I'm still not sure how to use this blog. Frankly, I would like lots of readers to read about my problems and have them be so gripping that a lot of learning--on both sides of the keyboard--is happening around this place. But my struggles are so routine and rookie-ish that I feel strange assuming that there's any insight to be worked out from them. But, you know, forget it, it's my blog and I'll be boring on it.
OK, here's how I'm introducing slope to my geometry class. I'm trying to get better at easing students into concepts, though this is a concept that my students have seen before.
Core idea: Slope measures how steep a line is.
1. Start with drawing two lines with a stick figure standing on them. Ask them, which line is the guy more likely to fall off of? (Draw a floor with a dotted line to give some orientation.)
2. How can we make this idea more precise? (Some students will remember the formula for lines, and just push them into concepts at this stage.)
3. Draw a unit forward, and ask, "how much higher up is the guy when he walks one foot forward?" for each line. Ask for guesses of numbers.
4. (Re-)Introduce slope as the ratio of your height up when you walk forward.
5. But how do we describe walking forward and going up? Introduce the (familiar?) formula.
6. Time for practice calculating slope from two points. Then, at the end of that set, draw a line given a point and the slope.
7. At this stage, students are able to draw lines given a point and the slope. Now they're off to practice given a bunch of problems containing parallel lines and perpendicular lines. They need about 15-20 minutes to work on these.
8. We come back together to discuss the relationship between parallel, perpendicular lines and slope.