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.
Say, for example, a student is trying to solve 36 x 27 and they are really not secure with their 7s facts. The first strategy is a Tic Tac Toe strategy. It also resembles a hashtag! To use this strategy, students draw a tic-tac-toe board. In each of the nine spaces on the board, students write a multiple of 7. Notice the dots under the board? Students use those dots to count on, so they don’t write incorrect multiples. It sounds like this: After writing 7 (7 x 1) in the first space, the student touches each of the dots with their pencil tip saying 8, 9, 10, 11, 12, 13, 14 and writes 14 in the next space, because 2 x 7 = 14. You can see that solving this problem (36 x 27), they only really need to complete up to 7 x 6 in the board, although the picture shows the board completed. I have seen teachers post these charts in their classrooms as a visual support for students as they are learning their facts. Remember, we don’t want students to practice incorrectly! Another great idea is to make a T Chart, as shown below. The dots can still be used to ensure accuracy.
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!
I *love* the idea of facilitating that work ethic. If you approach it that way, you’re not saying “your punishment for not knowing your sevens is that you have to copy them…” but you’re saying “okay, you’re not there yet… but there are different ways of getting there.” So it’s more than talking — because if you’re hte kiddo who doesn’t know the 7’s, you’re thinking (( well, let my little invisible self stay invisible ’cause you ain’t talkin’ to me )) … but if you stick that tic tac toe stuff up on the wall and put smileys next to the students’ version of the tic tac toe or the T chart…
ABSOLUTELY!! What a masterful way to explain how to turn something negative into a positive. Thank you so much for sharing your insight!
My students know that Ms. B is going to ask them, “What strategy did you use to solve that?” It has taken them a while to understand that the strategies aren’t tricks but sound mathematical thinking. The persistence and effort doesn’t come easily but they have crossed over to thinking of themselves as math thinkers instead of lucky math problem solvers.
Well, this is awesome! I can’t wait to use it with my skip counting songs tomorrow!!!!