Distributive Property of Multiplication

For many years I dreaded having to teach my 3rd graders the Distributive Property of Multiplication. They just always seemed to struggle!


Then one day I had an idea that changed ALL of that and teaching the Distributive Property has actually become one of my FAVORITE math lessons of the year!


What’s my secret you ask?
The Distributive Doctor
more on Doctor D. in a little bit…
But first, let’s talk about planning… I like to block out a few days (usually 3-4) in order to provide my kiddos with plenty of practice at all 3 levels of instruction: concrete (using manips), pictorial (making drawings), and abstract (using numbers).
  We begin by…
Manipulatives are key in order for students to be able to “see” and truly understand this property. So we use them quite a bit in the beginning!
I’ll start off by having my students show me an array. (This step is usually easy, since we’ve already learned about multiplication and arrays.)

Next, I tell them that we’re all going to be distributive doctors or surgeons for the day! They LOVE this! I even refer to them as Dr. Smith or Dr. Rodriguez :0) You should see their faces light up when I call them all doctors!!!!!

Our first “operation” as newly named Distributive Doctors is to use our scalpels, otherwise known as popsicle sticks, to cut our arrays.

Using an EXPO marker, I have them write on their desks a multiplication expression for each of the arrays. (Don’t worry, the writing comes off easily with a tissue.)

At this point we spend some time discussing that we haven’t added or taken away any counters so the number of bears we started with has not changed. What has changed, however, is how we’ve decided to group them.
Next, we add both arrays together to find the total. We repeat this a few more times and practice “breaking apart” the arrays in both horizontal and vertical directions.
The following day we practice some more!
Drawing Pictures is next… Once I feel the majority of my class has mastered breaking apart with counters, we move on to pictorial representations. We follow the same steps we practiced above, the only difference is that students are no longer using manips., but instead drawing pictures.
You can make things interesting by using a Q-tip and paint. The key is to provide plenty of time experimenting with the Distributive Property so that students become comfortable with it.


You can even set up a center with supplies such as graph paper, scissors, colored pencils, and glue sticks.
One of our favorite activities is Doctor D. You can check it out by clicking here.
Using Numbers is the last step. Now that students have had plenty of practice visualizing the Distributive Property, it’s time to remove the support.
Some students will reach this level sooner than others and that’s okay. The goal is for all kids to receive PLENTY of practice and support in the beginning, so that by the time they get to the abstract level of understanding they get what’s going on. All of the hard work and time that was put in in the beginning will pay off in the end!
I hope you can take an idea or two back to your classroom! If you have other ideas on how to practice the distributive property, share them in the comments below!
Many of the resources used in this post come from my 
Distributive Doctor resource which can be found here.
Looking for more great math ideas? 
Click here to follow my Math Pinterest board…


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  • Reply
    Chrissie Rissmiller
    February 13, 2016 at 1:13 am

    This is so smart! I just taught this lesson a few weeks ago. It is a difficult concept for many third graders, but this makes it so much easier! 🙂
    Undercover Classroom

    • Reply
      Melissa Yalesias
      April 5, 2016 at 7:27 pm

      Thanks, Chrissie! Yes this is such a tricky concept. I used to dread having to teach it… Now I look forward to it since I know my students usually get it this way. I'm glad this way made it easier for your kiddos.
      :0) melissa

  • Reply
    Your Thrifty Co-Teacher
    February 27, 2016 at 7:22 pm

    I even used this with fifth grade as an introductory lesson and it was great!

  • Reply
    September 10, 2018 at 8:43 pm

    Where do you get your manipulative from? ☺️

    • Reply
      January 13, 2019 at 2:50 pm

      I’ve purchased a few throughout the years, and others have come with different math series we’ve had. A great way to get manips is also to ask around your building. Sometimes people have too many of a specific kind and want to get rid of them.

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