Monthly Archives: December 2013

What to do if they STILL don’t know their multiplication facts

You tried flashcards, timed tests, songs, even games and nothing is working. There are still some students in your class who are not mastering their multiplication facts. What do you do?

What if we embrace the idea that students don’t need to be able to do 100 multiplication facts in under ten minutes to be successful in math class. Yes, it’s great if they can, but they shouldn’t be prevented from moving on to other more exciting and challenging topics. I know some of you are shaking your heads. It goes against what many believe is important in math class.

Many of us believe that memorizing our multiplication table makes math easier. However, for some students the memorizing part isn’t so easy. This does not mean they are lazy or don’t care. Instead, memorizing a bunch of seemingly unrelated facts is harder for them then repeated addition.

Interestingly enough, these students will often invent their own strategies to compensate for their lack of fact fluency. I worked with a fourth grader who didn’t have a strong mastery of his multiplication tables. What he did have were great mental math strategies that allowed him to solve more complicated multiplication problems quicker than those who had their facts memorized.

He used a doubling and halving strategy when trying to solve a problem that was difficult for him. When presented with 15 x 4, he would double fifteen and half four, which gave him a problem (30 x 2) that he could easily do. Not only could he solve this problem quicker than his peers who memorized all their facts, I’m guessing that when he gets to algebra, creating equivalent algebraic equations to solve a problem will make sense to him.

When we look to the research, it pushes this further and suggests that students’ intuitive abilities to double numbers can be used to build their multiplication fluency.

A group of researchers worked with middle school students that were struggling with their multiplication facts. Students first strengthened their ability to double by starting with simple doubling problems (1,2,3,4,5,10) and eventually moved to more complex problems (double 97 or continuing a sequence of doubles). Throughout all of these sets, students were encouraged to explain their strategies.

Once students were fluent in doubling, the connection to multiplication was made. Through a series of progressively harder tasks, students build on their ability to double to find facts they don’t know. Eventually, students could reason about a fact like 8 x 7 by knowing double 7 is 14 and double 14 is 28 and double 28 is 56.

For more details about the activities, check out:

Flowers, J. M., & Rubenstein, R. N. (2010). Multiplication Fact Fluency Using Doubles. Mathematics teaching in the Middle school, 16(5), 296-301.

3 games to help students master multiplication facts

If you want to avoid drilling students on multiplication facts, games are a great way to encourage fluency.

In one study, researchers used multiplication games instead of worksheets or timed tests with third graders in a Title I school. At the end of the school year, students were tested on 100 multiplication facts. All the students in the class, except one, completed all 100 problems correctly in under 10 minutes.

Here are three of the games they used:

1.  Rio This game is played in groups of three. Each group needs 10 tiles, 15 chips, and a 10-sided number cube with the digits 1-10 on it. Students work on one multiplication table at a time.  So if they are working on 3’s, they write the products for the 3 times table (3,6,9,..) on the tiles.  The tiles are then mixed up and placed in the middle of the table. The first player rolls the cube and puts his or her chip on tile with the product of that number and the table they are working on.  The second player then does the same. If a player rolls a number and there is already a chip on the product, he or she must take that chip. The winner is the first person to get rid of all of their chips.

2.Salute. In this game, students are given a deck of cards and placed in groups of three. One student is the dealer and hands out a card to the two other players. Without looking at the card, the two students say “Salute!” and put the card on their forehead. The dealer, who can see both cards, says the product and each player (who can only see what the other person has) tries to guess what card is on his/her head. The player who guesses correctly first wins both cards.

3.Multiplication War:  This game is a modified version of the game War. A deck of cards is split between two players and each flips over the top card at the same time. The student who says the correct product of the two numbers first wins both cards.

The article mentions a number of other games and how the games were used with the students. For example, the games were only used for fluency AFTER the students developed an understanding of what multiplication was. The teacher also made strategic choices about the order in which the games were introduced, how students were grouped and what facts were used by different students.

Want to know more? Read the article below.

Kamii, C., & Anderson, C. (2003). Multiplication games: How we made and used them. Teaching Children Mathematics, 10(3), 135-141

Multiplication Facts in Middle School

I hear a variation on the following question almost every time I talk with middle school teachers:

How am I supposed to teach ratios (or algebra or operations with signed numbers or …) when my students don’t even know their multiplication facts?

Yes. There are middle school students who don’t know their multiplication facts. I was shocked by this when I first started teaching middle school. I seem to remember that when I was a student everyone in my class knew their multiplication facts. I’m willing to bet that my teachers remember this differently.

There are lots of good reasons for students to be fluent with their multiplication facts. Wallace and Gurganus (2005) argued that not knowing multiplication facts can affect students’ development in math as well as their confidence and attitude towards math.

What is still up for debate is the best way to foster students’ fluency. Some people think lots and lots of multiplication drills are the way to go. I sat in a class recently where students spent the first minute of class completing as many multiplication facts as they could on a sheet.

It was a mess. The kids who memorized their multiplication facts back in elementary school were bored. The others were embarrassed and/or frustrated. Not a great way to start class.

The research backs up my experience that timed tests alone won’t be enough to help those who are still struggling to master their facts in middle school. Especially if the tests aren’t combined with students setting their own learning goals or other interventions.

Baroody (2006) noted that drills are often inefficient since there are too many facts to memorize and that they can limit students from developing flexible strategies. Frequent timed tests can also cause anxiety and create a culture where speed is more important than understanding (Issacs & Carroll, 1999). The pressure to memorize facts can turn children away from math.

So if we agree we want students to master their multiplication facts and that timed multiplication tests by themselves aren’t going to work, what do we do? I’ll talk about what the research suggests next time.

Baroody, A. J. (2006). Mastering the Basic Number Combinations. Teaching Children Mathematics, 13, 22–31.

Isaacs, A. C., & Carroll, W. M. (1999). Strategies for Basic-Facts Instruction. Teaching Children Mathematics, 5(9), 508-15.

Wallace, A., & Gurganus, S.P. (2005) Teaching for Mastery of Multiplication. Teaching Children Mathematics, 12(1): 26-33.