Reflection: Connection to Prior Knowledge Divisibility Rules for 2 and 3  Section 2: Group Work
As my students began working with the calculators, I heard some of them ask one another, "What do we do with the decimal?" They didn't make the connection between a quotient having decimals and a remainder when using long division. This is a topic that we will discuss in great dealing when changing fractions to decimals.
"How do we know 4 can be evenly divided by 2, but 5 can't be evenly divided by 2?" Students responses were appropriate and along the lines of 4 can be divided into 2 groups of 2, but when you divide 5 by 2 there is a remainder. I asked students to verify this with their calculators and they were able to see that 5 divided by 2 on their calculators gave them a decimal.
In the future this will be a brief discussion with students before handing out the worksheet.
Divisibility Rules for 2 and 3
Lesson 1 of 5
Objective: SWBAT discover the divisibility rules for 2 and 3.
Do Now
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.
 Write down your number
 Explain why you chose that number
 List 3 or 4 mathematical facts about your number
 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.
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Group Work
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?
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Mini Lesson
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.
 What rule can we come up with for the circled numbers, the numbers divisible by 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).
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Quick Independent Practice
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 checkmark.

Divisible by 2 
Divisible by 3 
1,386 


24,603 


104,000 


8,671,245 


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.
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Lesson Review
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.
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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