Vectors is one of my favorite topics in Pre-Cal. Probably stems from the affinity I had for statics years ago. It's also an opportunity to delve into a very deep topic. Most of my students kinda sorta see them in Physics, but I think the delivery is lacking.
In a week or so we're going to delve into the 3D coordinate system, which means I'm about to buy a few thousand straws. Before we get there, I wanted to do a better job of demonstrating the 2D components of a vector.
To start, I asked them to describe a space shuttle launch. Cue debate about whether or not it shoots straight up. Many said it rolls but didn't know why. Then we had a discussion about the best ways to fight gravity.
Second, I brought up a Desmos demo I made. Imagine my surprise when the brains of Desmos themselves offered a much cooler version.
By now we've talked about right triangles so much that the breaking a magnitude and direction into components was no big deal. I wanted to improve on the visual component. What does a vector and its component parts look like as a system?
A few hundred straws later, I had a project. I put 7 sets of magnitude and direction on the board for them to find the components. They had to construct the system for two of them. All the pieces had to be to scale and the triangle should be oriented towards the correct quadrant.
There was some initial confusion about how to build the triangles, but that only took a few minutes to solve. Normally I do vector operations first (add/subtract/scale when given the components) and then talk about magnitude and direction, but I think I like this order better. Several asked the interesting question "why did this component come out negative?" which is the perfect segue to discussing quadrants. It's nice to put quadrants in their head this early so that when we do this in reverse we can correct angle values properly.