Challenge Level

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Challenge Level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Challenge Level

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.

Challenge Level

Can you fit the tangram pieces into the outlines of the convex shapes?

Challenge Level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Challenge Level

What is the greatest number of squares you can make by overlapping three squares?

Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Challenge Level

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?

Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

Challenge Level

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?

Challenge Level

Can you fit the tangram pieces into the outline of this teacup?

Challenge Level

Can you fit the tangram pieces into the outline of the butterfly?

Challenge Level

An activity centred around observations of dots and how we visualise number arrangement patterns.

Challenge Level

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?

Challenge Level

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.

Challenge Level

Can you fit the tangram pieces into the outline of the house?

Challenge Level

Can you fit the tangram pieces into the outline of the candle?

Challenge Level

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Challenge Level

Can you fit the tangram pieces into the outline of Mah Ling?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Challenge Level

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.

Challenge Level

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Challenge Level

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.

Challenge Level

Which of these dice are right-handed and which are left-handed?

Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Challenge Level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Challenge Level

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Challenge Level

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.

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Challenge Level

Can you fit the tangram pieces into the outlines of the people?

Challenge Level

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Challenge Level

Can you fit the tangram pieces into the outline of the telephone?

Challenge Level

Can you fit the tangram pieces into the outlines of the chairs?

Challenge Level

Can you fit the tangram pieces into the outlines of the numbers?

Challenge Level

Can you logically construct these silhouettes using the tangram pieces?

Challenge Level

Can you fit the tangram pieces into the outline of the sports car?

Challenge Level

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Challenge Level

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

Challenge Level

Can you fit the tangram pieces into the outline of the dragon?

Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Challenge Level

Can you fit the tangram pieces into the outlines of the rabbits?

Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Challenge Level

Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?