Thursday, 19 June 2014

Hands on Maths: Polyiamonds

Recently my eldest has been working on some Geometry and I know she likes me to find ways of making her education more hands on so I had a think... 



 
This is a fun way to learn about polyiamonds in a simple and fun way but can also stem into an algebra project too for older children who want to 'play' with maths.
 
You may, or may not have seen my blog post: How to make a DIY geodesic dome.  It  was my inspiration for this project and it surprised me that it was entertaining enough for all 4 girls I just wish I had had more newspapers in so they didn't have to share the ones I made. 
 
WHAT IS A POLYIAMOND?
A polyiamond, sometimes refered to as a polyamond or an iamond, is a polyform - a polyform shape made by joining together identical basic polygons, in this case equilateral triangles.
 
The word polyiamond is a back formation of the word diamond, meaning that diamond was a word before polyiamond.  This is because the word diamond is used to describe the shape of two equilatrial triangles placed base to base and because the greek prefix  'di-' meaning two.
 
What you will need for this project:

  • Newspapers
  • A full staple gun
  • Masking tape (just to strengthen and if you are doing this with younger children protect little fingers from any sharp points made by the stapler)
Instructions:
 
STEP ONE
 
I made my triangles in the same way as I had for my Geodesic domes and cut them all to the same lengths using a metre rule and a pen to mark off the cutting points. 
 
HOW I DID IT: I found the smallest rolled up newspaper tube and then cut it to make it as long as possible, and then measured all my others and made them all the same length as the first.
 
CHECK OUT THIS POST: GEODESIC DOMES, TO SEE HOW TO ROLL YOUR PAPER TUBES.  THEY NEED TO BE ROLLED AT AN ANGLE AND VERY TIGHTLY, ADULTS MAY HAVE TO HELP YOUNGER CHILDREN WITH THIS PART AS IT CAN BE TRICKY.
 
STEP TWO
 
Staple the ends of three of the rolled up paper tubes together and then wrap tape around the corner to protect fingers when playing! 
 
Now for the PROJECT!
 
STEP THREE
 
When you have all your triangles, we had 6, first give the child one triangle and ask them how many shapes they can make with it - obviously it will only make one but this can amuse very small people - then give them two and ask the same question. Repeat this again with 3 triangles, then 4, then 5 and so on...
 



Ideas on ways you can do this...
 
You can get the children to draw out their findings or you can take photos of all the different shapes they have made. 
 
With younger ones you can just talk about the fact that they are creating tessellations. Talk about different shapes they can make.

 
What do the shapes look like?  A crab?  A bird? A house?


 
FIND A PATTERN - for those who want more of a mathematical challenge...
 
It can be how many different shapes you can make from how many triangles and then work it out to the nth term - if you are not sure what the nth term means: "the nth term" of a sequence is an expression that will allow us to calculate the term that is in the nth position of the sequence.  Here is a post with more about it: Leap Frog.
 
Can you find any other patterns that can be made into an algebraic equation? 
 
I have, for your convenience, put on here how many shapes you can make with the following amount of right angle triangles if you want to check if you have found them all.  They are here:
 
1 triangle - This makes only 1 shape, the equilateral triangle  - a moniamond
 
2 triangles - this will only make one shape: a diamond - a diamond
 
3 triangles - the same as 2, it will only make one shape - a triamond
 
4 triangles - will make 3 different shapes - a tetriamond
 

 
5 triangles - will make 4 different shapes - a pentiamond
 
6 triangles - will make 12 different shapes - a hexiamond



There are more, if you want to do your own research polyiamonds go on forever...
 
Alternative ideas for this project
 
Use:
  • matchsticks
  • spaghetti
  • cocktail sticks
 
Find other patterns:
 
How many sides does each new shape have?
 
Make some more triangles so you have at least 12 but start with 9 and see how many shapes can you make that have a hole in the middle?
 

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