To 3-Act Math or to not 3-Act Math?

Recently, I was tutoring and a student asked me for help with what I found to be an interesting question.

"There are 2 stools, one 3-legged and one 4-legged. One of the stools wobbles slightly.

• Which one is it? How do you know?
• Suppose that each stool is placed on a flat surface that is slightly sloped. Do you expect either of the stools to rock side to side? Explain why or why not. 

 Life experience led me to the correct answer yet I had to think for a moment to consider how to help the student understand the underlying concept that any 3 points make a plane.

Concurrently, I was thinking that a much better way of presenting this question to the students would be during an inquiry activity. It would allow students to discuss their ideas with one another and collaborate in order to make a precise statement defending their position. It would allow students to make a connection between "real-life" and mathematics - an opportunity to understand that there is a mathematical explanation for an what many students may have already observed during their lives. It demonstrates that people use math to explain the world around them. This idea also has applications such as the use of tripods.

I thought more about the question as I drove home and considered how I might have introduced this to students and what tools I may provide to them in order to experiment and get them interested in the task at hand. I turned to my PLN for ideas and posted the question and asked "Could this be improved? How could tech be integrated?"

A conversation followed between myself, +Jeremy Bell, and +Kyle Pearce. They both offered suggestions. The conversation then turned to whether or not the concept warranted the creation of a 3 Act Math Task or not. I would argue that this is an opportunity for students to have a math talk about a concept that is pretty simple, yet difficult to explain without mathematics vocabulary. Perhaps I view this activity as one that could be done at the beginning of the semester in Geometry. It could be used as an opportunity for the teacher to demonstrate to the students how to engage in math talks and share ideas. Also of emphasis could be that learning will take place through inquiry and discovery activities. This is a significant change for many students as they have been taught in a more traditional direct instruction model.

I also understand the other side of the argument. The same idea may be conveyed through a quick demonstration or even an explanation. The concept is not one that is of great focus in Geometry. It may be wasted time to create a 3 Act Math Task for this small concept and it may be a waste of time to have students work through a process.

So the question stands. Do you think that a 3 Act Math Task is an effective way to help student uncover the idea that 3 points always make a plan, or is it wasted time and resources for this particular topic?