Unlocking the "Secret Code" of Multiplication Memorization

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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:

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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.

Click on the picture to download for FREE from TpT

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 scaffolds.  Make 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,

 

"Teacher, Your Penguin is Too Fat!"

Allow me to introduce you to my Emperor Penguin.  Her name is Penelope.  I made her in one of those incredibly rare and much beloved moments in teacher time, twenty minutes spent student-less in the classroom.  

I gathered my butcher paper, scissors, and heavy duty glue stick, looked at my inspiration picture from Pinterest (click HERE for the original pin), and began to cut.  I had to give up my lunch for this... but it was worth it.  Or so I thought.

When the students walked in after lunch, Penelope was attached to the cabinets in the back of the room.  Immediate chaos ensued (they're eight years old and they get excited, which is part of why I love teaching), as all 26 students needed to see her and touch her.  We have been studying about penguins for a few weeks, and she was to be a part of our culminating activity.

Finally, all the students were sitting down and quiet.  We were preparing to do our math fluency test when a hand went up in the middle of the room.  I called on this student, who said, "Teacher, your penguin is too fat!"  

Now my signature way of dealing with kids who do not use my name is to smile and call them "Student".  They usually smile back and use my name.  Not this kid.  It's November, and he still calls me teacher.  But I digress.

So I said, "Student, why do you think Penelope is too fat?"  He said, "Penelope is too fat because she should only weigh 66 pounds."  Be still my heart!  He can't remember my name, but he remembered what we read about penguins!  AND he answered in a complete sentence!  I asked one more question, "Student, what evidence do you have to support this statement?"  He then opened his penguin folder and removed the research page he had filled out, showing me the average weight of an adult Emperor Penguin.  

Well.  I would have done the happy teacher dance if I were not hobbled by a bad knee.  We went together to look at Penelope more closely.  I asked the class whether they agreed that she was too fat to look as though she weighed 66 pounds.  They all agreed (which third graders tend to do, no matter what question you are asking), so we put Penelope on a diet.

 

And here she is, newly svelte and waiting outside so that the younger students can see if they are taller than an Emperor Penguin.  We looked up the meaning of svelte, and chose the first definition.  Penelope is now slender, and while I doubt she is graceful while walking on the ice, we choose to believe that she is very graceful in the water!

Normally I do not recommend a diet that relies on scissors for results, but in this case, it worked out well. =) 

Before I go I must share with you this picture of my cat.  His name is Riley, and he looks a bit like a penguin.  Riley loves to stand up on his back feet and be petted on the back of his neck.  This is what I imagine might happen if a penguin came to visit.  Can you tell which one is Riley?  

One more quick penguin item... here's a freebie from my TpT store.  It's the same multiplication game in color and black and white.  Click on either picture to download.

 I also have a Pinterest board with lots of links to penguin activities, freebies, art projects, and videos.  You can find it HERE.

Happy teaching with penguins,