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 least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
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?
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?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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?
What happens when you try and fit the triomino pieces into these two grids?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
A game for two players. You'll need some counters.
Can you cover the camel with these pieces?
Move just three of the circles so that the triangle faces in the opposite direction.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
A variant on the game Alquerque
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?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will 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?
Can you fit the tangram pieces into the outline of Little Ming?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of this sports car?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Here's a simple way to make a Tangram without any measuring or ruling lines.