Divisibility Rules for 6 and 9

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Objective

SWBAT discover the divisibility rules for 6 and 9.

Big Idea

Students use calculators to find the shortcut for dividing with 6 and 9.

Do Now

10 minutes

For today's Do Now, my students will apply what we have learned so far about Divisibility Rules. In the table, they will identify which numbers are factors (divisors) of the number in each row.

 2 3 4 5 4,106 76,335 329,751 6,528,970

I will give my students about seven minutes to complete this task. To review their work I will have students come up to the board to share their answers for a complete row, explaining how they used the divisibility rules.

Group Work

15 minutes

For today's Group Work each student will receive a calculator, but each group will receive one copy of the worksheet 6 and 9 Divisibility Rules. I want to make sure that my students work together and discuss their ideas. Students will be directed to complete the worksheet together.

The Divisibility Rules for 6 and for 9 are often more difficult for my students. They may get a little frustrated as they work, so I like to go over the questions with them before they get started. For example, on Question #19 I clarify for students that every number in the chart is divisible by 1, but there is another number that they are divisible by. The goal is to find the non-trivial factor.

Before they start, I remind students that they can use the divisibility rules that they have already learned to answer the questions. "The fun part," I say, "is finding a new Divisibility Rule!"

Mini Lesson

10 minutes

The goal of today's Mini-Lesson  is to review the Divisibility Rules that students discovered as they worked on 6 and 9 Divisibility Rules in their groups. The primary work of the Mini-Lesson is to review the answers to the worksheet. The answers to questions 19 to 23 will lead to the rule for 6:

A number is divisible by 6, if the number is divisible by 2 and 3.

The answers to questions 24 to 25 will lead to the rule for 9:

A number is divisible by 9, if the sum of the digits is divisible by 9.

Although it is not included on the worksheet, I will conclude the Mini-Lesson by discussing the divisibility rule for 10 with my students. Many of them already know this rule, but it is important to state all of the rules as we work through this topic:

A number is divisible by 10, if the ones digit is a 0.

Independent Practice

10 minutes

Since students worked collaboratively for much of today's lesson, I want to give students the opportunity to practice on their own for a few minutes before we bring the lesson to closure. I will ask my students to use the table to identify which numbers are factors of the quantity given in each row.

 2 3 4 5 6 9 10 1,568 23,791 65,042 128,865 359,273

If students do not remember a rule, I will help them. As I do so, I will ask them to write down the rule, so that they have it in their notes to refer to. After 5 minutes, I will ask volunteers to come up to the board and complete a row in the table, explaining the rules as they go. I will encourage students to listen carefully, knowing that I will ask for verbal explanations of the rules in our closing discussion.

Summary Discussion

4 minutes

At this point in our Number Sense unit my students have learned the Divisibility Rules for 2,3,4,5,6,9,and 10. As a group we will conclude today's lesson with a class discussion. I will ask students to summarize one of the divisibility rules that we've learned. I will encourage my students to attempt to do this without using their notes. Rather than refer them to their notes if they are unable to recall a rule, I will ask a peer to give them a hint. I want to encourage student ownership of mathematical knowledge at both the individual and group level. I also like to give my students practice at sharing without giving answers.