Building patterns and connecting them to algebra

Today we explored visual patterns again, and worked on connecting the pattern growth to an algebraic model.

When given the same term 3 we tried to make different possible patterns.

We made 3 of them, then explored the algebra that gets us from term number to the number of tiles.

We then colour coded the constant term (what stays the same in the pattern, aka term 0) and related that to the constant in the equation

We tried many different patterns, some were linear, some were not.  It was a good challenge to make the pattern rule and test it out by building more terms, or by making tables and charts, or using algebra.

In grade 10 we worked on similar things today.  We showed all the different ways to visualize patterns and create algebraic expressions from the visualization.

Here’s an example:

We looked at figure 3 in many different ways.

It’s neat to see how no matter the way you visualize it, and no matter the expression you create, it simplifies to the same thing in the end.