Regular Rings 1
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Age
7 to 11
Challenge level
Below is a picture of an unfolded piece of paper.
Can you work out what shape is made when it's folded up using the crease pattern shown?
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Click below if you want to see the shape.
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Can you make one of these shapes with a new piece of paper?
Now make several of the same shape from A4, A5 and A6 pieces of paper in two contrasting colours.
Challenge 1
Take a large and small shape made from your first colour and a medium shape made from your second colour.
Make a pattern from your shapes, by laying them on top of each other, that fits both of these rules:
You must be able to see at least part of each shape.
All three shapes must fit inside the perimeter (outline) of the largest shape.
Challenge 2
Use a new large, medium and small shape to recreate the same pattern but in opposite colours from Challenge 1.
Place these two patterns next to each other and continue to fold and add to your pattern until you've made a ring.
Can you predict how many of your original Challenge 1 pattern you will need?
We would love to see photos of the ring you make.
If you enjoyed these challenges, why not have a go at Regular Rings 2?
What do you notice about the different types of fold on the crease pattern? Can you tell which direction each fold is in?
What order do you think the folds were made in?
How could we check what we've done so far?
What order do you think the folds were made in?
How could we check what we've done so far?
Mae, Lewis, Matthew, Arthur and Jack from Brabyns Prep School said:
We started off by folding the pieces of paper and realising that they make equilateral triangles. Then we made 'triangle sandwiches' in red and yellow using A4, A5 and A6 paper. It was triangles galore in the classroom!
After that we made the first ring of triangles and it had 6 'triangle sandwiches'. The second ring had 18, and we tried to do the third but we didn't have enough, so we decided to use the interactive whiteboard to see if we could spot a pattern. We did! We realised that each ring had 12 more triangle sandwiches than the previous ring.
Then we tried to spot a link between the number of the ring (n) and the number of triangle sandwiches needed for that ring (t). We realised that t=12n-6. We worked out that the 100th ring would need 1194 triangle sandwiches.
Here is a photo of their creations:
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Regular Rings 1
Below is a picture of an unfolded piece of paper.
Can you work out what shape is made when it's folded up using the crease pattern shown?
Image
Click below if you want to see the shape.
Image
Can you make one of these shapes with a new piece of paper?
Now make several of the same shape from A4, A5 and A6 pieces of paper in two contrasting colours.
Challenge 1
Take a large and small shape made from your first colour and a medium shape made from your second colour.
Make a pattern from your shapes, by laying them on top of each other, that fits both of these rules:
You must be able to see at least part of each shape.
All three shapes must fit inside the perimeter (outline) of the largest shape.
Challenge 2
Use a new large, medium and small shape to recreate the same pattern but in opposite colours from Challenge 1.
Place these two patterns next to each other and continue to fold and add to your pattern until you've made a ring.
Can you predict how many of your original Challenge 1 pattern you will need?
We would love to see photos of the ring you make.
If you enjoyed these challenges, why not have a go at Regular Rings 2?
Why do this problem?
This problem provides the opportunity to develop visualisation skills. It requires children to solve the conundrum of what happens in between, when they are given a picture of a crease pattern and the finally-folded shape.
Possible approach
Just share/project/show the picture of the crease pattern first and allow children to talk about what shape they think it might make when re-folded.Then share the picture of the ready folded shape (or a real one you made earlier!) and ask children to talk about what they think now.
Give each pair of children a piece of A-sized paper (A4 is easier for smaller hands or beginner folders, but any A size will work) and ask them to try and recreate the shape. They can of course un-do their folds at any point in order to check whether their crease pattern matches the one in the picture.
Here are some examples of patterns stimulated by challenge 1, which you may or may not wish to share with your class:
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Key questions
What do you notice about the different types of fold on the crease pattern?What order do you think the folds were made in?
How could we check what we've done so far?
Possible extension
Pairs given one piece of A-sized paper could take it in turns to give an instruction whilst their partner carries out the fold. The instructor must do this with their hands on their hand, (no handling of the paper or pointing is allowed) in order to develop the accuracy of their descriptive and positional language. Children might be given larger A-sized paper (A3 for example) to act
as a model for the rest of the class, as folding with larger paper is more difficult and requires more accuracy.Some learners might like to have a go at Regular Rings 2.