I've always referred to the 8th grade function unit as "The Monster Unit".
There are so many concepts that are all interwoven together that it's hard to figure out where to begin and where to end.
Usually my scope of the unit looks like this...
1) Graphing Stories
2) Patterns --> Expressions and Equations
3) Function Representation --> tables, equations, graphs
4) Different types of function --> linear, quadratic, absolute values
5) Slope
6) y=mx+b
7) Systems
8) Bivariate Data
This year, however, I let the students lead the direction.
We had just finished Graphing Stories with my favorite problem from Impact, "Cars on a Highway".
As students analyzed the various car "stories",
I started to hear the "s" word creep into their conversations.
Instead of just talking about the speed of the car,
They were talking about the slope of the line!
It was at this point that I changed course...no pun intended.
Instead of jumping ship and changing to a totally new problem,
I would just introduce tables of values and equations in this context that they were already fluent in.
I created a matching activity that allowed them to see different representations for each car's story.
Follow up questions started to lead them in the direction of discovering the meaning behind y=mx+b.
I have to admit, it was a bit nerve racking to start off with the big picture in mind,
But I just had to follow my student's lead and continue with the understanding they were demonstrating up to that point.
Once the concept of slope and the y-intercept was established, we then dug a little deeper into slope.
So now, my scope for my function unit looks like this...
1) Graphing Stories
2) Function Representations --> Tables/Equations
3) y=mx+b
4) Slope
5) Bivariate Data
6) Function Tests
7) Different types of functions
8) Systems
Moving forward is a good thing. If you don't move, you become stagnant. If you become stagnant, you smell. (I'm going with a creek bed analogy here...stay with me). "It Is What It Is" helps us to keep our sanity as we try new things, but at the same time we should never settle for "what it is". We should constantly reflect and learn to move our teaching and our student's learning to higher levels so the classroom doesn't turn stale.
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