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I got an interesting question from a college instructor last week asking why the core excludes the divisibility rules. I wrote back with a comment that the core is very consistent in avoiding tricks or memorized systems without understanding. She wrote back with a very well reasoned response about the rules being based on place value and the properties of operations. She felt that if the rules were taught correctly and not through songs, games, or other “shiny stuff” they would serve students well. So, we are now considering adding the divisibility rules to our curriculum guides (<a href=”http://schools.utah.gov/CURR/mathelem/Core-Curriculum.aspx” title=”Utah Core Standards”>), with some pretty specific instructions about how they should be taught for understanding. So, Bill and the rest of the forum, what about it? Should the divisibility rules be part of a discussion of LCM and GCF and, if so, when and how?
She is quite right that the divisibility rules are based on the place value system. But the point of focus is not to include everything you might want to include just because it’s a nice topic. That’s how we ended up with the mile-wide-inch-deep curriculum in the first place. I think middle school is already pretty full, and would advise against this. In general, LCM and GCF are quite circumscribed topics in the Common Core, not intended to take up a lot of time in the curriculum. (I’m actually working on a draft of the NS progression as we speak.)
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