We’ve all had them. Those kiddos who understand the process for multi-digit multiplication problems, but miss them anyway because they don’t know their facts and guess incorrectly. Because if I think 6 x 7 = 41, I’m going to miss 36 x 27 no matter how well I know the process. Here are a couple of suggestions.
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First, include strategy-based instruction and practice in your classroom. A great resource for that is Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students Beyond Memorization. This helps students understand, for example, how knowing 6 x 6 can help them efficiently determine 6 x 7 (6 x 7 is one more group of 6, or 36 + 6). Or that 6 x 7 (42) is just double 3 x 7 (21). Admittedly, this is a long-term solution and, at this point, won’t help much on the test next Tuesday.
So my second suggestion involves teaching students a strategy for listing out the multiples or facts for numbers they are unsure of. Two such strategies are illustrated below. The Tic Tac Toe strategy involves listing the multiples in a tic tac toe type format. I was introduced to this strategy by one of my amazing 4th-grade teachers. She explained that when they first showed the strategy to the kiddos, they had them number the boxes with a small 1 to 9 in the lower right-hand corner of each box. Now that the students are familiar with the process, they just write the multiples. Another great idea, courtesy of a fellow math coach, is to make a T Chart, as shown below.
Which brings me to another topic. This week I coined what I think is a new phrase: mathematical work ethic. For these strategies to be effective, students have to actually do them. In other words, they have to be self-reflective and determined enough to say, Hey, I don’t know my 7s, but I want to get this problem right. I’d better draw a tic tac toe box. I’ve heard lots of teachers say they can’t make students show work or use strategies. No, but you can teach them the importance of hard work and help develop their mathematical work ethic. I’ve been in many classrooms this year where I’ve heard teachers constantly refer to their students as mathematicians and remind students of how mathematicians attend to precision, communicate to others about their work, defend their solutions, and persevere in solving problems. Sound familiar? Yes, those are the Mathematical Practices. But the key is that these teachers talk about and emphasize them on a regular basis!
I’d love to hear your comments. How do you develop the mathematical work ethic of your students??
UPDATE: Head over to this blog post for a tic-tac-toe multiplication freebie!