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