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?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Find all the numbers that can be made by adding the dots on two dice.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many different rhythms can you make by putting two drums on the
Can you find all the different ways of lining up these Cuisenaire
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
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
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
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
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
An environment which simulates working with Cuisenaire rods.
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?
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?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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?
My coat has three buttons. How many ways can you find to do up all
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.
This challenge extends the Plants investigation so now four or more children are involved.
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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?