Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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
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
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Use the clues to colour each square.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
What happens when you try and fit the triomino pieces into these
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you cover the camel with these pieces?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
A Sudoku with clues given as sums of entries.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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 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?
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?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Investigate the different ways you could split up these rooms so
that you have double the number.
How many different triangles can you make on a circular pegboard that has nine pegs?
In this matching game, you have to decide how long different events take.
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. . . .
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?