What is the best way to shunt these carriages so that each train can continue its journey?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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,. . . .
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
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?
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 triangles can you make on a circular pegboard that has nine pegs?
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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
A game for two players on a large squared space.
Have a look at these photos of different fruit. How many do you see? How did you count?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Watch this animation. What do you see? Can you explain why this happens?
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?
Can you fit the tangram pieces into the outline of the dragon?
Can you fit the tangram pieces into the outlines of the chairs?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Can you fit the tangram pieces into the outlines of the rabbits?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of the clock?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Can you fit the tangram pieces into the outline of the playing piece?
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Which of these dice are right-handed and which are left-handed?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?