Tutoring math, you might explain algebra tiles a few times a year.  The math tutor introduces them.

 
If algebra tiles existed when I was in school, I never saw them. Everything back then was symbolic, and teaching didn’t have the directive of making the learning easier.

Nowadays, attitudes towards teaching and learning couldn’t be more different. Manipulatives, as they are called, are used to explain counting and even variables in a visual, physical way. An abacus could be used thus.

Algebra tiles are used to depict expressions with variables. A big square means x^2, a rectangle means x, and a small square means 1. Consider the following example:

Example 1: Show 3x^2 + 4x +5 with algebra tiles.

Solution: We need three big squares for the 3x^2, then four rectangles to make 4x, and finally five small squares to indicate 5. Like so:

Depending on the situation, you may need to show the rectangles horizontally and/or group the small squares in various different ways. Here is another depiction of 3x^2 + 4x +5:

How do you show negative values? With color, is the answer. Often, the light coloured tiles are taken to mean positive, while the darker ones mean negative.

Example 2: Show -2x^2 -x + 3 with algebra tiles.

That’s a pretty good beginning with algebra tiles. In future posts I’ll show some of the math concepts you can illustrate with them:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.