# Multiple representations

In grade 9 we’ve been working on patterning. We use visualpatterns.org to supply some patterns, and we are getting good at making our own as well.

Those two show examples of what c=3n+1 looks like. The constant is 1, and we see 3 groups of “n” (the figure number) in each figure. We also notice that each pattern adds 3 each time, so it is linear, growing at a consistent rate.

We placed the squares from each figure on the graph, and coloured in the column. We showed the constant is always there (in orange here), and it doesn’t change. The number of blue changes, it goes up by 3 each time. This corresponds to c=3n+1. We noticed that it is partial, that the constant is the initial value on the vertical axis, and that the rate of increase is 3 squares for each increase of figure number.

Each small group was then given 2 equations to draw, and notice things about. Here the constants are different, and the rate is the same. The lines are both positive, partial, and also parallel.

We looked at some with negative constants, and different rates. If the coefficient is bigger we noticed that the line is steeper. The other graph shows the same constant, of 6, and one with a positive rate, and another with a negative rate. That was a bit tricky to figure out how to manage a rate of decrease.

We noticed that if the constant is 0 then it is a direct graph, passing through (0,0).

We did a lot for our first day graphing lines! Good job everyone. We can now connect the representations of visual pattern, equation and graph.