Multiplication Memorization Made Manageable
Do you struggle to help your students to memorize their multiplication facts? In order for students to progress through higher-level math classes, they need to have their math facts memorized, but how do you help your struggling learners?
Sandra from The Brighter Rewriter is here today to tell you about a few strategies she uses in her classroom to help students make progress with their multiplication facts. I love how she helps students recognize generalizations and patterns in the multiplication table. It takes their stress level way down.
How many of you have students that just can’t seem to memorize their multiplication facts, no matter what you do? Like me, maybe you’ve tried using manipulatives, making arrays, drilling with flashcards, drawing circles and stars, playing games, rapping the facts, and (gulp) even giving timed tests.
When I hear that memorization really isn’t necessary for this day and age, I have to respectfully disagree. I firmly believe automaticity of multiplication facts is a worthy goal and useful life skill, and I’d love to share the approach that finally turned the impossible into the possible.
The Preliminary Speech
I ask my students if they know how to skip count by 2, then have them demonstrate. I do the same thing with 5 and 10. Kids love skip counting!
I calmly point out that skip counting is really multiplication. I have each student put out both hands palms up, then skip count again while slightly bending one finger in for each number said aloud. I explain that skip counting while doing this is the same as a multiplication problem. For example, if you are counting by 5’s, and bend in your 2nd finger, then 5×2 = 10.
Never take this simple thing for granted, as there are always kids who are absolutely amazed by this revelation! Tell your students this means they already know their 2’s, 5’s, and 10’s…maybe not automatically, but that will come with practice and repetition.
The Wonderful Commutative Property of Multiplication
Students will (hopefully) recall the commutative property of addition, which means that two numbers can be added in any order, but the sum remains the same. Give them the BIG NEWS that there is a commutative property of multiplication too! This means that since 2×6=12 (and they already “know” their 2’s), then they also know that 6×2=12. Then, we do lots and lots of practice with 2’s, 5’s, and 10’s, always emphasizing the commutative property.
The Awesomeness of Zero and One
The next big revelation is that any number × 0 = 0 (and vice versa) and any number × 1 = the number besides 1 (and vice versa). Kids love and embrace these rules because they seem so simple, but be aware that they may mix them up at first, or will say 1×1=2.
I like to pull out all my 0 and 1 flashcards and run through them with the students, flipping the cards in very rapid succession. They love to answer these at hyper-speed. I explain that this is the goal with any multiplication problem. Students also love it when I randomly call out problems such as 0×189 or 1×9000, because they can answer quickly and easily, and begin to believe in their own multiplication brilliance!
The Hook
At this point, I get out a blank multiplication chart and make it available for class viewing. I announce that this is a chart of ALL the times table facts they need to memorize. Cue the whining and the groaning.
But then, I tell the students that I’m going to color in all the multiplication facts that they “already know” and that they only really have to concentrate on memorizing only the facts that are left.
I color in all the 0’s, all the 1’s, all the 2’s, all the 5’s, and all the 10’s, in rows and in columns. (I really ham it up here!) There will be 36 spaces left uncolored. The chart looks like this:
Then I tell students that they must memorize these facts. However, they don’t have to do all of them due to the commutative property! I go to the 3’s column and say, “You will need to learn all these facts. But once you learn 3×4=12, you will know that 4×3=12.”
Then I go to the 4’s column and color in the 12. “When you learn 3×6=18, then you will know 6×3=18.” And I go to the 6’s column and color in 18. I keep going. By the end, I have also colored in 6×4=24, 7×3=21, 7×4=28, 7×6=42, 8×3=24, 8×4=32, 8×6=48, 8×7=56, 9×3=27, 9×4=36, 9×6=54, 9×7=63, and 9×8=72.
As I color in more and more facts, I see eyes light up and smiles break out on formerly sad faces. Once I am finished, there are only 21 multiplication facts left on the chart.
Cue the shock and awe! Working with 21 “hard facts” seems manageable to even the most reluctant math student. Of course, the automaticity is still to come. But these simple steps provide hope to kids who would otherwise see this as an impossible task.
You can download 3 free 21 New Facts Charts here, including a blank one to color in while breaking the good news to your students!
The Hard Work
Now it’s time to practice. Students must keep working with the concept that multiplication is repeated addition. I like to tell them that multiplication is a math shortcut, and 3rd graders love shortcuts!
All of those ways to learn and practice I mentioned at the beginning are still good (well…except maybe for timed tests). Pick your favorites!
In dealing with these 21 hard facts, I’ve had great success with a resource I created called Times Rhymes, which is available in my TpT store, The Brighter Rewriter.
I’ve written a chant for each of the 21 new facts, to go along with a poster illustrating the rhyme. (Some of these rhymes are in the task cards in photo 3.) Kids who love pictures love the visuals, and kids who love words love the rhymes. Win-win!
However, what’s important now is to keep working towards the automaticity. In the meantime, you can be secure in the knowledge that you’ve made multiplication memorization as manageable as possible. And that’s marvelous!
Here is the link to the complete Times Rhymes set available in my TpT store.
More Multiplication Resources
Here are a few more resources and information about how to teach multiplication and help students memorize their multiplication facts.
I have known Sandra Riddle for several years as her principal and friend. She was a most effective teacher. I am happy to see her sharing some of her methods and techniques with others.
I too have had the pleasure of working with Sandra. She has a plethora of ideas and can fill a teacher’s toolbox in a click. If you are needing fresh ideas, new ideas, or are starting from scratch, Sandra is your go to person! Thanks for sharing Mrs. Riddle!
Great strategies suggested!
I have used all over my 30+ years of teaching!
Thanks for sharing your effective ideas!
Good luck!
Pat and Lori
My daughter learned skip-counting by 3’s and 4’s last year in second grade, up to 50, so multiplication has been no biggie. I highly recommend going that route!
Thank you for the free resources! I am looking forward to using this with my kiddos that are having difficulty learning their facts!
Thank you this will help my son in 3rd grade. I like the ideas and will use them.
My granddaughter has had no problems doing multiplication due to her learning skip counting in the first grade. She is in second grade now and is a whiz with multiplying numbers.