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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the clues to colour each square.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you find all the different ways of lining up these Cuisenaire
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
What happens when you try and fit the triomino pieces into these
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Can you cover the camel with these pieces?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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....?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This dice train has been made using specific rules. How many different trains can you make?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These practical challenges are all about making a 'tray' and covering it with paper.
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.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
How many triangles can you make on the 3 by 3 pegboard?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you find all the ways to get 15 at the top of this triangle of numbers?