Shaping it
Problem
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You can, of course, start with any straight-lined shape.
Here's one where I've coloured each new halving line to help to see what has happened more clearly.
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So, it's your turn to have a go.
It's probably good to start with a fairly large shape since it's going to get smaller and smaller each time.
- Having made a design like one above, cut out the triangles and the smallest inner shape and rearrange the pieces to form a new shape/design.
- Talk about and record the things you notice as you have drawn more and more halving lines.
- What is happening to the enclosed area each time the sides are halved? (Try investigating a regular shape first.)
Getting Started
It might help to have some large sheets of paper for this activity.
Student Solutions
We had just three contributions sent in, which is sometimes the case with these more visual challenges. However it is good to receive anything you have to say about your work having had a go at the challenge. Imogen-Rose from Sutton Bonington wrote;
You start with a square, then all you do is tilt the square into a diamond and then back to a normal square and so on.
That's interesting - I wonder what a 'normal' square is? Does a square change shape if it is tilted?
A pupil from Pownhall Hall School wrote;
It got small really quickly at first and then it got smaller slowly. The shapes got more regular as it went smaller. The measurements got harder as the shape got smaller.
Finally Chris from Northowram Primary School wrote;
Well Chris, it is good to see that you went further in investigating this challenge. So, thank you for these contributions and do feel encouraged to send in ideas from any challenge even though you may not have 'completed' it.