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Divisibility Rules for 6 and 9
Lesson 3 of 5
Objective: SWBAT discover the divisibility rules for 6 and 9.
Do Now
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
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 nontrivial 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!"
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Mini Lesson
The goal of today's MiniLesson 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 MiniLesson 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 MiniLesson 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.
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Independent Practice
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
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.
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 UNIT 1: First Week of School
 UNIT 2: Properties of Math
 UNIT 3: Divisibility Rules
 UNIT 4: Factors and Multiples
 UNIT 5: Introduction to Fractions
 UNIT 6: Adding and Subtracting Fractions
 UNIT 7: Multiplying and Dividing Fractions
 UNIT 8: Algorithms and Decimal Operations
 UNIT 9: MultiUnit Summative Assessments
 UNIT 10: Rational Numbers
 UNIT 11: Equivalent Ratios
 UNIT 12: Unit Rate
 UNIT 13: Fractions, Decimals, and Percents
 UNIT 14: Algebra
 UNIT 15: Geometry