There are so many steps to teaching multiplication. It starts with understanding what multiplication is (area or arrays), moves into learning the math facts, and proceeds into conquering two digit and three digit multiplication. There is a step that I often skipped as a classroom teacher: properties of multiplication.
*This is a guest post from Rachel of You’ve Got This Math.
Teaching the Properties of Multiplication:
As a teacher, mastering words like associate property and distributive property sounded hard, and took away from the time needed to learn those multiplication facts!
The more I learn about math, though, and teaching the concepts and not just formulas…the more I realize that the properties of multiplication are important too. Essential, really.
When we teach children the properties of multiplication, we are actually equipping them to solve numerous expressions…and even begin to build a foundation for algebra. Important stuff, right?
So today, I have a few cut and paste multiplication properties pages to help your children learn these important properties.
Preparing the Properties Cut & Paste Pages:
These multiplication properties cut and paste activities are really no prep. Woohoo!
First, print out the pages you need on regular copy paper.
Then provide glue and scissors to your kids and you’re ready to go.
How to Complete the Properties of Multiplication Pages:
Before you pass out these multiplication properties cut and paste pages, it’s important to understand what each word means.
I would also help kids draw or build visual models of each property before working out these cut and paste pages. This will help solidify their understanding and help them to visualize each problem in their mind as they solve them.
Commutative Property of Multiplication
This is probably the easiest of the three properties included in the cut and paste packet.
Just like addition, the answer does not change if you add 5 + 6 or 6 + 5. You can multiply 3 x 4 or 4 x 3 and you will get the answer twelve either way. A simple definition is that order does not matter in multiplication.
In the Cut and Paste packet, there is only one page for this, as this is pretty simple for kids to see and understand. To complete it, kids simply find the multiplication expression that will make the equation true.
For example, the first question is 6 x 4 = ___________.
Therefore, kids must find 4 x 6 as this will make the equation true and models the commutative property.
Associative Property of Multiplication
As we move to our next multiplication property, things get a little more complicated.
We are no longer multiplying two numbers, but instead are multiplying three or more.
But once again, the order does not matter. Or more specifically, where we put the parenthesis does not matter.
Let’s look at the problem 2 x 3 x 4.
I could solve the problem like this:
(2 x 3) x 4
6 x 4
or like this:
2 x (3 x 4)
2 x 12
As you can see, no matter where I put the parenthesis the answer is 24 (or again, the order in which I multiply the numbers doesn’t matter).
There are two cut and paste activity pages for the associative property.
The first one has problems like 4 x 6 = _______. The children then have to find the expression that makes the equation true.
In this case, the answer is 4 x (2 x 3).
There are also some problems that just show the parenthesis switched. Like (8 x 5) x 15 = 8 x (5 x 15).
The second cut and paste activity has kids solving expressions where they could use the associative property to solve.
Now this is a fun one. Distributive property basically says that you can either multiply the sum of two digits or multiply those two digits separately.
For example, in the problem 5 (3 + 2) I could do two things:
I could multiply five times 3 and then five times 2 and add those quantities together:
5 x 3 + 5 x 2
15 + 10
or I could add up the addends first, and then multiply:
5 (3 + 2)
5 x 5
It’s especially helpful to use an area model to show kids this, with the length of one side of the rectangle equal to five, and the width equal to (2 + 3).
Related: Understanding the distributive property through problem solving (free printable)
There are also two cut and paste activities for the distributive property.
They require that kids once again make the equations true.
They may be asked to find the equivalent expression to 9 (5 + 2) which would be (9 x 5) + (9 x 2).
Sometimes, they may be given (2 x 3) + (2 x 5), which would be an equivalent expression of 2 (3 + 5).
If you’d like more equivalent expression cut and paste pages, try this additional free download!
Enjoy playing with these different properties of multiplication!
You’ve Got This
Looking for more multiplication practice to build conceptual understanding? Check out my Introduction to Multiplication Bundle!
This includes skip counting activities and games, hands on lessons to make sense of multiplication and low-prep games to help kids develop fact fluency.
Rachel is a homeschool mom to four little ones, ages 2 to 6. She is a former public elementary teacher, and has recently begun blogging at her page You’ve Got This. You can also find her on Facebook and Pinterest.
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