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

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

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

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

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?

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.

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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?

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Can you cut up a square in the way shown and make the pieces into a triangle?

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?

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

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

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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?

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

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

Can you fit the tangram pieces into the outline of the playing piece?

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

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

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.

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 outline of Granma T?

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.

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

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

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

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

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

Can you fit the tangram pieces into the silhouette of the junk?

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Can you fit the tangram pieces into the outline of the plaque design?

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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.

See if you can anticipate successive 'generations' of the two animals shown here.

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?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Explore our selection of interactive tangrams. Can you use the tangram pieces to re-create each picture?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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