The advantage of these algorithms, of course, lies in the fact that we can carry out calculations quickly. If we follow the steps precisely and avoid making mistakes with our number facts, we will consistently generate correct answers. The disadvantage of using algorithms is that genuine understanding of math concepts is less likely to occur. When using algorithms, we are merely applying a series of memorized procedures, whether we understand their rationale or not. I remember, for example, being taught as a kid to “carry the one” when multiplying a one-digit number times a two-digit number, but I never understood why. I just did it because I was told it was the way to get right answers.

A child using algorithms can quickly solve problem after problem, but one tiny computational or procedural mistake will lead to an incorrect answer, and the student applying that procedure may never notice this error. Since my school adopted the CGI approach, I have been exploring with my students a wide variety of alternatives to these traditional algorithms. We are always on the lookout for strategies that are reliable, efficient, and rely on our number sense, not the application of memorized procedures that we may or may not “get.”
 

In this tip I highlight the “Break Apart” method of multiplying larger numbers. Though it is officially known as the distributive property, I prefer the term “break apart” method because I believe it’s less intimidating to kids and because it accurately conveys the heart of the approach.

When multiplying, for example, 6 x 247, the students break the 247 apart into 200, 40, and 7. Then, they multiply the 6 times each number separately. Finally, they add the parts together to arrive at the correct product. Here’s how it might look on a child’s paper:

6(200) + 6(40) + 6(7) =
1,200 + 240 + 42 =
1,482

This strategy is not quite as fast as the traditional algorithm, but it’s not that much slower, and it is certainly more efficient than other conceptual strategies I have seen that require children to use a great deal of time and workspace. My favorite part about this strategy is that it strengthens children’s number sense and understanding of place value. Each year, more and more of my students are using this strategy.

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Note: There are several online masters programs for teachers for people interested in becoming a math professor.