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?

How fast would you have to throw a ball upwards so that it would never land?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Look at the advanced way of viewing sin and cos through their power series.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Which parts of these framework bridges are in tension and which parts are in compression?

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?

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

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?

Sort the houses in my street into different groups. Can you do it in any other ways?

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.

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

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

These pictures show squares split into halves. Can you find other ways?

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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.

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?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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

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

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Formulate and investigate a simple mathematical model for the design of a table mat.

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. . . .

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

Numbers arranged in a square but some exceptional spatial awareness probably needed.

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

Investigate constructible images which contain rational areas.

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

A follow-up activity to Tiles in the Garden.

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.

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

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

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

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?