Talking about divisibility rules

Earlier this week the math club that my younger son is in handed out a list of divisibility rules. It was 3 pages of rules to memorize – I was dumbfounded.

Later in the week my older son asked me about the divisibility rule for 11, and that question planted the seed for a little talk about divisibility rules today.

I started today’s project by asking them for some simple divisibility rules that they knew – they mentioned the rules for 2 and 3. Then we investigated why these two rules were true:

 

Next I asked for two more easy rules – they mentioned 5 and 6. So, we investigated these two rules a little more just as in the last video. Then we talked about the rule for 8.

 

Next we moved on to talking about the divisibility rule for 11. Sorry that this part of the conversation went a little long, but the boys had some interesting ideas and we just kept talking 🙂

 

Finally we looked at a challenging problem involving divisibility rules. The question is problem #2 from the 1984 AIME, and asks us to find the smallest multiple of 15 whose digits are either 0 or 8.

 

The ideas behind the divisibility rules are really neat and give kids a chance to learn some basic number theory and also get a little arithmetic practice. I really think that kids will have fun learning a little bit about why these rules work – ESPECIALLY in comparison to the fun they’ll have memorize a 3 page list of rules!

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