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?
In Teddy Town, teddies are either red or yellow and they live in
red or yellow houses. There are 4 teddies - 2 red and 2 yellow, and
4 houses - 2 red and 2 yellow.
Can you match each teddy to a house so that the four pairs are
all different from each other?
Imagine now that there are three
different colours of teddies and houses. red, yellow and blue. In
Teddy Town now there are 9 teddies and 9 houses:
What are the nine different combinations of teddies and
Here is a map showing Teddy Town:
The streets are very special. If you walk along a street from
east to west, or west to east, all the houses are a different
colour and the teddies living in the houses are a different colour
too. The same is true if you walk along the streets in a
north-south or south-north direction.
In other words, looking at the map grid, each row and column must
have different coloured houses and different coloured
Can you arrange the nine different combinations you've found on the
Teddy Town is expanding rapidly as green teddies move to the
area and green houses are built. Now there are 16 teddies and 16
Find the sixteen different ways to combine the teddies and
How could these sixteen households be organised on the map now?
Remember that in each row and column there must be both different
coloured houses and teddies.
Now ... yes, you've guessed it. Another colour teddy bear has
moved to Teddy Town. As well as red, yellow, blue and green teddies
there are now purple teddies. Of course, this means that purple
houses will have to be built. So, now in Teddy Town there are 5 of
each colour bear, making 25 teddies in all, and also 25 houses,
again 5 of each colour. Can you make the 25 different combinations
of teddy and house now?
Arrange these on the street map below in the same way as
Teddy Town is becoming very overcrowded! However, there is just
enough room for some black teddies to join. Living there now are 36
teddy bears: 6 red, 6 yellow, 6 blue, 6 green, 6 purple and 6
black. There are 36 houses for them to live in: 6 red, 6 yellow, 6
blue, 6 green, 6 purple and 6 black. Make the 36 combinations of
teddies and houses.
Do you think it will be possible to put these 36 combinations in
the street grid? May be it's not. Have a go!
Now, look back at what you have done and ask yourself some of
This activity is based on a Bernard's Bag problem from December
1997 called Tea Cups. The idea for the teddies came from Andrew
Massey who is an Advisor for Worcestershire County Council. Thank
you! Many thanks also to learningresources.com for
the use of the bear images.