I'm delving back into the nitty-gritty linear concepts with my 8th-graders. I came up with an idea of teaching perpendicular slopes using Geoboards. I haven't tried it out yet, but I think it's going to work. They can first try and build a right-side-up square on the Geoboard and draw it in their notebooks on graph paper. Introduce the term perpendicular. When you ask them to draw it on their graph paper, remind them that when we look at shapes and their side lengths, we're counting space units along the side, and not the number of pegs. Then, the plan is to switch it up:
Challenge them now to build a diagonal square in the geoboard. Have them discuss when they think they have found one. Ask them to draw it on their graph paper. And then, once they've found/drawn in their notebooks a bunch of different diagonal square examples, have them look for commonalities. If I now put just one rubberband or segment down to represent one side of the square, can you find out exactly where its perpendicular side needs to extend from/to? What are their slope values? Is there a pattern? Use this to lead in to the idea of reciprocal slopes with opposite signs.
I like this activity idea, because potentially, if it works, you don't have to teach the kids the "negative reciprocal" idea like they are robots. I'll try it this week and then report back. Maybe we'll even have some photos! (I need to keep reminding myself that I need to start accumulating photos of my homeroom kids, for the yearbook.)
And, anyhow, I am excited about my first Geoboard lesson of the year!!! There's nothing quite like handing rubber bands over to 8th graders and expecting them to put them to serious use. :)