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?
In this matching game, you have to decide how long different events take.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
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?
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.
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Try this matching game which will help you recognise different ways of saying the same time interval.
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
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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.?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
What could the half time scores have been in these Olympic hockey matches?
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
My coat has three buttons. How many ways can you find to do up all
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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. . . .
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different triangles can you make on a circular pegboard that has nine pegs?
Find all the numbers that can be made by adding the dots on two dice.
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 make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?