Divisibility Rules

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SWBAT use the rules of divisibility for 2,3,4,5,6,9,and 10.

Big Idea

The students will be investigating mathematical rules for division to assist them with fluency. This lesson will be added to their tool box!


5 minutes

Divide or be devoured. 

I chose this problem because the students will try and divide the big number out by nine.  The problem asks them to do it quickly otherwise their friend will be eaten by the dinosaur.  It’s a good problem to start with because they haven’t had much exposure to the divisibility rules and by the end of this lesson, they should be able to quickly decide if their friend is in danger or not by applying the rule of 9

I would give them a few minutes to decide if their friend is in danger.  They will be frustrated because they want to work out the problem.  Keep the problem for the closure to let them make the connection between this problem and using the rules of divisibility.

Direct Instruction

40 minutes

Today the students will be learning about the rules of dividing.  Since division is a big part of 6th grade CC I felt it important that the look at some of the rules.  Students will learn about each rule: 2,3,4,5,6,9,10 and decide if those numbers can evenly go into other numbers.  I will go through each slide talking about the rule and showing them problems that the rule works for and problems that rule won’t work.  I’ve chosen larger numbers to, again, reinforce that the rules for divisibility come in handy as a starting point for dividing numbers (MP 1)


Students struggle with the divisibility rule for 4, looking at the last two digits.  They confuse it with the rules for 3 and 9.  To eliminate this issue, I have the students draw a box around the last 2 digits to get them looking at the number as a whole, not as parts. 

Numbered Heads Together

30 minutes

I chose to use a Numbered Heads Together 1 because this is new learning and there are a lot of supports put into place with this structure to help out the struggling students.  The activity starts by asking them to apply only one rule.  I will want them to show me how they applied the rule and then give me an answer yes or no.  Additionally, if the answer is yes, I want them to divide it out to convince me and their tablemates that their answer is correct 

Numbered Heads Together supports 

SMP2:  students need to know which rule to apply

SMP3:  students are working together to talk about math

SMP6:  students will use the appropriate rule to support their answers.


10 minutes

I want the students to go back to the DO NOW problem (divide or be devoured) and decide if their friend will be eaten by the dinosaur.  As students are working on this problem, I’m going to be walking around to see who is using the rule of 9 and who is not.  For those that are not using the rule of 9, I’m going to be asking them if there is a quicker way to solve.  When students have decided on their answer, I want them to explain in words how they got their answer and why they took the steps they did to get to their answer.  This is an opportunity for students to think about their thinking.  I’m going to collect this for evidence of student learning.