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Analyzing Math Mistakes

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

Look at the following multiplication problems and see if you can tell why each one produced the wrong answer. I’ll wait…

FIGURE 1

FIGURE 2

FIGURE 3

Okay, so did you figure it out?

  • Fig. 1 represents the most common error made when multiplying by a 2-digit number. The student did not adjust for place value when they multiplied using the 4 in the 10s place. This error is easy to spot. First, you don’t see a 0 in the 1s place of the second product. Second, the result is always unreasonably small.
  • Fig. 2 is an error I have been noticing more often, and it only occurs when there is a 0 in the top factor. I’ve also noticed that students typically only make this error when multiplying by the 10s digit. Notice that when the student multiplied 3 x 8, they properly regrouped the 2 tens. But when they multiplied 4 x 8, they regrouped the 3 all the way over to the hundreds place. You might look for this error when you have a kiddo who multiplies correctly pretty consistently misses a problem.
  • Finally, another 0-in-the-middle problem. For some reason, the 0 in the middle just throws kids off. In this fairly common error, instead of adding the extra tens, students multiply by the regrouping number.

Which brings me to my next (and real) point. When you look at student work, be sure to look at why they missed the problem instead of just looking for right or wrong. You would do the kiddos above a disservice if you remediated them all the same way. Different mistakes require different instruction.

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