During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Try this matching game which will help you recognise different ways of saying the same time interval.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
In this matching game, you have to decide how long different events take.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
The pages of my calendar have got mixed up. Can you sort them out?
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 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.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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....?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Use the clues to colour each square.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find all the different ways of lining up these Cuisenaire
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?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Number problems at primary level that require careful consideration.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?