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This problem follows on from Mirror, Mirror... but it works equally well on its own. It could be used as extension work for students learning to draw reflections accurately.
Alternatively, this problem and the two related problems Mirror, Mirror... and Who Is the Fairest of Them All? could form a unit of work on combined transformations. All three problems ask students to consider the effect of combining two transformations, and then challenge them to describe the single transformations that produce the same results.
These printable resources may be useful: ...on the Wall,
As an extension task, all that is needed is to provide the problem verbally or as a worksheet to pairs of students who could then make sense of it together. When they have established the combined transformation for one specific example, a teacher intervention may be appropriate, to move the focus to the general case -asking the key questions below.
What if the flag was in a different place?
Ensure students use square paper and encourage them to draw their reflections accurately.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?