Multiplying and the Area Model

Today grade 9s learned how to represent multiplying in a few different ways.

Some saw this as 3 groups of 2x-4

Others saw it as 3 groups of 2x and 3 groups of -4, which is 6x-12

Some could see it as a rectangle, with the area representing the multiplication of length and width.

In each case, it is the same answer, just represented in a slightly different configuration.  This might not seem to be a big deal, but when we make the question a little more challenging….

We no longer can group things as easily, since we don’t know the value of x.  The area model continues to be useful though, and we can build a rectangle with the dimensions of x and 3x+1

Here’s a representation of 2x(x-4) the rectangle dimensions are placed up on the ledge and the rectangle itself is on the lower level.  The results of the multiplication are 2x^2-4x.