## Lesson abstract

This lesson is a substantial investigation of the shapes formed by joining points evenly distributed around a circle. Students generate and test hypotheses and explore the connection between the HCF and LCM of the number of points on the circle and the jump size, and the shape produced. The lesson moves to then look at how prime factorisation can efficiently determine the HCF and LCM of two numbers. Students explore why the HCF (a,b) x LCM (a,b) = ab.

## Mathematical purpose (for students)

To carry out a substantial mathematical investigation, by looking for patterns, making and testing hypotheses and writing generalisations.

## Mathematical purpose (for teachers)

The lesson provides a purposeful, rich and aesthetically pleasing activity that builds on the knowledge developed during the first two lessons related to prime factorisation. There are also smaller tasks to investigate the many connections between HCF and LCM and prime numbers.

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