Silly carpets and the light switchers- investigating prime and square numbers

This is just a short post about a very simple idea I did with my yr2 class a long time ago when I was still a class teacher. It sort of follows on from my previous ‘ hooray for an array’ post. It was a way of children investigating prime and square numbers. Our class carpet was made from carpet tiles.  We were learning area by counting squares. I had a few spare carpet tiles….not quite sure why. So I showed them that with some numbers like  8 you could make a sensible (rectangular) carpet, and some numbers like 9 you could even make square shaped carpets. But some numbers, like 11, no matter how you tried,  you could only make a silly carpet that was very long and very thin. There was something about the notion of the class trying to fit onto a long thin carpet, one behind the other, that the class found hilarious- and with squared paper quickly found all the squares and primes to 50. Made a great maths display. Hardly an original investigation, but I hope an interesting context that your children will enjoy doing.

For older children (upper ks2, secondary, adults) here’s an interesting problem. With primary children I’d use something like two coloured counters or paper cups for them to model this- basically anything that could be used to indicate if a switch is on or off. The problem starts like this…..

There is a long corridor in school with fifty light switches- numbered 1-50.  There are 50 pupils also numbered 1-50. All the lights are off, so pupil number one helpfully goes along the corridor and flicks every switch on.

Pupil number two,comes along and thinks- what a waste of electricity, I’m going to flick all the switches for lights that are multiples of two. So she turns off lights number 2,4,6,8 etc.

Pupil number three comes along and wonders why some lights are on and some off. She  flicks every third switch ( so if it were on she flicks it off and if it was off she flicks it off).

Pupil four flicks every fourth switch, pupil 5 every fifth and so on, until finally pupil number 50 just flicks switch 50.

At the end of this, how many lights are left switched on? Which ones? Why these?

I will post the solution tonight, but the title should help a lot!

Silly carpets and the light switchers- investigating prime and square numbers