# Improving Number Sense with the Divisibility Rules

I decided to make divisibility my first lesson of the year for 7th grade next year for a couple of different reasons: it is a skill used in many different concepts throughout the year and it really helps promote overall number sense in students.

The divisibility rules (hopefully) help students be less dependent on their calculators, which is an area I am hoping to improve on this year.  So even though it isn’t the most exciting lesson of the year, it is an important one, and I think it’s a good way to begin the year.

I go over the rules for 1 – 10 with my students.  (I used to skip over 7 but every year students ask me if there is a rule for 7….so now I give them the rule along with an example for which the rule could be useful (i.e. 231) but then explain that 9 times out of 10 it is easier to just do the division than it is to use the rule).

In addition to the rules I give students tips, like if a number isn’t divisible by 2 then it isn’t divisible by any other even number.  Tips like that help with divisibility by 8, since that isn’t the most useful rule.  I tell students to only check for divisibility by 8 if (1) the number is divisible by 2 and then (2) if it is divisible by 4.

I made half-sheets the students can stick in their notebook with the divisibility rules.  You can download it free by clicking the picture below.

To make the lesson more exciting I enlisted the help of my programmer husband.  He was able to build an interactive divisibility rules game that my students can play on their chromebooks, which I am super excited about!  In the “Divisibility Challenge” game, you can choose which rules you want to practice and then either play for mastery, speed, or just for practice.  I think I am going to originally have students play for mastery, where they need to play until they get 10 questions correct.  I plan to begin class the next day with a speed competition to see who can get the most questions correct in 3 minutes.  Competition always seems to get middle school students involved and engaged!  Click below to try a round free.  (It should open right in your browser).

If you are interested in getting the full game for your class it can be purchased in my tpt store for \$6.