Monday, 2 July 2012

an investigation into hexagons

We are fortunate to have a huge plastic bucket of wooden shapes in our classroom.  We call these shapes ‘pattern blocks’ because they are great for making (tessellating) patterns.  There are yellow hexagons, green triangles, blue ‘diamonds’ and red trapeziums.  As well as orange squares.

I had set a challenge a while back, to see how many different hexagons we could make that were exactly the same size and shape as one of the yellow hexagons, using just green triangles, blue ‘diamonds’ and red trapeziums.

Time, I think, to revisit the problem - and to see just how many we can find.

Here’s the yellow one to remind you. 


How about trying to make one using just red trapeziums?


Look - and count.  Two red trapeziums make one yellow hexagon.  Now, what about blue ‘diamonds’?


Look - and count.  Three blue ‘diamonds’ make one yellow hexagon.  And now.  How many green triangles do you think you will you need to make one yellow hexagon? 


Count them!  Yes, you need six.  Six green triangles make one yellow hexagon.

So now we’ve found three different ways to make a hexagon the same size and shape as one of the yellow ones.

Are there any more ways do you think?  Can you maybe make one using a mixture of all three shapes? 


Or you might like to try making a hexagon using just green triangles and blue ‘diamonds’.


Each time you find a new one, record it on your paper using shape stickers.


How are these two the same?


And how are they different?


Look at how many different ways we found.  Do you think we have found them all?


I wonder; how many ways can you find?

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