order of the digits: 56 = 7x8.  Now it's my favorite fact to teach =)

Happy Multiplication Fact Teaching,

1. Woohoo! I saw this post just in time! I'm getting ready to start my multiplication unit for my third graders in my first year as a classroom teacher. Thanks for helping me feel super well-prepared and psyched!!

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2. You are so welcome! Multiplication is so much fun! I'd love to hear how it goes...

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3. Do you have a set time that you require to students to finish in before they "pass" a test? In other words, if a child takes 6 minutes to finish the twos, do they go on to the threes?

4. Hi Lisa, good question! I find that it varies from year to year, depending on the group of students I am working with. One very memorable year I was able to stop at four minutes! This year is very different, and I decided to give them seven minutes. They have to get 100% to move on, and they can't pass the level until they can do the mixed up flash cards.

Hope this helps,
Denise

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6. Love when teachers believe that memorization isn't all bad. Love the building a sundae idea. 7x8 was my toughest fact as a kid and so it became my favorite. I always share that with students. But how have I missed the 56=7x8 number order connection? Thanks for sharing.

7. You are amazing!! Thank you so much for sharing.. I am working practicing multiplication with my fourth graders that are still struggling so this tool is wonderful! Thanks again!

8. The information concerning teaching Multiplication Facts are excellent . I will be implementing some of the strategies within our classroom.

Thank-you, Ms. Carlyn Ashford

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