Ensuring that pupils see alternative views of the same family of objects is an important feature of good teaching. We need to ensure that our learners experience what is sometimes called a ‘rational’ set of examples that highlight non-prototypical aspects (Ryan and Williams, 2007). In other words, examples we consider and problems that we meet need directly to challenge misconceptions and develop a deep understanding of geometrical forms.
In considering characteristics of a rectangle, this set would challenge some students’ thinking:
![](data:image/png;base64,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)
Other useful ideas include encouraging pupils to rotate their work (or themselves), imagining a final product, or including additional components in a diagram to search for known objects that otherwise may be hidden.
Now try this: How would one find the area of each square in the diagram below?
![](data:image/png;base64,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)
Some pupils say it’s impossible because no measurements are included. Some choose a numerical value for a dimension of a shape and work through the problem.
Others label the radius of the circle r and work through the squares separately.
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)
The large square has a width (and therefore height) equal to the diameter of the circle. Hence its area is 2r x 2r = 4r2
The smaller square …?
This is where these pupils often start to scratch their heads. One pupil in particular went through the following argument:
The small square has diagonal 2r, which is also the hypotenuse of the isosceles right angled triangle.
![](data:image/png;base64,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)
So, applying Pythagoras’ theorem, the side length of the square, s can be found by solving;
(2r)2 = 2s2
4r2 = 2s2
√2 r = s
The area of a square is the square of its side length so the area of the square is 2r2
2r is also the base of an isosceles right angled triangle whose height is r, so the area is a half of 2r2. Since we have two of these the answer is 2r2
I was genuinely impressed, but the pupils in question thought that the answer was too simple to warrant this train of thought.
Another then suggested simply rotating the central square 45º. Is it all a lot clearer now?
![](data:image/png;base64,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)
You may now realise that you really don’t need to think much beyond the fact that the small square is half the area of the large square. Not only is life so much simpler, but I would argue that this gives us a much more general answer that doesn’t require including measurements and variables; in fact the relationship between all three shapes can be derived no matter which shape has a dimension included.
Allowing pupils to adapt mathematical objects in a way that doesn’t affect important characteristics encourages careful consideration – this pupil knew that rotation left area invariant – and can result in some much simpler problems to solve.
SOMETHING TO TRY:
KS1: Which shapes are triangles? Why or why not:
