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?
Some of you reading this live in different continents and know
about other animals but I've chosen sheep since they are pretty
common across many parts of the world. The young lamb
has a piece of land which it likes but the shepherd is concerned
at night time that wild animals may come and attack, and the sheep
also needs protection at those times from cold weather. So the
thoughtful shepherd used bales of straw:
He arranges these bales of straw around lambs, sometimes one,
sometimes two ... sometimes 10 lambs together.
You can see by the area of dark green just how much space each
lamb needs. You can also see how the bales are arranged so that the
corners are strong and deep around the lamb.
It would not be so good to have them like this
Here are some examples of how it could be done for 1, 2 and 3
If you are doing this in school you may find that a teacher has
some useful blocks to help. Ask about Cuisenaire blocks that are
differently coloured according to how long they are and you could
use a white block to stand for a lamb and a RED  for a bale of
straw. You could also use multilink blocks as a help.
There are also some graphical computer programs that may help,
isometric grids are probably better than square ones on this
Remember these particular rules:-
Any other rules that you might wonder about are up to you to
When you send in your results make sure that you tell us what
the rules are that you have made extra to my rules.
It will be interesting to see how you put your results together
for 1, 2, 3, 4, 5, 6, 7, 8, 9 and10 lambs.
Well Good luck!
Once you've done a set of solutions for 1 ... 10 lambs then have
a go at altering the rules, saying "I wonder what would happen if .
. . ?"
Here are some possible questions:-