Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Can you fill in the empty boxes in the grid with the right shape and colour?
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?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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 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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Investigate the different ways you could split up these rooms so that you have double the number.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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.
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?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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....?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?