Non-linear patterning

In grade 9 we were exploring linear and non-linear patterns. We had to decide if this pattern is linear or non-linear.

Students knew that the patten works by adding one each time, so the pattern rule is y=1x+3.

There was a lot of discussion about this next pattern. Some saw it as linear, where we’d add 7 each time.

This would continue as follows, adding 7 each time…but with a few more figures people decided that the vibes were off, and the visual pattern didn’t look right.

so maybe it’s not linear.

we explored the growth in a few ways. We can see it as a big square (the green square) which is always one bigger than the figure number…or (x+1)^2. Plus we need one group of the figure number. Y=(x+1)^2+x.

We could also see a yellow x^2 and 3 groups of x and 1. Y=x^2+3x+1

This pattern works much better in the long run! We know it’s not linear because we add a different amount each time.