Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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?
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Make one big triangle so the numbers that touch on the small triangles add to 10.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
A game for two players. You'll need some counters.
Move just three of the circles so that the triangle faces in the opposite direction.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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.
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,. . . .
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?
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. . . .
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 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?
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.
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you make a 3x3 cube with these shapes made from small cubes?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
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?
A game for two players on a large squared space.
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?
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 plaque design?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you fit the tangram pieces into the outlines of the convex shapes?
Can you fit the tangram pieces into the outlines of the camel and giraffe?
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
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?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the rabbits?
Can you fit the tangram pieces into the outline of Granma T?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of the clock?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.