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# Divisibility Rules

Lesson 1 of 26

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

#### DO NOW

*5 min*

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.

#### Resources

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#### Direct Instruction

*40 min*

Today the students will be learning about the rules of dividing. Since division is a big part of 6^{th} 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.

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#### Numbered Heads Together

*30 min*

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.

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#### Closure

*10 min*

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.

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*The Divisibility PowerPoint is wonderful!! Thank you for taking the time to create...really made my job today easy. | 2 months ago | Reply*

*Responding to Pamela Olmstead*

Hi Pamela,

Thank you for inquiring about my thoughts on independent practice time. I have found that the more students engage in "accountable" talk, the better math learner they become. In order to engage in this type of learning, they have to be able to hear how other students think about solving problems. Leraning is still taking place! If needed, students can always do independent work at home. I use some websites that help promote what I'm teaching and will also give feedback. Good sites to use: buzzmath, IXL, and thinking blocks. Additionally, as students are working in groups/partners, you can always walk around and have them show you what they are talking about.

| 3 years ago | Reply

I love and appreciate so much the time and effort you have given so that others can benefit. I have used so many of your lessons in my own teaching. I sometimes feel concerned that I am not giving enough practice problems. Some of my students rely so heavily on their peers for support. Do you give extra practice problems (not even necessarily homework) that kids can do? I love the idea of together (whole class), partner (in my case I use groups) but then I seem to be missing the independent piece. Any advice or thoughts? Thanks Pam

| 3 years ago | Reply

@Yacelys The scaffolding strategies I have in place center around cooperative learning. At each of the tables, I have them mixed by ability. High, Medium High, Medium Low and Low level learners. The High and the Low always sit diagonally across from each other. This way, learners benefit from their table-mates in the most effective way. Additionally, all students are required to participate and they can participate at their level. Students work independently first, then they use team time to check their work.

| 3 years ago | Reply

@Jeff,

4 and 9 should be in the power point. I'm guessing that you may have been looking at it through the preview lens. You will need to download to see it all. Our school has a blocked schedule and we do have math class daily, for 85 minutes. If I were to teach this in a shorter time frame, I would introduce the rules and apply it on the nest day.

| 3 years ago | Reply

On the direct instruction for divisibility rules, 4 and 9 at least are missing. Is all four steps designed for ONE class. That is a long class, 85 minutes long, or is it broken down into a couple of days? Thanks for your help and your hard work.

Jeff M from Massachusetts.

| 3 years ago | Reply

Michelle great lesson! You have provided students with deep understanding to divide multi-digit numbers and your activity gives an opportunity for accountable discussion. I did not have an opportunity to read any scaffolding strategies, can you please clarify that part! Thank you so much for this great lesson!

| 3 years ago | Reply*expand comments*

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- LESSON 1: Divisibility Rules
- LESSON 2: Finding the Greatest Common Factor
- LESSON 3: Distributive Property
- LESSON 4: What's really going on with division?
- LESSON 5: Division of multi-digit numbers
- LESSON 6: Checking your quotient
- LESSON 7: Finding the Least Common Multiple (LCM)
- LESSON 8: LCM stations activity
- LESSON 9: Finding Equivalent Fractions
- LESSON 10: Benchmark Fractions and more
- LESSON 11: Adding and Subtracting with Fractions
- LESSON 12: Multiplying with Fractions
- LESSON 13: Dividing Fractions
- LESSON 14: Dividing Fractions - Stations
- LESSON 15: Dividing Fractions within word problems
- LESSON 16: Review & Assessment 6.NS.A.1 and 6.NS.B.4
- LESSON 17: Dealing with Decimal Models
- LESSON 18: Reading and Writing with decimals
- LESSON 19: Dewey Decimal system for ordering decimals
- LESSON 20: Adding and Subtracting with decimals
- LESSON 21: Multiplying Decimals by Whole Numbers
- LESSON 22: Multiplying Decimals by Decimals
- LESSON 23: Dividing Decimals by Whole Numbers
- LESSON 24: Dividing Decimals by Decimals
- LESSON 25: Prepping for the Exam!
- LESSON 26: Final Assessment 6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4