What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

What shape is made when you fold using this crease pattern? Can you make a ring design?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

What can you see? What do you notice? What questions can you ask?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Exchange the positions of the two sets of counters in the least possible number of moves

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?

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

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

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?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

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.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

How many loops of string have been used to make these patterns?

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?

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

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

How many pieces of string have been used in these patterns? Can you describe how you know?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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 2 people. Take turns joining two dots, until your opponent is unable to move.

Can you fit the tangram pieces into the outline of these rabbits?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Here are shadows of some 3D shapes. What shapes could have made them?

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

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 fit the tangram pieces into the outline of these convex shapes?

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

Here's a simple way to make a Tangram without any measuring or ruling lines.

Can you fit the tangram pieces into the outlines of the candle and sundial?

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 hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?