Filling and Dilation

From MathWiki

The links and documents posted come from the SSHRC funded project of Professors Margaret Sinclair (Education) and Walter Whiteley (Mathematics). They are designed to link the kinesthetic activity of filling an inverted pyramid (dilating the surface of the liquid from the bottom 'vertex') with the plane dynamic geometry exploration of dilations of 2-D shapes. Overall, they offer an exploration of the proportional changes in lengths, areas, and volume under these types of geometric scalings.

The linked activities provide a visual and kinesthetic exploration of the process of scaling - and link to a variety of other spatial visual reasoning tasks, such as cross-sections of 3-D shapes (where the surface of the water is such a cross-section) how areas scale when lengths are scaled, ... .

The documents are available for use in educational contexts, including teacher preparation courses and professional development programs. They cannot be used for commercial purposes, without permission of the researchers.


As we have developed to activity, the participants do two linked activities, and then explore the connections between them.

In our current iteration, the first activity involves pouring water into 3-D shapes.

Activity Sheet of Filling Inverted Pyramids

GSP Sketch for Dilations

GSP Sketch for Dilations (GSPv.4)


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