Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Use the clues to colour each square.
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 work out how to balance this equaliser? You can put more than one weight on a hook.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
How many different rhythms can you make by putting two drums on the wheel?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you find all the different ways of lining up these Cuisenaire rods?
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
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?
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?
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?
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.
Investigate the different ways you could split up these rooms so that you have double the number.
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. . . .
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.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
How many different triangles can you make on a circular pegboard that has nine pegs?
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 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?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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!
An activity making various patterns with 2 x 1 rectangular tiles.