Although I made both terms positive, I could have easily made one or both negative by using two different colors. One would represent positive terms while the other would represent negative terms.
I defined terms as:
2 by 2 = x^2
2 by 1 = x
1 by 1 = one.
I created almost a lattice set up with the x + 2 across the top and x + 3 down the side.
The next line, I broke the x + 2 down into x + 1 + 1 and set one 2 x 1 under the x and a 1 by 1 under each of the ones.
I repeated the same for the x + 3 so each term was represented by a lego.
The last step was being the multiplication of x * x = x^2 which gives you a 2 by 2 block. The next step was to multiply all the x's by the ones to give an x represented by the 2 by 1 blocks. Finally it was time to multiply 1 by 1's or the single block. It is easy to see the answer is x^2 + 5x + 6 just by counting.
If I had to, I could also multiply x^2 by x using the 2 by 3 lego block. Again based on the visual representations, its much easier to see how the multiplying the various terms works and at the end, its easy to combine like terms.
Yesterday, I shared how Legos could be used to show combining like terms in a similar way. It will be a while before I try multiplying binomials with my students but I'd love to hear what you think.
Have a great day.
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