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Centre for Research in Mathematics Education (CRME)
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Circle pattern
This task is designed to assess how well students understand
The initial problems shows a black circle with radius 2r, inside of who two smaller circles of radius r are drawn. Students must show that the fraction of the diagram that is black is equal to a half.
The initial problem is altered with four black circles of radius 0.5r drawn inside the white circles. The task is to calculate the fraction of the circle that is black.
The task continues by alternating between colours and halving the radius of circles added to the diagram. Students must write a description of what happens to the black and white fractions as the pattern continues.
This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. A full rubric is given for the task, together with examples of student work and suggestions for helping students overcome misconceptions. Further information on the collection is given here.
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Downloads
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Circle pattern (rubric) 74.53 KB
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Circle pattern (student work scored) 318.48 KB
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Circle pattern (student work unscored) 196.23 KB
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Circle pattern (task) 73.85 KB
Show downloads
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Circle pattern (rubric) 74.53 KB -
Circle pattern (student work scored) 318.48 KB
-
Circle pattern (student work unscored) 196.23 KB
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Circle pattern (task) 73.85 KB
Download all files as a .zip642.39 KB
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