## Friday, September 30, 2016

### Divisibility rules 7, 11 and 12

OK, I admit it. Divisibility rules for 7, 11 and 12 are not part of my curriculum but I have so much fun teaching them that I find the time to squeeze it into my lessons.

I do use the divisibility rule for 11 quite often. And because seven and eleven are prime numbers needed for prime factorization and factoring out GCF, I feel it is worthwhile to spend a little time on these rules. I put 12 in this foldable because we use that number quite a bit as well.

As you all know, I am addicted to making foldables. Usually when I have lots of problems to cover I will make one of these booklets. It is a nightmare getting everything to line up and to have the pages in the correct order. This one took awhile and I still wasn't able to  line up the two pages correctly. UGH!

I never see the divisibility rule for 7 taught. It really isn't that hard and it is a great way to practice mental math with the kids.

Before we do the divisibility rule for 11, I have the kids put their pencils down and I write several three digit numbers on the board.

For example:

792

473

396

594

I tell them that, "All of these three digit numbers are divisible by 11. Can you see the pattern?" They look for awhile, I wait and then I add a few more. And I wait and add a couple more. I start to hear, "Oh, I see it!" I tell them not to say the rule but to give me another three digit number that is divisible by 11. I will write down the number and then say, "Yes! That is a number divisible by 11." Then the fun begins. Hands go up and I keep adding numbers to our list. We write down a very long list and then the students explain the pattern to the class.

Next I place some four digit numbers on the board.

Like these:

7546

2981

1364

5698

I tell them that,  "All of these four digit numbers are divisible by 11. Do you see the pattern?" I will wait and place a few more on the board and then they start to guess the pattern just like they did with the three digit numbers. I'm telling you, they love this rule and find it so much fun! One of my students said to me, "Math was so much fun today! We should do this everyday." Oh please repeat that for me again. That is probably why I keep teaching this or should I say having the kids discover the pattern. I can see this being turned into a group activity where the kids talk together to find the pattern as well.

The next day we start on this part of the foldable.

Next we go over rules for 12 and I briefly tell then the rule for 15 because it is so similar to 12 and 6.

And of course, there's a practice page.

There are some extra pages at the end that I used for the students to summarize the foldable. In that section we wrote in full sentences. They groaned. Imagine that!

I would love to hear how this works with your classes. Enjoy.