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Total Recall: Helping Our Students Memorize Multiplication Facts

By Alycia Zimmerman on January 18, 2012
  • Grades: 1–2, 3–5

As a young student, I railed against memorization and my “Draconian, pseudo-fascist teachers” who demanded that I spit out the answer for “6 times 7” like a soulless automaton. (I was also given to overblown metaphors and florid tirades.) As a teacher, some small part of me still cringes every year when it is time to encourage my 3rd graders to memorize the multiplication/division facts. “Long live the calculator!” the former freedom fighter in me cries out. 

A multiplication display with arrays made with beads.My students created multiplication cards with arrays made with beads.

 

Given my rocky relationship with memorizing math facts, I am always on the hunt for effective and motivating ways to help my students achieve “automaticity.” And now that the Common Core Standards explicitly require 3rd grade students to “fluently multiply and divide within 100,” I am particularly focused on effective strategies to help my students meet this standard (Standard 3.OA.7). Here are some strategies that simultaneously help my students’ math memories and mollify my conscience.

 

 

 

 

 

Stage 1: Understanding Equal Groups — The VERY Important Precursor

Things that come in groups chartFirst off, my students must internalize what multiplication means long before they begin to memorize the multiplication facts. They must have an intuitive understanding about the reciprocal relationship between multiplication and division, and equal groups and equal shares, and the connection with repeated addition and skip counting.

My students live with these ideas for months, exploring multiplication concepts with arrays, area models, pictorial representations, and hands-on experiences. Only when I am confident that all of my students truly understand why and how multiplication and division work do I begin to emphasize memorization. Just as in reading, accuracy and fluency without comprehension is useless.

 

 

Area Model Chart Array Model Chart

Equal Groups Chart  Number Line Model

 

Stage 2: "Figure-It-Out" Tricks

Now that my students have internalized what multiplication and division are all about, it’s time to begin to teach them some “tricks” to quickly figure out multiplication/division facts, and to help them develop their own tricks. In fact, these are not tricks at all, but ways to analyze multiplication patterns, apply partial-product principals, and use “landmark numbers” to quickly use what they know to figure out unknown facts. At this stage, I want to help my students realize that they can find the products for multiplication problems that they haven’t yet memorized.

I begin by having my students fill out blank multiplication tables several times a week. The first few times, I have the students highlight the “easy” rows and columns such as the 1s, 2s, 5s and 10s. They fill in these parts first, and then realize that they can use those landmark numbers to help them figure out the remaining facts. For example, I might encourage a student who knows 2 x 6 = 12 to add another six to figure out 3 x 6. My students share their strategies, and we chart these tricks. Then I have my students color in their completed times table charts with crayons to create “quilt patterns” by shading in multiples. The multiples-of-4 quilt is always a favorite.

Best of Times Book CoverI also read our “multiplication bible,” The Best of Times by Greg Tang, with my class, and we practice his strategies for figuring out multiplication facts. For example, Tang writes,

Four is very fast to do

when you multiply by 2.

Here's a little good advice:

Please just always double twice!

Through Greg Tang’s Web site, you can have your students play the Break Apart game focusing on multiplication. (The nines level is free.) This further reinforces partial-products thinking strategies, or “Breaking It Up,” as we call it in my class.

Example: 9 x 7 = ?

Breaking It Up: “I know that 10 times 7 is 70, so one 7 less than 70 is 63.”

 

Stage 3: Approaching Automaticity

At last, we get to memorization! I only begin to focus on memorizing the multiplication facts after my students are already solving multiplication word problems and are using a wide range of strategies to figure out the necessary multiplication facts, from drawing arrays to using their own “break it up” strategies. I point out to my students that automaticity is far more efficient, and that the speed inherent with automatic fact recall will help them to solve multi-digit multiplication and division problems efficiently. Memorization is about speed, efficiency, and freeing up brain space for other math thinking.

 

Recall Tip 1: Timez Attack

In my opinion, the free downloadable computer game Timez Attack is the best computer program to help students learn the multiplication facts. This first-person adventure game feels like a “real” video game, and it uses built-in assessments to advance students at their own pace. My students love this game, and I’ve seen it really work with them.

