How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different triangles can you make on a circular pegboard that has nine pegs?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Use the clues to colour each square.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find all the different ways of lining up these Cuisenaire
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
How many different rhythms can you make by putting two drums on the
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many triangles can you make on the 3 by 3 pegboard?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Investigate the different ways you could split up these rooms so
that you have double the number.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
In this matching game, you have to decide how long different events take.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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 shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
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?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?