Properties of Shapes: Age 7-11

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?

This activity focuses on similarities and differences between shapes.

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.

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

Use the isometric grid paper to find the different polygons.

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

This problem shows that the external angles of an irregular hexagon add to a circle.

Use the information on these cards to draw the shape that is being described.

Are these statements always true, sometimes true or never true?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

How many different shaped boxes can you design for these sweets?

How would you move the bands on the pegboard to alter these shapes?

How much do you have to turn these dials by in order to unlock the safes?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

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

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

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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 parallelogram.

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

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?

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

This problem explores the shapes and symmetries in some national flags.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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.

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

The challenge for you is to make a string of six (or more!) graded cubes.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Can you draw a square in which the perimeter is numerically equal to the area?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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

A task which depends on members of the group noticing the needs of others and responding.

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

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.

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

Can you find all the different triangles on these peg boards, and find their angles?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.