An environment which simulates working with Cuisenaire rods.
In how many ways can you arrange three dice side by side on a
surface so that the sum of the numbers on each of the four faces
(top, bottom, front and back) is equal?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Using only the red and white rods, how many different ways are
there to make up the other colours of rod?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Can you find all the different ways of lining up these Cuisenaire
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?