## Sunday, September 19, 2010

### Graphing: What do beginning algebra students need to know?

Here's what I said my students will need to know:

• Graph a line given equation (slope-intercept form)
• Graph a line given equation (standard form)
• Find slope given two points
• Find equation of a line given two points
• Find slope given equation (any form)
• Find slope given graph
• Find y-intercept given two points
• Find y-intercept given equation
• Find equation of line perpendicular to given line and through given point
• Find equation of line parallel to given line and through given point
• Explain meaning of slope in a real problem
• Explain meaning of y-intercept in a real problem
• Create an equation based on a real problem
• Make a graph for a real problem
Am I missing anything? I'm thinking of adding 'convert any equation in two variables to slope-intercept form'. And I'm thinking of taking out 'graph a line given the equation in standard form'.

What do you all think?

1. I think this looks a pretty good list.
Maybe the only extra i'd throw in there would be finding points on lines.
For example on the line y=3x+2 complete the coordinates (15, ??), (??, 62) but to be fair I tend to use this to reinforce the other skills you've listed.

2. This seems like a good skills list.

Throughout algebra, I always have an overarching theme going of different representations. You've touched on a number of ways one can translate between word, algebraic, table, and graph representations (with the greatest focus on going between algebraic and graphical representations). I might add the big picture question of when is one representation easier/better/more appropriate/more useful than another?

But that's the easy answer. How you actually DO this and assess this is a different monster.

3. I think I'd include the x-intercept for completeness (some students may ask why it's not 'important'...), and also for cases where a straight line is parallel to the y-axis, eg x = 2.6, particularly because it may create a link with being unable to divide by zero when calculating slope, because x doesn't change, and so y is undefined... or is that Albegbra II...? ;-)

4. After posting this, I saw that our textbook doesn't even cover all this. I guess I they wait until intermediate for a lot of it. But I think it's best to paint a complete picture.

I do work with 'given x find y, and given y find x' as you suggest, Ryan. But I won't test on that, as it's a smaller piece of so many of the other skills, which you mention.

Avery, I think that's a great big picture concept, and I think I address it some in class, but I don't want to test them on it in this course (probably in intermediate algebra).

Colin, I like including the x-intercept. The book includes horizontal and vertical lines, but I'm thinking of graphs as representing functions and so vertical lines don't come up (and horizontal would be too boring to bother graphing). I think I won't test on those in this class.

Thanks all! (Did my Twitter request bring any of you here?)

5. I like qualitative graphs. Match an unlabeled-axes graph with functions (equation or context), using cues like +/- y-intercept, function type, increasing/decreasing.

I'm also big on the idea that a point on a graph connects two pieces of information, often input to output. And it probably sounds dumb, but that a graph is a collection of these points.

6. Yeah, I plan to work with some qualitative graphs in class (person drives, walks, waits, etc, which graph goes with the story), and may put that on their applications test.

I'm giving a basics test on all the procedural stuff, and an applications test on meaning of slope and y-intercept, and using graphing and equations with real problems.

7. I'd add something like "understand that points on a graph represent pairs of values of the variables x and y" and "be able to explain how a line on a graph represents the set of solutions to an equation with two variables". It amazed me when I first realised how many students memorise techniques but don't actually understand the basic concept of the application of cartesian coordinate system to algebra. 