Scaffolded exploration for the span of two vectors?

[StevenClontz]

Students do pretty well with figuring out the span of one vector is a line: Activity 2.1.5

But I got a lot of parabola votes from this exploration: Activity 2.1.6

Any pitches for how to maybe better scaffold this exploration so students see the planar geometry a bit better?

(For whatever it's worth, they did all decide the next activity drew out a line: Activity 2.1.7)

[siwelwerd]

Not sure how to improve it at the moment, but I also typically get a lot of parabola votes.

The IOLA materials have a nice "magic carpet" task sequence that might have some ideas for us:
https://iola.math.vt.edu/media/unit1/docs/u1t1.pdf
https://doi.org/10.1080/10511970.2012.667516

[StevenClontz]

One thing I think we might be missing is a visualization of vector addition to begin with.

Or maybe this is another opportunity for an interactive to save the day, rather than having students spend a lot of time computing linear combos to try out.

PS: am I a bad teacher, or am I justified in looking through that facilitation guide and thinking "who the heck reads all of that"?

[StevenClontz]

Here's a Doenet.org interactive (a bit slow, sadly): https://www.doenet.org/portfolioviewer/_gDhVzoC33ojk4E28hTWmQ