Tuesday, June 2, 2015

6/2 Pentagrams and some inspirational math.

Just in the nick of time for the end of the year, I received the notice that Jo Boaler's Week of Inspirational Math. https://www.youcubed.org/week-of-inspirational-math/  was released. I took a glance through and thought the first day activity four 4's looked like a decent warm up.  The basic idea is you have four fours and you can combine them using basic operations (add,substract, multiple, divide) as well as factorials and square roots. You then try to find a combination for all of the first 20 whole numbers 1 - 20.  Example: 4 + 4  + 4/4  == 9. Over all this went okay but not as well as I hoped. I'm going to look at the material again and watch some of the videos. It didn't seem to capture the kids imagination as much as I wanted even compared to just using game of 24 cards which we've done in the past. I could certainly add a competitive element to this which might draw more kids in and  have teams compete against each other to find the most equations. This is very anti-Boaler but sometimes effective in practice.  In any event, I may retry this again and see if I can frame it differently/more effectively.

We then transitioned into our main activity. I went with my own passion and pursed the pentagram geometry problem. To start I used the whiteboard to discuss how many degrees are in polygons of increasing size. We approached the problem by breaking them up into triangles.  I had kids volunteer to draw dissections and asked along the way if anyone could find a pattern.  We made it up to a 7gon fairly quickly. Unfortunately no one came up with a general strategy and we had already covered pentagons so I  made  an executive decision to demonstrate the technique of drawing lines from one vertex to all the other ones.


This was in the interest of moving along the sequence I wanted to follow but this activity could be broken out more. I also skipped proving why a triangle has 180 degrees and left that as an assumption. Interestingly the general technique did produce a few aha moments for a few kids which was gratifying.

I then had them work through a packet that terminated at the pentagram problem from my prev. post.



To approach it first I had a few more rote worksheet on angle tracing that I took from:
http://www.mathworksheets4kids.com/triangles.html. I had them the work on the interior, exterior and interior with algebraic variable sheets.  As I walked along the tables I asked each kid if they understood the techniques and if they said yes I told them to skip to the next page.

I then had a few more complicated angle tracing problems that required applying supplementary angles, triangle angle addition and occasionally some lines intersecting other parallel lines. These are essentially mechanical as well but require using several techniques at once. Most kids made it at least this far with a few needing some prompting on which angles to look at next.

Beyond that I included two more fun angle tracing/algebra problems from the five triangles site that are closely related:

http://fivetriangles.blogspot.com/2014/11/204-three-isosceles-triangles.html

and

http://fivetriangles.blogspot.com/2012/04/isosceles-triangles.html

These were a real hit with the kids who made it this far. Finally, I terminated with the full blown pentagram problem. However, most kids had run out of time just when we reached that point. So overall it was an effective sequence and I think it kept everyone's attention but next time I'm going to have more confidence and skip any warm ups and jump right in. Unfortunately, next week is our last session and I've already committed to doing an algebra readiness assessment or I would just pickup where we had finished.


1 comment:

  1. A slightly different direction you might take the polygon angle sum: proof for 5yr old

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