If there’s one thing I’ve figured out about teaching the basics of slope, it’s that there’s not one single method that will reach every single student. (This is true of any topic). However, it is still possible to reach every student since different methods work for different students. Here’s a few slope memory tricks that I’ve used when remediating students, if they just don’t get it after being shown the traditional ways:
Mr. Slope Guy
This was actually the favorite method of my below-level high school students. On every assessment relating to linear equations, the first thing most students did was sketch this on the top page as a guide. This isn’t my creation, but I can’t remember where and when I came across this to give the proper credit.
Since we write from left to write, people inherently will write the word “slope” from left to write, and this gives students a visual. Without moving the paper around, write the word “slope” on the line and if you find yourself writing upwards, it’s positive. Writing down is negative. Straight across is zero. And since there’s not really a place to write the word “slope” on a vertical line (without moving the paper), that’s undefined.
This only works for distinguishing positive from negative slopes, but simply tracing the line with a fingertip from left to right lets students physically feel the direction of the line as to whether it’s going up or down. I prefer that students write the word “slope” as mentioned above since writing is inherently left to right and tracing is not, but some students prefer this method.
One test asked “what is the slope of a horizontal line,” and a student told me that she couldn’t decide whether to write zero or undefined until she remembered that I had told them horiZontal has “z” for zero. Whatever works…