How to Multiply Binomials Using Algebra Tiles

I had never even heard of Algebra tiles until my third year of teaching.  Our school invested in a bunch of Algebra tiles, and I quickly had to learn how to use them.  I tried searching the internet to understand how to use these with my students...but I couldn't find a lot of information.  So I took some time at my desk alone with my blocks and started figuring these things out...and it was like gold.  So awesome in so many ways. Suddenly integers, solving equations, simplifying expressions, factoring trinomials, and multiplying binomials made so much sense.  When I used Algebra tiles in my classroom I was able to reach all students.  They are magic! Today I am going to share with you how to use Algebra tiles to teach multiplying binomials.  

Start by reminding your students how to find the area of a rectangle.  Connect the fact that when you multiply two factors together you also are calculating the area of a rectangle with the factors as the side lengths.  Polynomials work the same way.  If you are given the factors (x + 2) and (x + 3), those are the side lengths of a rectangle, with the product as the area.  

Algebra tiles showing x^2 + 5x + 6 as a rectangle with side lengths x + 2 and x + 3
  • Students line up the factors to represent the length and width.  
  • Students fill in the the area with blocks that are the same length and width as the blocks on the sides of the space they are trying to fill.  
  • Once the space is filled they will have a rectangle.
  • Students will see what blocks are in the area space of their rectangle, and that's the product of the binomial factors.  
Algebra tiles showing 2x^2 + 5x + 2 as a rectangle with side lengths x + 2 and 2x + 1Algebra tiles showing x^2 + 5x + 4 as a rectangle with side lengths x + 1 and x + 4

If you need some activities to practice multiplying binomials in your middle school math classroom you can check out these products below.  Click on the photo for more details.  
Factoring and Multiplying Polynomials Stations      Factors and Models with Algebra Tiles Task Cards

If you don't have Algebra tiles for your classroom you can use these printable ones.

Algebra Tiles Printable FREE

x^2+5x+6 factored using algebra tiles

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