marbleslides and desmos for 6 year old

J2 and I were playing around with Marbleslides last night. He had a lot of fun and clearly validated that the Desmos team has achieved their objective to "design for delight" (see their blog announcement of Marbleslides here).

Our version of bedtime math

While J3 has seen axes and graphing before, this was his first exposure to equations for lines. Really cool to see how Desmos lowers the threshold for exploring enough to make this easy and (again) fun for a young child. Now, I'm not under any illusion that he fully understood everything he was doing, but I believe these types of experiences build a comfort and background that is helpful whenever he formally encounters these ideas again. Feel free to disagree with me and let me know in the comments!

Use of Sliders

For some of the challenges, I gave him a generic equation and added sliders for the coefficients. Here's an example:

His choice of variable names

I wasn't really sure whether it was better to have him change the coefficients and parameters in the equation or via a slider. The great thing about the slider is the animated, continuous (looking) change in the graph as the parameter changes. The cost is that the extra variable introduces another level of abstraction ("this slider changes A which is a parameter in this equation which describes this line.") I'm not convinced either choice dominates, so we did some of both (with and without sliders).

The challenges: Spoiler Alert

J3 asked me to post his solutions to the first three challenges. Can you solve them with fewer lines?

Four lines for the first challenge

Can you even see how this solution works? Some kind of quantum effect, I guess? Solution has 2 lines

Whoa, a new kind of line! Solution has 2 lines