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This problem offers an engaging context in which to search for patterns, gain insights into the structure of numbers, and lay the foundations for an appreciation of the prime factorisation of numbers.
This task was the focus of an NRICH webinar in September 2023.
The way that the problem has been set out suggests a structure for a lesson, and assumes that students will have opportunities to work in pairs, and then share their insights and strategies with the whole class.
In the Settings menu of the T-shirt, you can specify a circle you'd like to include in a Window/Block/Zigzag - that number will appear top left. In Explorer mode, the number will appear in the middle.
In the Settings menu of the scarf, the number you specify will appear at the start (far left).
Notice that when you hover over each of the circles of the full T-shirt in the interactivity, you are told which number it represents.
Some students could be asked to annotate or colour this sheet, in which the circles have already been split.
Dancing factorisation might provide a good follow-up activity.
These two group activities use mathematical reasoning - one is numerical, one geometric.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.