If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What happens when you try and fit the triomino pieces into these
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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
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?
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 cover the camel with these pieces?
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?
How many different rhythms can you make by putting two drums on the
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Use the clues to colour each square.
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. . . .
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
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 smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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 triangles can you make on the 3 by 3 pegboard?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you find all the different ways of lining up these Cuisenaire
How many trains can you make which are the same length as Matt's, using rods that are identical?
These practical challenges are all about making a 'tray' and covering it with paper.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
An activity making various patterns with 2 x 1 rectangular tiles.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 find all the different triangles on these peg boards, and
find their angles?
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
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.