Thursday, April 9, 2009

Solving Quadratic Equations by Graphing Mini-Project

Here's a simple, tiny alternative assessment for solving quadratic equations by graphing:
Finding Zeros Mini-Poster Project
1. Graph one quadratic function that has two zeros (create one or use one we did in class).
2. Show how to find the zeros using a table.
3. Show how to find them using the graphing calculator’s “zero” function.
• Buttons to press
• What to do when it says “Left bound?” “Right bound?” and “Guess?”
4. Mark the zeros on your graph clearly.
Alternately, you could ask students to graph three equations: graphs with one, two or no zeros. I also stress that solutions, zeros, x-intercepts and roots are all different words for the same thing, and you could have them work it into the title of their posters.

This project can be scaled up or down (a huge poster vs. a single piece of graph paper) and easily incorporated into a larger unit on the various methods for solving quadratic equations.

Kate Nowak said...

Hi Mr. D - I've noticed you've done a few of these kinds of poster projects - show me what you know, or explain a procedure. I'm just wondering how much explicit instruction do you give the kids? Do they get creative with it, or do all the posters look the same? I can just imagine mine not really knowing what is expected, and being reluctant to start. But then, if I provide an example, everyone's would look exactly like it.

Matt said...

This part of your post got me thinking:

solutions, zeros, x-intercepts and roots are all different words for the same thing

Are they? I guess for our purposes (and depending on the grade level) they are. That's one thing I always wrestle with, though, because if I let myself, I could get really nit-picky about language. (Equations have solutions, functions have zeros, graphs have x-intercepts, etc.) Part of me thinks that it's more important than most think, but then I have to decide its importance relative to all the other things I want my students to learn!

Mr. D said...

@Matt: I certainly share your concern about vocabulary usage, but as you said, we have to decide how important it is in relation to everything else (especially how they understand the underlying concept). There is a line I won't cross, of course:

Years ago, the number of students writing about the "slop" of a line was quite alarming. So I decided to do a little spelling/vocabulary lesson. I wrote "rope" and "hope" on the board and asked, "How do you pronounce these words?" They all happily responded correctly. "Then why, when you're writing the word slope, are many of you writing slop?" I don't recall reading about the slop after that!

I recently had to revisit this lesson when my Algebra II students kept referring to the "sin" of an angle. They now know that I consider "sin" a sin!