One of the things my students struggle with is combing like terms. Although they see the X^2, the X and the numbers, they do not see them as separate entities.
I do not know who to make it easier for them to see they are different. So I came up with the visual representation of the problems using Legos.
I decided the 2 by 2 are great for X^2 because they are square and easy to see a relationship. The 2 by 1 blocks are perfect for X and the 1 by 1 blocks are great numbers. Yes I stacked them and laid them on the sides so the number of blocks could be easily seen.
Although I used strictly positive terms in the example, I could easily have used negative terms by designating two different colors, one as positive and one as negative. If I used negative, I'd have them "take the negative" number away, leaving only the remainder in the problem.
Normally in class, I think I would have students actually combine the like terms from the left side and move them over to the right where the total is but for the illustration, I put them on both sides to see it in the picture.
I hope since the students can see the blocks are different sized for each term, it will be easier to see why X^2 can only combine with X^2 because they keep trying to combine everything into a single answer. If they try to do it with all the blocks, they won't fit nicely together and I'm hoping that makes it easier for them to learn to keep the sizes separate.
If I want, I can use the 2 by 3 for x^3 since it is larger than the x^2 and differentiates it from the x^2 block and adds one more possible term as they learn to combine like terms.
I honestly believe my students do not "see" the terms as something other than written versions with no real meaning. I'm hoping by using these "manipulatives" students will begin to connect the written version to the visual.
I'm going to try it. I'll let you know how it goes once I've tried it in my classroom later this week. Let me now what you think, I'd love to hear.
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