What is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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?
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.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
A game for two players. You'll need some counters.
Can you cover the camel with these pieces?
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?
What happens when you try and fit the triomino pieces into these two grids?
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 activity centred around observations of dots and how we visualise number arrangement patterns.
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Move just three of the circles so that the triangle faces in the opposite direction.
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?
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.
Make one big triangle so the numbers that touch on the small triangles add to 10.
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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.
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?
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?
Watch this animation. What do you see? Can you explain why this happens?
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.
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 silhouette of the junk?
Can you fit the tangram pieces into the outlines of the chairs?
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.
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Can you fit the tangram pieces into the outline of the dragon?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the rabbits?
Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?
Can you fit the tangram pieces into the outline of Granma T?