Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
"We did this sum at school last year and this is what I think
the answer is. First I did this kind of boxes. They were 4 squares
down, 1 square at the top left and one at the bottom right. I
looked for more and I found that there was only 1:
Then I did this kind of boxes. They were 4 squares down, then
at the left and opposite it the right one. There were 2 of
After that I did this kind of boxes. They were 4 squares down, 1
square at the left and then a right square which will be opposite
then 1 square up or down. There were 2 of these:
Fourthly I did this kind of boxes. They were 4 squares down, 1
square at the left and a right one which will be opposite then 2
squares up or down. There was only 1 of them: At last I did this
kind of boxes. They were 3 squares down and 3 squares which the
last of their square is touching the last of the 1st 3 squares.
There was only one of them:
The answer is you can make 7 boxes".
Jannis (Long Bay Primary) then correctly found
the other 4:
Finally, Matthew (Eastwood Primary)