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Centre for Research in Mathematics Education (CRME)
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Hopewell geometry
This task is designed to assess how well students understand similar triangles, using Pythagoras’ theorem, and using trigonometry to find angles.
The Hopewell people were Native Americans whose constructed earthworks using right triangles. The task shows eight right triangles.
The first tasks are to calculate some lengths and angles for Hopewell triangles. An extended task looks at a shaded triangle surrounded by three other triangles to form a rectangle. The surrounding triangles are similar to the Hopewell triangles, students must identify which ones. The final task is to determine if the shaded triangle is a right-angled triangle.
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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Hopewell geometry (rubric) 141.52 KB
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Hopewell geometry (student work scored) 380.89 KB
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Hopewell geometry (task) 91.37 KB
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Hopewell geometry (rubric) 141.52 KB -
Hopewell geometry (student work scored) 380.89 KB
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Hopewell geometry (task) 91.37 KB
Download all files as a .zip823.93 KB
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