**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:

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!

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

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!

I would love your feedback! Establishing collaborative conversations can only make us better together!

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