In Ontario, today marks the THIRD week of school! As teachers have gotten to know their students more and students have begun to settle into their classrooms, teachers will begin to start teaching new concepts (like division!). Note teachers have been teaching this whole time. They have been teaching routines and expectations, assessing what students know and don’t know and reviewing concepts from past grades. As a result, your child may find school a little bit trickier than the past two weeks.

On our last math Monday blog, we talked about transitioning from addition to repeated addition to multiplication. Today our focus will be going from multiplication to division and understanding the properties of division.

What is Division?

Division is repeated subtraction. We are taking a large number and we are repeatedly subtracting the same number from it and then seeing how many times we can subtract that number.

Division is taking a large collection of objects and then splitting it evenly into groups.

In a division question, the largest quantity is the first number written.

Example: 12÷4=6

This differs from multiplication and addition where the largest quantity is the answer.

Example: 4x6=12 or 6+6=12

This is similar to subtraction.

12-6=6

Fact Families: Subtraction and Addition (A quick review)

Subtraction and addition are inverse operations of each other. As a result, you have what are called fact families. Fact families are three numbers that can make up four different questions. I like showing the three numbers as a triangle with the largest number written at the top of the triangle.

Example: 12, 4, 8

4+8=12

8+4=12

12-4=8

12-8=4

Fact Families: Multiplication and Division

The above strategy for teaching addition and subtraction is quite common in the primary grades. However, we can use the same fact family concept to teach multiplication and division.

Example: 12, 6, 2

6x2=12

2x6=12

12÷6=4

12÷4=6

Starting with counter blocks are great because it lets the student understand what is happening when you use a multiplication or division symbol.

Properties of Division

While students are exploring the connection between multiplication and division, we also want to take some time to explore some unique properties of division.

Dividing a Number by One:

When we take any number, let’s say 12, and divide it by 1, our answer is 12.

It is really fun to use blocks and have students’ model this. Students count out 12 blocks. Then they make one group and put all the blocks in that one group. How many blocks in total? 12.

Dividing a Number by Itself:

When we take any number, let’s say 12, and divide it by itself, our answer is 1.

Again, really fun to have students try it out with blocks. Count out 12 blocks. Then have them make 12 groups. Then have the students evenly split the blocks between the 12 groups. They will discover that 1 block can go in each group.

Dividing a Number by Zero:

When we take any number, for consistency let’s say 12, and try dividing it by zero, finding an answer is illogical.

Again, have students try it out. Count out 12 blocks. Then have them make zero groups. Ask them to split the 12 blocks between the zero groups. Can they do it? NO! It’s illogical. It is fun to pull out a calculator and show them what happens on a calculator when we do that!

Dividing Zero by Any Number:

When we take the number zero, then try dividing it by 12, the answer is zero.

Again have the students try it out. Count out zero blocks. Then make 12 groups. How many blocks does each group get? Zero.

Division on its own and when exploring it’s relationship to different operations, can be really fun! Our Latch onto Learning tutors utilize these mathematical principles to make learning fun and engaging. If your child is struggling with division, I hope this blog post gave you a few ideas on ways you can explore division at home.

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