As a child I loved running out in the backyard and finding the exoskeleton of a cicada. I’d bring them in and freak my mum out but as a teacher I have grown to love using the life cycle of the cicada as a great teaching point when dealing with PRIME NUMBERS!

The fact is that many cicadas species emerge from their underground habitats after a prime number (7, 13 or 17) of years. Explaining why they do this is a great teaching point for students!

My local Sydney cicada, ‘The Black Prince’ emerges every 7 years.

Prime numbers are numbers that can be divided only by themselves and one. So 2, 3, 5, 7, 11, 13 and 17 are all prime numbers – but 18 is not a prime number, because you can divide it by both 2 and 9.

Cicadas are all sucking insects, which pierce plants with their pointy mouthparts and suck out the juices. The breeding cycle begins when huge numbers of adult cicadas emerge in the spring. They mate within a week, and a few days later, the female lays her eggs. She lays up to 600 eggs. These eggs hatch up after two to six weeks. The little babies make their way down to the ground (by crawling down, or just dropping), dig their way into the soil and begin the next phase of their life, feeding on the roots of shrubs and trees for the next 6, 12 or 16 years.

It can’t just be a coincidence that all of the periodic cicadas have prime number life cycles – (7, 13 and 17 years)!

So why do they do it? Different cicadas are running on different cycles, and if these cycles are prime numbers, they’ll cross over only very rarely. For example, a 13-year cycle and 17-year cycle will meet only every 221 years. That means that both species of cicadas would come out in huge numbers and all have to compete for the same amount of food only once every 221 years. The rest of the time, there will be enough food.

A few days ago I had a wicked Prime Number lesson with my maths class and one girl even brought in a surprise for me the next day!

Some of my girls also found some other number patterns in nature. Here is a YouTube video they located:

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