How many different triangles can you make on a circular pegboard that has nine pegs?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you find all the different triangles on these peg boards, and
find their angles?
How many triangles can you make on the 3 by 3 pegboard?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you cover the camel with these pieces?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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....?
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
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
How many different rhythms can you make by putting two drums on the
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the clues to colour each square.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you find all the different ways of lining up these Cuisenaire
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
My coat has three buttons. How many ways can you find to do up all
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
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the best way to shunt these carriages so that each train
can continue its journey?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered