Divisibility Rules... with a surprise.

 Okay.  Divisibility rules.  Students have been taught them before they come to my seventh grade class.  Maybe they retained some of them, maybe all of them.  But, we review.  Owning the divisibility rules is a HUGE help in pre-Algebra. Percentages, proportions, fraction operations, ratios, similarity, congruence... just to start.  
We use lots of vocabulary around this concept; factor, divisible by, multiple of, reduce, simplify, is in proportion to, equivalent ratios, etc.

This year, my seventh graders made posters for the divisibility rules.  I am a great believer in reuse and recycle.  We used old maps.  The number itself had to be at least half the size of the entire poster, and each poster had the rule, an example, and a "be careful".  We hung the posters around the room, where they were a great resource for the rest of the year.  Also, I chose one student to be the "go to person" for each rule.  Each student was very comfortable with their role, and was welcome to stand up to read the poster as a reference as long as needed, but eventually they all knew every rule cold.  
Quick review?                                                       

2 - one's digit is even
3 - if the sum of the digits is a multiple of 3
4 - if last 2 digits is divisible by 4 (as in 712)
5 - you know this one (ends in 5 or 0)
6 - 2 and 3 are factors
7 - there is no rule
8 - last 3 digits is divisible by 8 (as in 91,824)
9 - sum of the digits is a multiple of 9 

So, what's the surprise?   All this time, I thought there was no rule for seven.  You just divide.  Truth is, I never minded, and would toss in a few big multiples of 7 just so that my students could get the practice dividing.  But, turns out there is a rule for divisible by 7.  Whether you choose to use it or not is your choice...  I will teach it this year to give the students the option.
Here's the way it works.  Let's think about 5292.  

Double the last digit and subtract it from the remaining 3.  529 - 4 is 525.  Now double the last digit and subtract it from the remaining 2.  52 - 10 is 42.  42 is a multiple of 7 so 5292 is also a multiple of 7. 

Thanks for reading.  Were you surprised by the 7 rule?  I was.

Let me know.