Monday, August 4, 2014

Math party (and flexagons!)

Who: Baan Pathomtham First Grade Class+J3
When: 9am - 2pm
Where: our house
What will we used: see below
Why: oh why, oh why? (actually, it was fun!)

First, thanks to all the kids for being so friendly and polite.  Thank you for leaving everything tidy when you left, though that was under a mother's supervision and probably not surprising.  What did amaze me was when Tanya stopped everyone from rushing to eat a snack and you all went right away to collect the toys/games/crafts.

Second, did any of our plan survive reality? Yes, actually some of the things we prepared went well:

  • Passports: the kids enjoyed having their activities noted and getting stamps in the passports
  • Flexagons: everyone got to play a bit and learned about flexing the hexaflexagons and tetraflexagons. A couple even made their own hexaflexagons and someone decorated a blank I'd left around.
  • Pizza: as usual, kids enjoyed assembling their pizzas and were astoundingly patient while they baked.

  • Origami stars: some kids were interested in making these
In truth, though, this was simply a group that wanted to play games and could nearly have been left alone the whole day with a selection.  As it was, they played a lot of Uno, managed part of a game of Settlers of Catan, and played some assorted other games: Sum Swamp, Walk the Plank, Spot It!, and Squares

Some lessons (for me):
  • Though fairly small, our play room is large enough to host two distinct stationary activities, but they have to be child-selected to be sufficiently engaging for the two groups to remain intact
  • Origami (including flexagons) for this age probably needs a smaller group (one-on-two likely works). The kids have the skills required, but either they found it to concentrate, I found it too hard to concentrate, or a friend would suddenly come over and try to take control of the project.
  • Activities requiring a meaningful amount of preparatory instructions either need to make sure the whole group is listening first, or have the instructions delivered by one of the children.
  • Kids need more encouragement taking things apart (see Flexagons, below)
Below are a sample of the passports, the flexagons, and folded stars from today.

I promised to write up our flexagon experience. After the party today, I'm even more enthusiastic about this activity. There are three reasons why I strongly suggest you start playing with them today:

1. Cheap and easy to make
This is great because, if you break them, then just make more! Since even learning how to flex the shape takes some investigation and practice, there's a danger of tearing a flexagon. That should be encouraged! Cut them open to see how they are folded, force them if you can't see how to flex it. Taking things apart is a great habit/skill.

I think the kids today were overly anxious about their investigation. Perhaps this was the other side to the coin of them being so polite? In any case, this is something I would actively seek to encourage in the future.

2. Mix Art and Math
A blank flexagon isn't much fun, it has to be decorated to make the mystery really come out. For people with a traditional conception of mathematics, this may seem odd: art as a tool to explore the mathematical structure? Yes, yes!

So, if your child doesn't like art, this is a back-door into drawing some patterns or pictures.  If they love art, then this is a back-door into equilateral triangles, angles, rhombus, hexagon, how many sides a piece of paper has, state diagrams, etc.

3. You probably don't know much about flexagons
That means you can let the child lead this activity and just let it develop. That's great because they can be the teacher or you can be equal partners.

Alternatively, you might get excited and have your own questions about flexagons. In this case, this is a chance for you to investigate and for your kids to see you investigating. Do you try to figure it out on your own, draw diagrams, build other models, dissect specimens, experiment, watch videos on youtube, look at wiki pages, ask a friend, talk with your child, all of these things? A great opportunity to show your child how you explore something that interests you.

My flexagon recipe:
Only steps 1 through 6 are really required
1. Watch the Vi Hart video:
2. Make a trihexaflexagon by using tape to complete the loop
3. Color it
4. Flex it and think about how it works
5. Take it apart (this is why we used tape)
6. Make a bunch of additional trihexaflexagons, use different ways to make the series of triangles (folding, compass, 30-60-90 drafting triangle, printed template, etc)
7. draw more pictures and patterns
8. Try making a hexahexaflexagon (again, using the basic comments from the video)
9. Look at some templates online, including Tri-tetraflexagon, Flexagon Portal, More templates and more
10. watch the second part of the Vi Hart flexagon series:
11. watch this third Vi Hart flexagon video:

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