Distributive Doctors


One of the trickiest concepts to explain to my 3rd graders is the Distributive Property of Multiplication. It seems that every year I have a few students that have a hard time “seeing” why

3x4 =(3x3)+(3x1).

I think part of it has to do with the fact that my babies get overwhelmed by seeing so many numbers and operations in a single problem. I mean I can understand that… up until now they’ve become accustomed to seeing simple expressions such as 4x6 or (3+2)+5.


However, with the distributive property they seem to go into a state of panic, shock, or both and just freeze up. That’s why I came up with Distributive Doctors.

I always like to begin the unit by reviewing arrays using manipulatives and this year was no exception. Here we are forming arrays out of dinosaurs.

(Did you notice how this child chose to use different colors for each row?… Do you think she’s a visual learner?)


Next up, we made an array on our Distributive Doctor sheet using blue cubes… and recorded the expression 4x5. (Tip #1-Place the recording sheet inside of a page protector and you can reuse it. Tip #2- Glue a pom pom to the end of an expo marker and you have a handy eraser)


Students then pretended they were surgeons “cutting” apart their arrays (We chose to use yellow popsicle sticks instead of scalpels… SAFETY FIRST) into two smaller arrays like so…


Once again, students recorded the expression for each array. We then discussed how the array on the right (4x3) plus the array on the left (4x2) equals the array we started with (4x5)… that is why…              


We practiced a few more times and I began to hear music to my ears… “Ahhhh’s” and “Now I get it!” 

At this point, we were ready for one of my favorite activities  …


For this activity each student demonstrated their understanding of the distributive property at work by cutting out their own array, then surgically separating it into 2 smaller arrays (using scissors this time… still no scalpel) , and finally, completed the equation at the bottom.

My kids had SO MUCH FUN with this activity that some asked if they could complete both a male and female doctor… Of course, we don’t discriminate in this classroom!…  (insert happy dance here)…{you can find this activity in my TPT store by clicking on the picture above}

After sufficient practice at the concrete level, we moved on to the representational level where my students completed the same activity but WITHOUT manipulatives. Take a look…


As you can see, they performed the same steps but with X’s instead of squares. My ultimate goal was to build enough scaffolding so that they could eventually carry out the distributive property without manips. or pictures.

Finally, we moved on to the abstract stage where they put the distributive property to practice …


So as you can see, we have been busy bees lately… or should I say

Daring Distributive Doctors…

I wonder if any of my kiddos are going to dress up as doctors for Halloween? Can’t wait to find out…

Much love,



  1. What a great way to see the math! Thanks for the post!
    The Picture Book Teacher's Edition

  2. I just LOVE this idea! I am definitely using this idea this week with my third graders as we attempt to understand the distributive property!
    Short and Sassy Teacher

  3. Very creative! Thanks for sharing!

  4. Love this lesson! Just shared it on my Five on the Fifth post. Such a fun way to teach this confusion concept!

    I Teach. What's Your Super Power?

  5. Like you, I teach my fourth graders to cut large arrays into smaller arrays. I LOVE the fun and creativity you put into this lesson. Thanks for sharing.
    Tales from a Fourth Grade MathNut


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