Tomorrow, we'll start class by reviewing the homework (as always), and then I get to give students back their quiz and congratulate them on doing so well. That's always more fun for everyone than when they do poorly.

Next, students will work individually on more graphical analysis work, as in the last lesson. I'm convinced that fluidity with graphical representation is a key skill that must be continually reinforced. When I first started at DCP, I taught primarily Algebra 1. I never understood why students could graph a system of equations and find the intersection point, solve a system algebraically, but not make the connection between the point of intersection and the algebraic solution. It took me a while to see that they did not really understand the relationship between "y = 2x + 3" and the graph that they knew how to produce. Without that understanding, it becomes clear why a point of intersection seems to have nothing to do with algebra.

Anyway, following this, there will be some direct instruction where I show students a series of graphs, and help them understand how to determine the domain and range, and write them in interval and inequality notation.

Finally, there will be time for pair work practice where students will determine the domain and range of given graphs. They will also have to graph a linear function over a restricted domain. Understanding how to do this will make the upcoming piecewise functions lesson much more successful.

The homework will be practice of these concepts, with some review problems thrown in. I've been thinking about including function decomposition in the curriculum - I decided to put in some problems on this homework (shown above) where they must match a composite function with a pair of component functions as a sort of first step in that direction. We'll see how they do with it.**Update:**

I've compiled six graphs with related questions that push on students' understanding of how a graph represents a function. I've uploaded them to ILoveMath in the Algebra: Misc Topics section. If you use any of my stuff, I'd love to get any feedback.

A beautiful combinatorics argument

19 hours ago

## 1 comment:

I was going to leave a comment here, but it got too long, so I left you a comment on the message boards at ILoveMath.org

http://www.ilovemath.org/forum/forum_posts.asp?TID=295&PN=1&TPN=1

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