This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
"The Pied Piper of Hamelin'' is a story you may have heard or read. This man, who is often dressed in very bright colours, drives the many rats out of town by his pipe playing - and the children follow his tune.
Suppose that there were $100$ children and $100$ rats. Supposing they all have the usual number of legs, there will be $600$ legs in the town belonging to people and rats.
But now, what if you were only told that there were $600$ legs belonging to people and rats but you did not know how many children/rats there were?
The challenge is to investigate how many children/rats there could be if the number of legs was $600$. To start you off, it is not too hard to see that you could have $100$ children and $100$ rats; or you could have had $250$ children and $25$ rats. See what other numbers you can come up with.
Remember that you have to have $600$ legs altogether and rats will have $4$ legs and children will have $2$ legs.
When it's time to have a look at all the results that you have got and see what things you notice you might write something like this:
a) $100$ Children and $100$ Rats - the same number of both,
b) $150$ Children and $75$ Rats - twice as many Children as rats,
c) $250$ Children and $25$ Rats - ten times as many Children as Rats.
This seems as if it could be worth looking at more deeply. I guess there are other things which will "pop up'', to explore.
Then there is the chance to put the usual question "I wonder what would happen if ...?''