My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Use the clues about the symmetrical properties of these letters to place them on the grid.
How many possible necklaces can you find? And how do you know you've found them all?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
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?
What patterns can you make with a set of dominoes?
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?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
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?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you cover the camel with these pieces?
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?
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 quadrilaterals can be made by joining the dots on the 8-point circle?
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 many different triangles can you make on a circular pegboard that has nine pegs?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
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?
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
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?
Complete the squares - but be warned some are trickier than they look!
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
This problem is intended to get children to look really hard at something they will see many times in the next few months.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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 your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Investigate the number of faces you can see when you arrange three cubes in different ways.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
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.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Shapes are added to other shapes. Can you see what is happening? What is the rule?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
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?
Can you sort these triangles into three different families and explain how you did it?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?