Home School Life Journal From Preschool to High School

Home School Life Journal ........... Ceramics by Katie Bergenholtz
"Let us strive to make each moment beautiful."
Saint Francis DeSales

Hands-on Algebra: Polynomials

Just as we used tiles and cubes to learn basic math, we can use them for more advanced math.
For this lesson, you will need to have three sizes of tiles in two colors to represent tiles and their opposites. 
Notice that these are not perfect or measured exactly. How neat and perfect they are does not matter for older students. They get the idea. All you need is two colors of paper and it will just take a few minutes to cut out what you need. You do not need to spend anything on this as you can use whatever you have around the house and hands-on math should not take you much time to prepare.
Now here are the rules to this game:
  • Each tile has an opposite. For this post, white is positive and yellow is negative. It doesn't matter what colors you use, just so it is clear which is which. 
  • A zero-pair is formed by pairing one tile with its opposite. 
  • You can remove or add zero-pairs without changing the value of the polynomial. 
  • Like terms are represented by tiles that are the same shape and size.

Demonstrate how to use the tiles to show each monomial or polynomial.
 Start with 3x to the second power (sorry I don't have any superscript).
 Then demonstrate x to the second power - 2d.
Your student should now be able to do 
2x to the second power + x - 2.

Now use algebra tiles to simplify 2x to the second power + x to the second power + 2x.

Now combine like terms. In its simplest form, 2x to the second power = x to the second power= 2x = 3x to the second power + 2x.

Now use algebra tiles to simplify 3x + 2 - 5x +1. Rearrange the tiles so that like terms are next to each other.
Form zero-pairs, and then remove all zero-pairs.
In its simplest form, 3x + 2 - 5x +1 = 2x + 3.

Math Journal Activities

Now your student should be able to model and simplify any monomial or polynomial that you give him. He can even make up his own problems to solve in his math journal. For some of them, have him sketch a drawing to show how he got his answer. He could also include in his journal a sentence or two to explain how subtracting polynomials is related to adding polynomials.

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