Teaching the Distributive Property

The distributive property can be a very tough concept for children to grasp. It seems that every year, I have to slow down and really take my time with this concept. Like I previously stated in the blog post Teaching Math So Students Get It, it’s crucial that you apply this methodology so students can grasp the distributive property.

Many upper elementary students find the distributive property to be tricky, so I prefer to take it slow while teaching it. In this post, I describe my exact steps for introducing the distributive property and working through mastering its basics with my students.

CONCRETE COUNTERS

The week or so before the lesson, I start to use the word “distribute” regularly. I’ll ask a student to “please distribute these worksheets to everyone” to start familiarizing them with the term. Once the lesson begins, I remind students of the area model and how to make arrays. I start with a simple array, such as 3 x 6. After students have created the array, then I ask them to brainstorm all the ways that we can break up the six. I model an example:  1+5, 2+4, 3+3, 4+2, 5+1 (which lends itself to reminding students about the commutative property). Then, we pick one, and I have the students use my really “fancy” mat and these yellow and red counters. I have students choose one of the sets we created (such as 1+5) and choose the first number (such as the one) to model in red and the other number (such as the five) to model in yellow, but the entire thing still equals six. We practiced this several times and even practiced filling in the pre-filled template. (See the picture below for an example.)

CUTTING THE GRAPH PAPER TO MAKE IT SEMI-CONCRETE

After students have mastered the counters, I then hand them some scissors and some graph paper! I provide students with some multiplication problems similar to the above to still keep it simple. Once they have all this mastered, then we will worry about the larger numbers. I’m more worried about the concept and understanding the meaning. I have students then take it, break it up, and cut it into two parts. They then glue it into two different boxes and label each very similar to the concrete method above.

FILLING IN PLOTS ON A FARM

Since the distributive property is such a difficult concept, I like to move s-l-o-w-l-y before I move into the abstract. So, I give them the next task of pretending they are farmers! Students love this activity because they get to draw and color “plots” of their favorite vegetables while drawing all the possible models of the distributive property to their multiplication expression. I like to use this as a quick assessment to evaluate if my students understand the distributive property (and the commutative property). As a bonus, I can differentiate the multiplication expression!

Once students have mastered this, then it’s time to move into the abstract and practice, practice, practice. If you liked these activities, then you can find them all in my Area and Perimeter Math Workshop Unit, complete with 14 other hands-on lessons and much more! No matter how you choose to teach the distributive property, remind yourself that your students will get it; it just takes time and lots of concrete modeling and practice.

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