This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

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.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

It starts quite simple but great opportunities for number discoveries and patterns!

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

I cut this square into two different shapes. What can you say about the relationship between them?

A description of some experiments in which you can make discoveries about triangles.

What do these two triangles have in common? How are they related?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

What is the largest cuboid you can wrap in an A3 sheet of paper?

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 these hexagons drawn from different sized equilateral triangles.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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?

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

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

A challenging activity focusing on finding all possible ways of stacking rods.

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

How many faces can you see when you arrange these three cubes in different ways?

How many models can you find which obey these rules?

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

A follow-up activity to Tiles in the Garden.

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

In how many ways can you stack these rods, following the rules?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

An activity making various patterns with 2 x 1 rectangular tiles.