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| | Filed Under: Math, Multiplication & Division

Do you have students in your 4th-6th grade class who just can't seem to master their multiplication facts? No matter what you try (flashcards, incentives, computer based programs), they just can't get past their 5s (and are shaky with their 3s and 4s)? I have always had several students in my classrooms over the years that really struggled memorizing and recalling their multiplication facts so I feel your pain if you are in this situation. It can be very frustrating, to say the least.

I knew I needed something other than my go-to flashcards, so I researched a few multiplication facts strategies and finally found one that I knew would help my students.
I will tell you that it is not a "quick fix" strategy.
Using the Distributive Property of Multiplication to Master Multiplication Facts

However, this is a "I have got to be able to figure out what 7 x 8 is to solve this multi-digit problem, and I don't have time to draw a picture of 7 circles with 8 dots inside each circle." Yes, I literally have students in 5th grade who resort to this each year. And I also have had students who just sit there for several minutes because they don't know 7 x 8 and were not taught any strategies to help them figure it out.

I knew I had to change something the year I had half of my class not mastering their math facts in 5th grade.

This particular strategy that I tried (and used with success) has the students using the distributive property of multiplication, with a bit of additional scaffolding and support.When I first introduced this strategy to my struggling multiplication students, I immediately saw light bulbs go off. They were deepening their understanding of multiplication and feeling confident because they were able to solve the problem.

Basically, the students use what they know (their 1s, 2s, and 5s) to determine the answer, using the distributive property of multiplication. Here is an example:

The student in the above example knows that 5 x 8 = 40, and 2 x 8 = 16, so the two products added together give you 56, which is the answer to 7 x 8. Writing out their known facts (1s, 2s, 5s) provides extra support and scaffolding that many of my students needed.

When I first introduced this strategy to my students, I did a lot of conceptual talking about the numbers and even manipulatives to ensure they understood the concept. When talking about the equation, I would say 7 groups of 8 (versus 7 times 8). Then when I refer them to their "known facts: 1s, 2s, and 5s," I would say something like: "You need 7 groups of 8. Which of your known facts will give you the largest amount of groups, without going over what you need?"

After the student picks 5 x 8 (or 5 groups of 8) we talk about how many more groups are needed to make 7 groups, etc. Then we talk about why adding the products works. I really try to get them to conceptually understand why this strategy works. It keeps them from making mistakes, and eventually leads to quicker thinking and using those benchmark fractions that students with strong number sense can do. (i.e. I know that 6 x 8 = 48, so I just need another group of 8 to find 7 x 8)

Here is an example of one of my student's work when he used this strategy for 9 x 6. He marked out the 5 x 6 after he used it because he knew that he could not use it again. He then used the 2 x 6 twice. Eventually, the students will begin to make connections between the numbers and do 5 x 6 and 4 x 6, but this will take some time.

As I mentioned earlier, this does take a bit of time, but the students will gain fluency with it. They also will learn to do this without the need to write the list of known facts each time. This multiplication strategy also works well at building their number sense and conceptual understand of multiplication.

Click here to grab your copy of the poster shown in this post as well as a few printables that I use when teaching this strategy.

Need some multi-digit multiplication resources for your 5th graders? Click here to see my Multiplication Resource pack that includes teaching posters, self-checking printables, centers, task cards, and assessments for multi-digit multiplication.

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Multiplication Facts Strategy for Upper Grades {Freebies} - Teaching with Jennifer Findley

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Filed Under: Math, Multiplication & Division Do you have students in your 4th-6th grade class who just can't seem to master their multiplication facts? No matter what you try (flashcards, incentives, computer based programs), they just can't get past their 5s (and are shaky with their 3s and 4s)?

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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.

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

First 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.

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.

I 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

Rather 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.

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!

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Total Recall: Helping Our Students Memorize Multiplication Facts | Scholastic

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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.)

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Online Times Tables Tests - TimesTables.me.uk

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Test your times tables skills with our configurable online times tables tests. Includes division times tables.

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Factors and Multiples Puzzle : nrich.maths.org