 

Recall Tip 2: Totally “Unsquare” Flashcards

Multiplication Fact TriangleRather than using traditional flashcards that teach multiplication or division facts separately, I prefer “fact triangles,” three-sided cards that have an entire fact family on the three corners of the triangle. My students enjoy “playing” with their fact triangles by covering up one corner and then having a friend figure out the hidden number. This helps my students internalize the relationship between multiplication and division. A free printable set of all of the multiplication fact triangles is available online.

 

Recall Tip 3: Play Kakooma

Greg Tang of The Best of Times didn’t just stop with an awesome book. He also developed a fun mental math game that can be played online or with paper and pencil. Kakooma challenges students to use multiplication to solve a series of deceptively difficult puzzles. The rules are easy: just find the one number in the diagram that is the product of two others. Like all great puzzles, however, looks can be deceiving. Often, the answer is right in front of you, yet your brain won’t let you see it! This is another game that my students beg to play. You can download a sample packet of Kakooma multiplication puzzles from Greg Tang’s Web site.

 

Multiplication Masters Board

Tip 4: Multiplication Masters

I use a management system to help my students keep track of which multiplication facts they have mastered, and which they still have to study. I’ve named the system “Multiplication Masters,” and I explain to my students that any student who makes it into the “Twelves Club” by the end of the school year will be considered a Multiplication Master. At the end of June each year, I hold a party after school for the Multiplication Masters. The students receive certificates and decorate T-shirts with multiplication facts.

Twice a week, my students take three-minute multiplication quizzes with twenty questions. (Download my Multiplication Masters quizzes.) Each student takes the quiz on the level above his current club. So, a student who is currently in the Threes Club will take the fours quiz. I photocopy the quizzes and cut them into strips at the beginning of the year, and I store dozens of copies of each quiz in an accordion file folder sorted by level.

When a student earns 100% on a quiz, he moves into that club, and then begins studying for the next higher level. Once a student becomes a Multiplication Master, I challenge my students to see how many problems they can solve in three minutes, working up in increments of ten.

Yes, this system is somewhat competitive, and yes, it does put some pressure on my students. Nonetheless, all of my students have seemed to enjoy the challenge, and I always emphasize that each student should focus on how high she can soar individually, without comparing herself to her classmates. Three minutes is a fairly generous time allotment for twenty questions, so I find that students who are comfortable using other methods can also get 100% on their quizzes, without having true automaticity.

To make my Multiplication Masters board, I used a rectangular piece of foam board and gridded out sections using colored masking tape. I attached bits of Velcro across the entire board, and then I labeled each grid section. Finally, I printed each student’s name onto card stock, which I laminated and backed with Velcro.

 

 

 

What are your favorite tips and tricks to help your students memorize the multiplication tables? Please share your favorite games, Web sites, and activities below in the comments section . . . I know I’m always looking for new ideas!

Comments (37)

You should look at Multiplication Education.com. It uses pictures,movement, colors, rhymes, and stories. Really a great way to teach all kids the multiplication tables, especially if they struggle with flash cards.

I use the following mnemonics:

8 times 8 fell on the floor, picked it up it was 64.
OR 8 times 8 fell on the floor, picked it up it was Nintendo 64.
(We chant this periodically to remind ourselves)

7 is an odd number, both literally and because it's known to be strange and have magical powers. So guess what happens when you multiply 7 times 7? You get a REALLY odd number--49! Isn't that the strangest, oddest number you ever heard of? (To remind ourselves of this story, every time we see 7x7, we blurt out "It's odd!" or "How odd!" or "Strange!") 49 really does seem like a strange number to a lot of kids.

I am teaching 4th grade LD Resource and I *love* this info!!! I've already purchased "The Best of Times" and I'm implementing the Multiplication Masters ideas too. One other idea that's working well for my groups - Multiplication War. It's funny that when nothing else motivates them, sometimes competition can make it happen! I find that building up their CONFIDENCE gives them an excellent push, and I love your concept of them being MASTERS... for children with learning disabilities, who believe by the age of 8 or 9 that they are "BAD" at a subject, this makes a huge difference. ;) THANKS!