![](data:image/png;base64,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)
(D Clements and J Sarama, Young Children's Ideas About Geometric Shapes, Teaching Children Mathematics, Vol. 6, 2000)
KS2: Is more of the rectangle blue or yellow? Why?
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)
KS3: Which of the following are parallelograms?
![](data:image/png;base64,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)
KS4: Explain the Bride's Chair proof (Euclid's Proof) of Pythagoras' theorem:
http://www.cut-the-knot.org/pythagoras/morey.shtml
KS5: How is a curve of a constant width constructed? E.g. A Reuleaux triangle
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJwAAACeCAIAAABIEvQRAAAGzElEQVR4nO2d3ZHrIAxG1QIt0IJacAu0oBbSgltQLdsCLWwtuQ8kHl/nZw3GRsYfc97u7J0kZxCSwJjuGN0Nav0BMOoPSO1wQGqHA1I7HJDa4VhK/f39FYzPI4TQ+iMsx99Sf35+nHMqAiZCCI6IiAaiGxERhRCaf6oE0ZtY+0YqM99jBHdVFfHeM5Ey358os3Muqrb/hDFC6lpUhJkd0Y0oznT+55XIgldI/QtVFXHODR9czok2vELqR6KqMDsiWaHTlFdIfa9zirQrXb56HccRUk0wjqP33v+fBBV7bTVfIfVBVE057fpIa9YrpD6CLW+enXa8Xlpq0rk92H6hSf16UalTZrufzoXX+4FeryhVRY7ROffqvYfUXYiqzrlQVKhs5EZ02G94GamqwzD4esltAYFIDvkZLyH1+Hj7CSZSEUjdRMN4+4kDipyepaYtTwsTdM4BxWufUlN7aLA0QefsnQx3KNXOCvoFIRqGAVJX8Gz4NUxx17Nf0tSP1HEc7U/QBTstrp1IDSG0rUHLeHQQIXWJqvfeVNGSxR4diXNLTWXouULuK772MYkTS01Z7ulC7iupcq24jXNWqSGEs2S5a6jb7j+lVGY+7yL6iYoVztmkqnrvyw75Gadi+/BMUvtIi76gzFV+59NIjap9pEXfqRKEzyE1dYu6N3pPQXhzO+IEUrspXVZy29yOsC71akYTflvGZFqqivgeE90/2bjhalfqZY0mwoaMyajUixu9b+sdWpQKo4kbUQihB6nXqV7WUNZjsiUVRhcoc0F5Y0jqRXpGuRRMVitSU18XRl8paAjbkNp7p34jub0IE1K99zD6hdzJ2l7qMAyCAuYvOOccU2OpKmL24QhTZDUOW0odxxFNhvWsT4ObSUUBk8v6mrWZVKS7BaycrG2kCnOXh8f2ZmU3uIFUFWEYLYWIzElNS2nzn+a8rNlnPVoqltKNrDmZdqhU9BmqMPyVLh0nFVvftVDm71cLHCcVmzAVcV/TpYOkCjOW0orI13TpCKlRFTVMXeLXVvARUhF49+DLJuvuUtE82gll/tRd2ldqVEXGux+fCtZ9pSLw7sqngnVHqSEEtBp25dNm3F5S0eM9hrcF615SGYXpIfC7CLyLVORHh/E2B95FKo58HsbbTZv6UnFA8GBeuxD1paKMOZjbSx+4slQV6e8uMuPEl/P7VaXi1GcjFoVNTakhBLR5m7BoLdWTim5DOxaFTTWpaAo2ZLGsVpOK1bQt82W1jlQkvc2Z9wvrSEVt2px5tVpBKlpIFphvw1WQimlqhGlZ3SoVTzvZYWoCb5WKDRk7hOe9EJuk4niDKZQ55UqbpKIvaIopV9okFQ0HU0zH9sulIkUySHrOvFwqjpYZJCXAhVIff9n6O4AFKQEulIo9GZukBLhQKrpINkkJcIlUPG9qlpQAl0gNISBFMotzrkSq9x6x1yxElC0Vj1QYxxVIVRG0Bi3DBVIRe40zZEvFtox5JFeqiqDnYBzNrVOZGbHXONlSEXvtkyc1quLUoH1illQVQSPJPnlSsaCeggyp3nssqKcgQyoRYWfmFORJRXfwFORJxYJ6CvKkNv+4YA0ZUpElnQgkSh2S13zwWFnNk9d8uOP9mGcgW+rDK17tZZgSqWmrnJlxc4dNSqXGeI9R0pMbrb8DWLBJajoI4YgQik2xVerjxKj3CMV2qCB1OrOPUGyE7OMsXxjHEaHYAjWlpqzYe48jL31JRfZkgOxzvyuJqpxuFm79DS9I/gn9HDBlm1DyLE0uwzAwpuyBlDz1VkBqF+N5jWMoeT61mBACovHexOInybdM2dQxhtr9pBbe+bBdrfceC+0elN/OUoVxHJ1zKHuqSw0hNJOaSGVPgNpKCFH55Vj11WLW1oC33E24n1pGGrWBrbeI7sQ4jt57ZMgFTC/INSc1kbrHjkgQk1dT52buA9SGEBCT10tNr/EzLXUek1OnGnnyF+q87eJoVFMylVZc2F1Q7b00TZiH5RvmLvN9OvAQ41mlzu2qSMqWL2g3Mt+ImMg5J8yV38rYnGQ3Jcyh9+CszELkiLz3KjJ/cXVXUueoiDA757oRHJ8imcgRDcMwvVXzLR1KnTOOYwgh7UYNT8GncJxEBiL3jK5vJ+UVpc5J6RU/t5GZSMzM46TwRjQQeSIi8t6HEFKJksuFpL46VpGHZiJHxESB6EakzHvM6fhEn+F0SBORyHs/zcWV07GCVOecinRMspvuAFsMR+SJhieBSIhkpn/i9vynxPCcea//JxE55yaXdVkl9ff3d8Q41fhbKkYHA1I7HJDa4YDUDgekdjggtcMBqR2Of2dJFFoV1WrUAAAAAElFTkSuQmCC)
https://www.ics.uci.edu/~eppstein/junkyard/reuleaux.html
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