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!

Why now? Reflections and a call for your advice!

More on beginning this blog....

In teaching, I take my inspiration from all the connections I have in my online PLC.  My professional learning community helps me to understand and apply better instructional strategies to bring forth better learning.  My online Learning neighbourhood shares with me the best ways to  use technology as a learning tool (thank you Desmos) and not just as an informational resource.  My linkedIn connections (Daniel groenewald, Tom Barrett ) remind me that I have worked with some amazing, professional educators.  And at the end of a long week, if I am feeling frazzled, I know I need only to turn to Twitter or my weekly RSS feeds to find like thinkers, passionate educators who will put me back in that positive mindset about why I love teaching mathematics!

Reading tweets ( @aitsl, @d_groenewald,@edutopia) and blog posts (Desmos, Dan Meyer, Samjshaw) help me to connect and enrich both my own learning and that of my students!  It's a win win for me - I learn, I'm inspired, I teach better lessons, my students are inspired, grades improve..............and yet.........

Even with the great progress I've observed in the learning achievements of students as a result of implemented researched based instructional strategies, I feel that many teachers on the ground are still missing out! "Too much content to get through", they say, or "need to make sure they are ready for their end of year entrance exams...".

Sometimes I feel like I may not be making a difference.

So my questions are.....

     1.      How can I more effectively share my experiences, failures, triumphs, ideas, questions and curiosities with others?

     2.       What suggestions do you have to effectively share your learning about best practice?
and,

     3.         What is the best way to generate more discussion within my school based teaching community about the best way to teach a particular concept, topic, or idea?

And this is why I am going to build this blog.  If I can connect with even one maths educator as a learning partner, then I will be happy😊.