Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they 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?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
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 jugs.
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!
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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 rules.
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?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
What is the best way to shunt these carriages so that each train can continue its journey?
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 smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
How many trapeziums, of various sizes, are hidden in this picture?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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 numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
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.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
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?
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?
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.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
How many triangles can you make on the 3 by 3 pegboard?
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?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
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.
An activity making various patterns with 2 x 1 rectangular tiles.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?