## Reflection: Rigor Divisibility Rules - Section 2: Direct Instruction

During this part of the lesson, I wanted to make it more meaningful for the students.  In the past, I've taught this lesson and let them do practice problems deciding whether or not a number was divisible by another number.  This year, I wanted to challenge the students a little more so I used some different questioning to increase the rigor during this lesson.

After the rule for 2,5, and 10

I asked the students to come up with a number that is divisible by 2, 5, and 10.  I took 3 or 4 examples.  We proved that each number was indeed divisible by 2, 5, and 10 by using the divisibility rules.  Then I asked them if they noticed anything about the numbers that were divisible by 2,5,and 10.  I told them we would be practicing MP 7 and 8.  They told me that all the numbers ended in zero.  We talked about "why" this was.  They came up with: ending in zero means it is even. If it ends if 0 it is divisible by both 5 and 10. Next, I asked them if all numbers that were divisible by 10 were also divisible by 2 and 5? (MP 8).  They said "yes" and we talked about why.  Then I asked them if all numbers that are divisible 5 are divisible by 10. They said "no" because numbers that are divisible by 5 can end in 5 and zero.

After the rules 3, 9, 4, 6

I had the students come up with their own numbers and prove the divisibility.  I scripted on the board.  One student would give me the number and I would ask another student to prove that it was divisible by the number.  By doing this, I was able to call upon all students in the classroom.

Using the divisibility rules also allowed me to talk about prime and composite numbers and odd and even numbers.  As a final wrap up, I asked the students how the divisibility rules could help them determine whether a number was prime or composite.  They were able to tell me that the rules are good to find factors of numbers.  If you find that a rule works, then you know you have a composite number.  To determine if a number is prime, they said that if none of the rules work then you might have a prime number.

Questions to enhance learning.
Rigor: Questions to enhance learning.

# Divisibility Rules

Unit 4: Number Sense
Lesson 1 of 26

## 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!

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