Confused by all the different properties of multiplication and what students need to know and understand about multiplication? Join me to learn what the distributive property of multiplication is all about, how to teach it, and how it will help students improve their ability to work fluently with numbers.
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What is the Distributive Property of Multiplication?
The distributive property of multiplication means that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. Clear as mud, right?
If I was trying to define the distributive property of multiplication to my third graders, I would tell them that we can break larger numbers apart, multiply them, then add the products back together. But here is the thing, I wouldn’t rely on a definition to teach this, I would give them plenty of examples in different contexts to illustrate it and then go back and look at what is happening with the examples and try to come up with our own definition of distributive property.
What kind of Examples Could You Use?
The easiest one I can think of to use with students who are new to the distributive property of multiplication, and who may be fairly new to multiplication is this:
Let’s say I want to multiply a number by a two digit number. I would purposely use an easy number to start with. (Hint: Anything multiplied by 5 or 10 tends to be a bit easier). So I write 26 x 5 on the board. Going back to foundational place value, I would pull 26 apart and write them separately next to each other, each one multiplied by 5.
Once students multiply both, I would add the products together for the answer to 26 x 5. Other easy examples could be 12 x 4 or 11 x 5.
I would always teach students the distributive property long before I would take them through the algorithm for multiplying a 2-digit by 1-digit number or a 2-digit by 2-digit number. When students practice this, they can begin to do a lot of calculations mentally. Becoming fluent with numbers is definitely where we want to take our students!
How Else Can We Teach the Distributive Property?
Using the area model is a great way to teach the distributive property and strengthen students’ understanding of area. Consider this example:
Knowing how the distributive property can be applied to the area model comes in handy when students are faced with finding the area of an irregular shape. Practicing dividing up areas that are easy to determine the area gives students the spatial practice they need to look at an irregular shape and see the different, distinct areas.
Rich Math Conversations
The human mind is wired to look for patterns. Once students start to notice patterns, they begin to see connections between numbers that often leads to a new appreciation of math. I never let an opportunity to explore a new-found discovery. In fact, I think it is so important to encourage creativity and exploration in math that I will drop everything and focus on something when a student says the magic words “I just noticed something”.
This happened one day early in my teaching experience and it blew my socks off! We were working on the following problem:
One of my students piped up, “Why don’t you turn it into 48 times 6 so you only have to multiply it by one number instead of two numbers?” Scratching my head, I realized she wanted to divide the twelve in half and double the twenty-four to compensate. I really wasn’t sure if this would work with multiplication. My standard answer in this situation is always, “I’m not sure but I think you may be on to something.”
We did the math two ways to double check this hypothesis: standard algorithm, pulling apart the tens and ones, then adding back together (distributive method). The curiosity level was high as students leaned in to see if the student was right or not. I have to wonder if students were also searching for another pattern to validate that numbers are connected.
What we learned is that, yes, you can divide one number by 2 and double the other number and end up with the same product. Students began to come up with other examples of problems that we could use. We talked about examples that wouldn’t work, like odd numbers. We also wondered if we could triple a number and divide the other number. This led to more explorations.
Two days later, a student contributed to the conversation, “There are so many ways with multiplication. Much more than addition or subtraction.” I knew then that students were beginning to understand the concept of the distributive property.
Next Steps
Once students gain some confidence with this new way to add, it would be a great time to introduce the more abstract, mathematical notation to illustrate the distributive property. As upper elementary students get practice with this type of question, they get exposure to using parenthesis long before a formal algebra class.
More Resources
Not sure how to get started teaching the distributive property? Check out the Distributive Property Bundle for plenty of practice and activities to help students learn and understand the distributive property.
For more resources on teaching the distributive property, check out Jordan Nisbet’s 5 Effective Examples to use in Class .
