This prompt has generated questions and discussions about how one of the shapes has been transformed into the other. Initially students will often try to describe a combined transformation to map the smaller shape onto the larger. How many combinations are there? Can it be mapped in two transformations? How many ways?
In this episode of the inquiry, students might revise the concepts of rotation, reflection and translation and how to describe them fully - or may require, by selecting the appropriate regulatory card, the teacher to instruct them. (It is advisable to have support materials available for this eventuality.) The class will also come across the need for an enlargement. Depending on the first transformation, the centre of enlargement will be different, although the scale factor is the same.
Ultimately, students identify (possibly under the teacher's guidance) the one enlargement that maps the object (smaller shape) onto the image (larger shape). If the smaller shape is considered as the image, then the scale factor is different. At this point, a new inquiry pathway can open as students seek a link, and attempt to generalise that link, between the scale factors of a negative enlargement and its inverse.
Enlargement inquiry discussion This document contains a transcript of a conversation between Caitriona Martin and Andrew Blair, two teachers of inquiry maths, about the enlargement prompt. It raises some important issues about inquiry maths in relation to the curriculum.
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