Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
How many different symmetrical shapes can you make by shading triangles or squares?
A challenging activity focusing on finding all possible ways of stacking rods.
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 took.
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 clues about the symmetrical properties of these letters to place them on the grid.
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.
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?
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 it up?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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.
How many triangles can you make on the 3 by 3 pegboard?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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?
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?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?
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 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.
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?
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....?
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.?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
In how many ways can you stack these rods, following the rules?
How many necklaces can you make that fit the rule? How do you know you've got them all?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?