After a lot of searching of research based ways to teach math facts, this seems to sum everything up nicely. Thanks so much.

After trying to help math-challenged high school graduates learn basic algebra, it is clear that people must memorize the "times-tables." Watching twenty-somethings using their fingers is rather disturbing. Write out the 12x12 table ang look for patterns. But they must learn to work on the job without music pumped into their ears.

Emil, I totally share your sentiments! If I see another high school (or even intermediate) students struggling to recall facts, simply because they (and their teachers) were told that memorization is 'old-school', I'll scream! I think that the ideas shared on this site are all super! It's great to have a number of different ideas to use with our varied students!

help

A rhyme for 6x8 that a student once made up:

Six and eight went on a date. When they came back they were forty-eight.

It would be helpful to me if people would share ideas for developing automatic recall of specific number combinations. I find that children will often encounter a few combinations that are difficult for them to memorize and these combinations vary from child to child. I have used the 5678 trick for 7X8, 321 for 7X3 and using two 7's to form a 14 (the top of the first 7 is removed to make the middle horizontal stroke of the four) for 2X7. I am currently "rescue tutoring" a perfectly intelligent 15 year old whose addition skills are poorly developed, so even though 7X2 is a "two", the "trick" helped her. She understands multiplication fine and can figure out the answers. It's the development of immediate recall that has, for some number combinations, been hard for her. I especially would love to have "tricks" for 4x7,6X7,3X6,3X8, 6X8 and 4X8, but ideas for other combinations would be welcome as well. For this particular student, word associations with numbers has not worked at all.

when I was seventeen I was put through a litany of tests and though my language skills were excellent, I had the equivalent of dyslexia with numbers. They would not stick in my head, sometimes they moved around, I would focus hard on 4112 and when I looked bacm it would no doubt be 4211. If I didn't know better I would think someone was playing a practical joke. the poor ability at math had me thinking I was dumb, so I didn't try at English or writing or science with any effort. The more I can visualize math equations such as adding, subtracting and multiplication, as well as finding the logic behind it, helps a lot.

Hello!

I know of a new multiplication book/CD that has found a way to develope automatic recall of SPECIFIC NUMBER COMBINATIONS.
I think it is exactly what you are looking for! It has no factor rhyming words or stories to remember. It is based on the SHAPE of the factor combination. It is very unique and works for most kids, including those with special needs. Visual learners love it.

It is called "Times to Remember , The Fun and Easy Way to Memorize the Multiplication Tables."
the web site give free downloads so you can see if this is what you are looking for. the site is www.TheTimesTable.com.

Hope this Helps!

Jane

It is mnemonics (memory trick), not pneumonics. Just a friendly hint.
http://google.com

I love multiplication.com. They have drill type games that are fun for the class, and one called "Quick Flash" that is great practice. They also have online quizzes that can be printed out and automatically time the student. Quizzes are both fact family based and cumulative.

I agree that the competitive element really works! My students must pass the online quiz in 3 minutes to "beat the level". They get a prize at level 6, 9 and 12.

Songs work, but when kids get to 4th grade they can't answer 3 x 8 without singing the song all the way to 8!

My kids also like playing each other with multiplication games on Mathplayground.com and other sites.

