Working on representing math concepts

When we look at a visual pattern, we can analyse it in a few ways, and depending on how we view the pattern, we’ll have a different algebraic expression.

We are drawing more figures, and counting squares.  We are watching how the pattern grows.  Sometimes the numbers of squares increases by the same number each time.  Sometimes the increase is not consistant each time.

Sometimes we look at how the parts of the pattern add up.  Sometimes we look at what pieces have been subtracted.

We try, no matter what the method to relate the visual representation in terms of the figure number.

It’s very interesting that no matter how we express the original algebraic expression, each time they will simplify to the same expression in the end.