Divisibility Rules for 2 and 3

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SWBAT discover the divisibility rules for 2 and 3.

Big Idea

Students will work with calculators to discover the divisibility rules

Do Now

10 minutes

For today's Do Now students are going to select a Special Number.  This number will be referred back to throughout the unit as students learn more about divisibility rules, prime vs composite numbers, factors and multiples.

The directions for the Do Now are as follows:

Many people have a number that they think is interesting. What number do you think is interesting? For this unit you are going to have a Special Number. Your number must be a whole number between 10 and 500 that you especially like.

  1. Write down your number
  2. Explain why you chose that number
  3. List 3 or 4 mathematical facts about your number
  4. List any connections you can make between your number and your world

After students have completed the Do Now, I will ask a few students to share what they wrote with the class. 

Group Work

25 minutes

After spending some time thinking about special numbers, students will work in groups of 4 to discover the divisibility rules for 2 and 3.  Since this is the beginning of the year students are randomly grouped together.  I will give each student a calculator. Each group will share a copy of the 2 and 3 Divisibility Rules worksheet.  I will insist that students work together in their groups to complete the worksheet:  

Using their calculators, each student will divide each number on the sheet by 2 and by 3. Following the instructions on the worksheet , students will decide as a group whether to draw a square, circle, or triangle around the number, based on their calculation.  All students in a group must agree on the answer before they write it on the worksheet.

When groups finish their calculations and comparisons, I will ask them to begin discussing the first two questions on the worksheet:

1.  What rule(s) can we come up with for the circled numbers, the numbers divisible by 2?

2.  What rule(s) can we come up with for the boxed numbers, the numbers divisible by 3?


Mini Lesson

10 minutes

As a class, we will quickly review the Divisibility Rules worksheet.  If students disagree on an answer, I will ask them to verify the answer with the calculators. This is a time for students to continue to look for patterns in the results.

After we have reviewed the answers, I will pose these two questions to the class for discussion.

  1. What rule can we come up with for the circled numbers, the numbers divisible by 2?
  2. What rule can we come up with for the boxed numbers, the numbers divisible by 3?

Students may observe that the circled numbers are all even.  If students aren't able to come to this conclusion, I will pose the question, "Are the circled numbers all one type of number?" Eventually, we will all agree to the rule: a number is divisible by 2 if the ones digit is 0 or an even number (MP7).

The Divisibility Rule for 3 is more difficult for my students.  If students have difficulty formulating a rule, I will ask them to add the digits of the first boxed number, 309. Then, I will ask them, "Is this number also divisible by 3?"  This will lead us toward the rule: a number is divisible by 3 if the sum of the digits is divisible by 3. Of course, I want to be careful about letting students jump from a single case to a statement of fact. My scaffolding is intended to launch an investigation to see if the pattern holds (MP8). 

Quick Independent Practice

10 minutes

I will post the below table on the board for students to complete.  I will direct students to indicate if the number is divisible by 2 or 3 with a check-mark.


Divisible by 2

Divisible by 3













After 5 minutes, I will select students to go to the board to share their answers. These students must also explain how they used the divisibility rule to find their answer (MP2).  I will ask the rest of the class if they agree with the students' explanation.  Usually students disagree because there has been an addition mistake.

Lesson Review

4 minutes

As a review of what was covered today in class, I will have students share a divisibility rule for 2 or for 3 in their own words. In other words, I will ask them to explain without looking at their notes.  At this point, I usually choose students who have not had an opportunity to share during class. It helps to be patient for this activity.