2 Rings
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Age
5 to 7
Challenge level
Problem
Two very special circles are on the floor:
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Very special because they can get bigger or smaller - as you like.
So you might like them to be like this:
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Maybe you like things small - so you would have:
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I'd like the blue one to grow:
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Whoa! That looks different.
The Red is inside the Blue.
So the Red and the Blue can grow - just as you like.
We've seen the Red INSIDE the Blue.
Can we change things so that we might use other words like:
TOUCHING?
OVERLAPPING?
OUTSIDE?
Have a go. Send us some pictures of what you do - we'd love to see them.
If you enjoyed this problem, you might like to try 3 Rings .
Getting Started
How about using different sizes of hoops on the floor? I once used bracelets and rings!
How will you keep a record of what you have done? It might be useful to have some things to draw round.
Student Solutions
Alice from the Perse Senior School for Girls said:
I've done 4 combinations with red and blue separate, red touching the blue, red overlapping the blue and red inside the blue.Here are the images which Alice sent:
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red and blue separate
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red touching blue
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red overlapping blue
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red inside blue
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Alyssa from Mason Middle School suggested:
You could make them overlapping by making them the same size.
You're right, Alyssa, you could. This would be quite difficult to draw, though, which is probably why you didn't send us an image! We would like to receive more ideas about how you could arrange two circles if you come up with some. Let us know!
Benjamin from Paradykes Primary School in Scotland sent in the followingTo make the two rings touch grow one slightly bigger than the other and put the smaller one inside and touching the other ring. To make the two rings overlap then make them both same size crossing each other. For the last challenge, putting one ring outside the other you just simply make one tiny and one huge and put the tiny one inside the middle of the big one.
Thank you everyone for your contributions, you may find something similar in our Open Spaces pathway, which is part of our sister site Wild Maths.
Teachers' Resources
2 Rings
Two very special circles are on the floor:
Image
Very special because they can get bigger or smaller - as you like.
So you might like them to be like this:
Image
Maybe you like things small - so you would have:
Image
I'd like the blue one to grow:
Image
Whoa! That looks different.
The Red is inside the Blue.
So the Red and the Blue can grow - just as you like.
We've seen the Red INSIDE the Blue.
Can we change things so that we might use other words like:
TOUCHING?
OVERLAPPING?
OUTSIDE?
Have a go. Send us some pictures of what you do - we'd love to see them.
If you enjoyed this problem, you might like to try 3 Rings .
Why do this problem?
This problem provides a great environment in which to discuss the meaning of words related to position, for example touching, overlapping (some children have added "underlapping"), inside and outside.
Possible approach
You may decide to use real rings (perhaps wooden or plastic), or you could ask children to make some rings as part of the task, maybe out of pipe cleaners.
You could introduce the task in a large space outside, or in the school hall, using P.E. hoops, for example. You could lay out two hoops and ask the children to describe what they see. By asking a child to place two hoops in a different way, and talking about this as well, you will begin to build up useful vocabulary. You can then set children off on investigating other ways. You may need to
address how they are keeping track of the different combinations - perhaps they could draw each, or there may be enough equipment to keep each one once it is made.
As a plenary, you could invite a pair of children to describe an arrangement and encourage everyone else to try to draw or make it.
Key questions
What could you do if one of your rings was bigger/smaller?
How would you describe the two rings?
Questions could well arise in a discussion about these sets of two pairs, for example, and whether any are the same or different, and why.
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Possible extension
Take the pupils onto the activity 3 Rings.