Slope

In math, recently, I've been working with the children in both my math group and Jesse's on the concept of slope. This is not something that is covered in the Singapore books, and it came about because some of my students had questions about the section on parallel and perpendicular lines in the 4B books. I started explaining how to draw parallel lines on a grid... and then thought, "Why not take this just a little farther and really talk about coordinate grids and finding the slope of a line?" That line of thought took us farther than I expected, into the land of formulas and Greek symbols: Δy/Δx is now a familiar set of symbols in the classroom, and we all know that it stands for the change in y (subtracting one y coordinate point from another), divided by the change in x (subtracting the corresponding x coordinates). While I'm not good at figuring out how to type mathematical formulae, here is the formula as it's properly written:

The children have been doing wonderfully. It's an interesting topic to study with children who are at this math level, because on the one hand there are a lot of new concepts to assimilate (coordinate planes, axes, plotting coordinate points, even discussions of different dimensions), and on the other, the math skills required are not beyond anyone's reach. It's been challenging in some ways, but the kids have risen to the challenge. They've practiced finding coordinate points, drawing coordinate grids, finding the slope of various straight lines, and creating challenging slope problems for their classmates. With Jesse, they've measured the slope fo their own bodies in various positions. They've even begun speculating on what it would take to find the slope of a curved line... and that's gotten them all excited about studying calculus, one day!