Desmos Learning: The Inscribed Hexagon

Making connections with  Desmos…..The Inscribed Hexagon

I get so excited when other educators share their learning experiences on @desmos with me via @MtBos or other blogs!  It motivates me, excites me, and the first thing I want to do is suss it out myself! 

Here is one construction I created in response to a calendar problem solution posted in NCTM Mathematics Teacher (vol.110, Number 1, August 2016) presented by Scott Smith in the Reader Reflections   I loved the solution so much that I immediately wanted to re-create it in Desmos!

Inscribing a regular hexagon into a unit circle.

When I play/create/explore/learn using Desmos, I have to think not only from the perspective of myself as the learner, but also myself as the teacher of my Year 9 students who will be the learners.

• What might my students be challenged by in this activity?  
• What might they be able to do  based on their existing knowledge
• What questions might they ask when stumped?
• How might this activity extend their thinking?

Questions /ideas that came into my mind:

1.      How do I graph a  unit circle ?
2.     How might I locate the vertices of the hexagon as coordinates on the circle?
3.     Should I use Cartesian or polar coordinates?
4.     What are polar coordinates?  Do I know about them to use them?
5.     Can I use Pythagoras or trigonometry to find the coordinates of the six points?
6.     How can I find the coordinates using function notation?
7.     How can I represent my circle as a function?
8.     How can I use the point coordinates that I have graphed to draw a line?
9.     How can I transform the lines that I draw using the point gradient formula?
10.    How can I change the intervals for which the edges of my hexagon are graphed?

This simple geometric construction, and all of the thinking (as a year 9 student) took me about 1 hour to construct.  And the learning I did was phenomenal!  I started with something simple, started asking questions, explored, realised I did not have enough knowledge, when back to the knowledge I have, then practiced and applied the learning I have done over the past few years using basic functions and simple coordinate geometry!

After thoughts - could I have done this as a simple compass and straight edge exercise - how?  How might you use a simple construction activity like this one to teach other topics?   

How many different ways are there to inscribe a hexagon into a unit circle?  I would love to know your thoughts and ideas - share your experiences in the comments section.

This activity really excited me as a teacher - and I believe it will excite my students as well.  Can’t wait to use it!