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2 Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

2 Rings


Two very special circles are on the floor:
2circles1
Very special because they can get bigger or smaller - as you like.
So you might like them to be like this:
changed
Maybe you like things small - so you would have:
change2
I'd like the blue one to grow:
Red-In-Blue
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.

pairs


Possible extension

Take the pupils onto the activity 3 Rings.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.