Thanks, Alycia for sharing your wonderful activities, and to everyone who has contributed! This really is a treasure trove. I have seen children memorize the multiplication facts with outrageous ease through chanting the facts while using rhythm sticks and a different set of motions for each group of facts! Tapping sticks, touching the floor, and flipping the sticks and different melodies and rhythms are all used in a different combination for each group of facts. This is very flexible, and the kids love making new rhythms and different patterns of movement. Example: 2_is_1x2_1x2is2_ _ _ 4_is_2x2_2x2is4_ _ _6_is_3x2_3x2is6_ _ _,etc. (The underscores represent pauses, or musical rests, to create the rhythm of the voice, while continuing to move the sticks on the vocal rests.) They can use a hand clapping rhythm with a partner, as well. This is incredible to watch. I have seen children with different learning styles doing this, and it's a little difficult in the beginning for the kids whose dominant style is not kinesthetic. I have some kids who are slower processors, and need to go slowly at first, but they pick up tremendous speed as they go. It gets easier as they learn each group of facts. IT IS ESSENTIAL that each group of facts retains the same rhythm and pattern of movement each time, at least until the table is learned, as the pattern is the signature and creates the neural pathway. Each time it is practiced, the pathway gets stronger. When the tables are memorized, it's fun and helpful to create new rhythms and patterns for the groups. Also, each group of kids can make up a different song for the same facts. These activities use multiple intelligences and facilitate differentiated instruction, besides being unbelievably fun!

Love these tricks! Very helpful for an 11 year old girl (similar to your student) who can not memorize the facts. Any other tricks would be appreciated.
SLC

Anonymous, I know that you wrote your post over a year and a half ago, but I am hoping that you will be inspired by others' interest to make a video of this method of tapping into children's rhythm to help them learn timestables. It would be great to see it!

I just started teaching and this website was really helpful

I am going to miss teaching third grade next year.

I love your ideas. Thanks!

great

I love this blog. You have some great ideas. How can I follow it on my blog?
Amy
http://amydbratton.blogspot.com/

This is really awesome! Thanks for sharing! I have started using it with my students, and they LOVE it! Even students who don't need to practice their facts want to do it, especially the follow-up work.

My students love Times Tables the Fun Way by Judy Liaqtaud and Dave Rodriguez and have worn my book completely out!

Brilliant - Thanks

I do a few of these "tricks" already in my class and I want to thank you writing about this topic and making me feel like I'm doing a good job!

Multiplication has been a fun element in my class and I wish everyone good luck! My students enjoy playing "multiplication war" which you can Google. We also use virtual dice to "roll" for factors.

:)

If you are going to reply to a comment from another teacher, please don't be rude. We are all on the same team. I am a good writer and a terrible typist. I usually don't have spelling errors unless I am terribly tired, but sometimes my brain just sends my fingers to crazy keys.Before I have a minute to check it...it is sent.
It doesn't cost anything to be nice. With all the pressures to meet standards..we need a cheering section, not a critical spirit.

Well said :) We need more teachers like you!

Thank you for the site! Studies show that children recall information that is set to music or a rhyme- why not bring that into math? I love all of these rhymes and jingles for the ones that do have the conceptual understanding but have trouble remembering some of their facts. After they understand the basics, they do need to memorize the facts. Why not make it fun for them to memorize their facts? I still remember the Multiplication -Songs from SchoolHouse Rocks with Cloris Leachman! Thanks for the tips!

Please do your students a favour and focus on developing meaning and NOT cute rhymes and verses that don't connect to the actual math involved. Better that they should have a variety of strategies (doubles, make-ten facts) and math principles (i.e. the commutative property)so that they will be able to make significant connections within their math learning.

My class is working on a banana split incentive to promote mastery.

Additionally, we sing songs to familiar tunes. Like the 3's song is to the tune of jingle bells:
3, 6, 9

12, 15

18, 21

24, 27, 30 Counting's fun!

Thank you so much for writing on this topic! I am a new third grade teachre and so badly want my students to know there facts (it will help them in math down the road). Thank you for the ideas!

Thanks for your comment! I am so happy that this is helpful for another third grade teacher. Third grade is such an amazing year as a big transition grade. As their first true foray into multiplication, it seems really important to me to build a strong foundation. Best of luck with your young mathematicians!
~ Alycia

Excellent ideas for concepts and memory. Perfect!

I like www.xtramath.org!

I just checked xtramath out, and it looks like a great, free resource. I'm going to try it with some students this week. Thanks for the suggestion!
~Alycia

Pneumonics is great! Who plays for 7 and 7? 49 'ers!

It is mnemonics (memory trick), not pneumonics. Just a friendly hint.

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