Algebra 1 8-2 Primer: Multiplying Polynomials with Tiles
By Matt Richardson
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Last updated about 2 years ago
6 Questions
Note from the author:
A polynomial multiplication primer activity with virtual algebra tiles.
Click here to create a copy of a Google Drawings algebra tiles. Use the drawing to complete the items below.
Onboarding:
The rectangles (aka algebra tiles) on the left of the drawing are positive. Those on the right are negative.
The large white area on the canvas in the center of the drawing is called the stage.
You may need to create duplicates of certain tiles in order to complete this activity. To do so, select a tile and copy then paste. The copy should appear on top of and slightly offset from the original tile.
10
1.
Exploration - Setting the stage: Note how I have arranged groups of tiles that represent two different polynomial expressions outside the boundary lines on the stage. What are these two expressions? Select all that apply.
Exploration - The area model of multiplication: Note that tiles placed neatly on the boundary of the stage can form the length and width of a rectangle. The rectangle is illustrated in the image below in blue. As you know, the area of a rectangle represents the product of its length and width. This applies to multiplying polynomial expressions as well.
Exploration - Finding the area (aka product) with tiles: Since the area of the rectangle represents the product of the polynomials, we need to fill the rectangle with tiles. The objective is to precisely fill the area using as few tiles as possible. Some techniques are difficult, messy, and don't work. Here's an example. Note how the rectangle is not filled correctly.
Exploration - Finding the area (aka product) with tiles: Some techniques are inefficient, but work. Here is an example. Note how the rectangle is neatly filled.
Exploration - Finding the area (aka product) with tiles: Some techniques are neat, efficient, and correct. Below is an example. Note the alignment of the tiles on the stage with their counterparts around the edge of the stage.
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2.
Analysis: What polynomial is expressed on the left edge of the stage?
10
3.
Analysis: What polynomial is expressed on the top edge of the stage? Enter the expression with a space on each side of the operation symbol.
10
4.
Analysis: What polynomial is expressed on the stage representing the product of the "edge" polynomials?
The model above represents this equation.
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5.
Your turn: Model the multiplication of these polynomials on your copy of the Google Drawing.
Complete your work carefully and take a screenshot of your stage and completed model. Upload the screenshot to the Formative canvas.
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6.
The product: What is the product of the expressions? Use your algebra tile model from the previous item.