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GeoGebraGeoGebra Classroom

Red shape

This applet is motivated by Tony Cotton's Starting Point to Chapter 8: Geometry in Understanding and Teaching Primary Mathematics (3rd ed., 2016, Routledge). Close your eyes and ask a friend to guide you through the following:
  • Create a large red rectangle that you can see clearly in your mind’s eye. Stand it on its end so that you can see it standing on its shortest side. Then slowly rotate it so that it is laying on one of the longest sides. Now rotate it again so that it is balancing on a corner. Move the rectangle round and round in your mind’s eye and make a decision about which way round you want finally to picture the rectangle and stop it in that orientation.
  • Now imagine a small, blue right-angled triangle that will fit inside the rectangle. Picture it inside the rectangle and slide it so that the right angle fits exactly into one corner of the rectangle.
  • Imagine another small, blue right-angled triangle, which can be a different size from the first one you thought of. Slide it into one of the other corners of the rectangle.
  • Notice the red shape that is left inside the rectangle. Open your eyes and sketch what you see.
Now look at the applet. Is this the shape you imagined? Play with the nine coloured points to explore possibilities ...