Multiplying with tiles

We revisited the algebra tiles today. This time, the times set up a rectangle of given dimensions and we found the area inside the rectangle by counting up the tiles inside the rectangle. Because area is also found by multiplying length times width, this model finds the product of the two polynomial dimensions.

Example: Find the product of (x - 3) * (x + 2).

1. Set up the dimensions to the side of the work space (as shown above and to the left of the diagram below).


2. Fill in the space with shapes matching the dimensions. Or, continue the lines down and across that are started in the dimensions.


3. Record the values of the shapes in the resulting rectangle as the product. Simplify zero pairs.

Product = x² - 3x + 2x - 6 = x² - x - 6

We also found the product of the two polynomials by using a chart that is similar to the Punnett squares that the students learned in Biology in middle school (and will see again this year).

Example: Find the product of (x + 2) * (x² + 3x + 1)

1. This process again requires the students to set up the polynomials on the top and side of the work space (this time as collected terms rather than individual tiles).


2. Each box in the grid is found by multiplying the term above and to the left.


3. Collect like terms for the answer (usually on diagonals).

We will continue working with this concept tomorrow. There is a quiz scheduled for Tuesday covering adding, subtracting, and multiplying polynomials.

Homework: Finish today's packet

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