Bats on Parade by Kathi Appelt
Students will visualize polynomials using algebra tiles
Lesson Created by:
Marilyn Kilgore, Susan B. Anthony Middle School, Manhattan, KS
- The book Bats on Parade, algebra tiles
1. Launching the lesson (engage):
- Read the story
- Talk about the pattern in the story. Discuss how this pattern could be written algebraically?
- We talked about polynomials earlier. Suppose we want to model polynomials using tiles. Today we are going to do hands on algebra using algebra tiles.
2. Developing the lesson
- Ask the students what a variable is in math. Today we will concentrate on the variables "x" and "y" in various polynomials. Hand out packages of algebra tiles to each student.
- Using the overhead algebra tiles show the students "x 2" Explain each side is x by x therefore equals x2. Show y 2 tile (y by y) and
- xy tile (x by y).
- Ask students to use their tiles and model 2x 2 and 3y 2 and 5xy and 3
- x 2 + 2 xy etc.
- Ask students what the additive inverse of x 2 is. Show the -x 2 tiles. Have the students show - y 2 and - xy and - 2 x 2 + - y 2 etc.
- Have students pair up. One student will make up a polynomial using their tiles. Their partner will verbally tell the polynomial that is modeled. Each student will practice this 5 times each. To make sure they understand model a polynomial on the overhead and ask students to verbalize. (4 x 2 ) (-2xy) (X 2 - 3xy - y 2 ) (-3x 2 - xy + y 2)
- Discuss like and unlike terms. Ask students to model like terms and then unlike terms. Ask student to model 0 with their tiles. Tell them this is the additive inverse or opposite.
- Have all students model a polynomial such as (x 2 + 2 xy + 3 y 2) ask them to also model (2 x 2 + xy - y 2) ask them what the sum of these two polynomials would look like. Discuss the zero principle. Practice addition using the given problems.
- Discuss letting xy tiles representing (x by 1) instead of (x by y) and y2 tiles representing (1 by 1). Ask student to model 3 x 2 - 5x + 4 and 2x - 6. Ask them to find the sum of the polynomials.
- Ask students to use the zero principle and show that the tiles x 2 and xy can be arranged in a rectangle whose dimensions are (x and x-y)