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Teaching Distributive Property Using an Area Model

Math can get boring if you get stuck in the 'worksheet' rut.  The worst thing during math (or any subject, really) is to look into the 'crowd' and see a bunch of blank stares on their lifeless faces.. you know what I'm talking about!!  B.O.R.E.D.

This week, I used a completely simple and effective method to teach my struggling third graders about the distributive property using an area model!

We all know that some of our learners retain info the best when they can manipulate things, hands-on.  First, I prepared these materials for our lesson:

one class set of grid paper copies
enough copies of the formula page for my students
to each complete four examples; there are 10 formulas per page

I also gave each student a blank piece of copy paper... blue happened to be what was on hand that day :)

To start the lesson, I modeled coloring in a rectangle with a highlighter on my own grid paper and asked them to recreate the same rectangle on their paper.  Then, we all cut out the rectangle and glued it onto our blue paper

After the first rectangle was glued, I passed out the copy of the formula and had students glue it underneath the rectangle.  We talked about what we already know about finding area (length times width) and wrote down the formula and the area for the first rectangle.

Next, I shaded in another rectangle with pencil that had the same height as the previous rectangle.  Once again, I asked the students to recreate this rectangle and cut it out.  We glued it onto our blue paper next to the yellow rectangle, and tried to make ONE shape out of the two rectangles.  Then, I used marker to trace around the whole rectangle.

We did four more examples together, and they were actually bummed out when I told them we were out of time!  My students even asked me if we could do this activity again the next day... I'll take it!

As homework, I gave them a practice page from my latest TPT resource: 3rd Grade Math - Common Core Print & Go - 300 PAGE BUNDLE.

As you can see, this practice page aligns perfectly with the activity students completed in class!

Interested in teaching your students about the area model using this hands-on method?  Click HERE to snag all of the printables you have seen in this post, including a freebie from my PRINT & GO Bundle on Teachers Pay Teachers.

Does anyone else have another effective way to teach this concept?  

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  1. Just did this activity with my third graders and they loved it! We guided the first two figures as a class and then let them create the next two. Thanks for the activity!

  2. How awesome! Thanks :)

  3. You don't got an answer sheet

  4. Replies
    1. no,According to the encyclopedia of brandon james jr. math is the most important thing to learn at school because of the fact that if you did not know math then you wouldn't be able to learn correctly and according to the article on Math gen it states, ¨Mathgen is a program to randomly generate professional-looking mathematics papers, including theorems, proofs, equations, discussion, and references. Try Mathgen for yourself! It’s a fork of SCIgen, a program which generates random papers in computer science.

      Mostly because it’s funny! But there are some other possible uses:

      Impress your friends, colleagues and/or tenure committee with your prolific research output.
      There are a lot of shady journals out there. I bet one of them would accept a randomly generated paper. Try it, and let me know what happens!
      Cheat on your Erdős number.
      As a way of producing something possibly worthwhile from this project, I am offering randomly generated books for sale via, and will donate $5.00 from each copy sold to the American Mathematical Society, in support of (actual, non-random) mathematical research. This would make a great gag gift for a mathematically inclined friend!
      A great way to come up with thesis topics for your grad students!
      More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. This program only knows a handful of sentence templates, and yet I think its writing style is not far off from many published papers. You could argue this is bad (shows a lack of creativity) or good (makes papers more accessible to those with a limited knowledge of English), but I think we could stand to pay more attention to our writing styles, instead of unthinkingly relying on stock phrases.
      Mathgen uses a handwritten context-free grammar, essentially starting from a basic template and filling in blanks with textual elements of various types. Those elements could in turn contain other blanks, so the process continues recursively.

      The generator itself is written in Perl. The text is then processed by LATEXLATEX and BibTeX to produce the final output file.

      The source code is available through Github at:

      If you don’t want to mess with Git, you can just get a zip file containing the code.

      Mathgen is free software and released under the terms of the GNU General Public License, version 2.0.

      Mathgen was written by Nate Eldredge, incorporating code from SCIgen, by Jeremy Stribling, Max Krohn, and Dan Aguayo, without whom this project would not exist.
      Jordan Eldredge wrote most of the web interface (the parts that are slick and work well; the ugly awkward parts are mine).

      A list of names of famous mathematicians, used in the program, was extracted from the web site The Greatest Mathematicians of All Time by James Dow Allen, and is used by permission. A list of countries and other place names was taken from Wikipedia.

  5. This was the only resource I found on distributive property with area. Thanks a bunch!!!!

  6. This has potential, but I'm afraid it does not show the distributive property. If it did, then it would show that, for example, (4 x 5) + (4 x 2) is the same as 4 x (5 + 2). This activity only finds the area of two joined rectangles.

  7. Thank you for this resource. It was such a great lesson to help my third graders understand the distributive property.