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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.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Can you describe the journey to each of the six places on these maps? How would you turn at each junction?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How much do you have to turn these dials by in order to unlock the safes?
Can you sort these triangles into three different families and explain how you did it?
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Use the clues about the symmetrical properties of these letters to place them on the grid.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Complete the squares - but be warned some are trickier than they look!
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and find their angles?
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Here are shadows of some 3D shapes. What shapes could have made them?
Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
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.
How many symmetric designs can you make on this grid? Can you find them all?
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 would you move the bands on the pegboard to alter these shapes?
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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 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?
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Use the isometric grid paper to find the different polygons.
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
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?
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
What is the greatest number of squares you can make by overlapping three squares?
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?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?