This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
I don't know whether in
your homes, at the weekend, there are lots of newspapers lying
about. Maybe you travel by train a lot and when you get into the
train there are lots of bits of newspapers on the seats and tables.
These things happen because they're not stapled together like
magazines usually are [like the ones that tell you what's on the
So what we're thinking
about is newspaper that has had the pages separated and they're
lying about instead of being like they were when they were bought
at the shop. We'll think about a very small newspaper in that it
only has eight pages. It would be a good idea to have two sheets of
paper [the same size] ready now so that we can talk this through
more easily. You could use two sheets of paper from a real
newspaper [ask the adult who bought the newspaper first!] or just
two pieces of A4 folded down the middle. They should look like
Now that you've got these
you will need to put one inside the other, fold the two together
and then number the pages 1, 2, 3, 4, 5, 6, 7 and 8.
To help you to see my
pictures better I've done the numbers in a special way.
When the pages are facing
you I put the numbers in a yellow box.
I've pretended that you can
see through the thin paper and so you can see the number that's
written on the side not facing you. That number I've put into a
You should write the
numbers the correct way round from 1 to 8.
So the middle sheet of the
newspaper looks like:-
If I remove that sheet the outside sheet will look like:-
Now you have all that you
need so let's have a look at the challenge.
When pages get separated at
home we have to try to sort them out and get things in the correct
order so that we can follow the stories and pictures.
Let's suppose that in our
eight-page newspaper there is just one complete story on each page
and so it does not matter what order the pages are in, as long as
the writing is not upside down!
How many ways can we
arrange the pages [no tearing!] so that the numbering may be
Here is a start I've
I N N E R - S H E E T - - - - - - - - O
U T E R - S H E E T
In A) I've turned the
inside sheet over so now the pages go 1, 2, 5, 6, 3, 4, 7, 8.
In B) I've got the inside
sheet the correct way round but have turned over the first sheet,
so now the pages go 7, 8, 3, 4, 5, 6, 1, 2.
In C) I've got both sheets
turned over so now the pages go 7, 8, 5, 6, 3, 4, 1, 2.
Now of course there are
other things we can do, like we can change the order of the sheets
so that one arrangement could be like this.
I N N E R - S H E E T - - - - - - - - -
- O U T E R - S H E E T
The page numbers now go 3,
4, 1, 2, 7, 8, 5, 6.
Well have a go yourself, be
as inventive as you like BUT the writing must be the correct way
It would be good to find a
way of recording all the page number orders, and look at them all
I usually ask you to
provide a question like "I wonder what would happen if ...?''. Well
I'm going to give you one this time:
What would happen if we had
three sheets of paper and so we had twelve pages to number?
If you found a way of doing
the first challenge you may be able to use that same system for
getting ALL the ways of arranging these three sheet and looking at
the numberings that occur. I guess it would be good to then explore
these sets of numbers that show the page numberings. [That's a