This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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.

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

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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?

Make a flower design using the same shape made out of different sizes of paper.

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Can you visualise what shape this piece of paper will make when it is folded?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

Which of the following cubes can be made from these nets?

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.

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

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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,. . . .

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

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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

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?

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?

Make a cube out of straws and have a go at this practical challenge.

Reasoning about the number of matches needed to build squares that share their sides.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?