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?
If the flag is reflected twice, which way will it be facing at the end?
Thinking about the distance between the lines of reflection might help --- squared paper might be helpful for this.