This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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?

How many models can you find which obey these rules?

Can you use the information to find out which cards I have used?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Can you find all the different ways of lining up these Cuisenaire rods?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

What is the best way to shunt these carriages so that each train can continue its journey?

What could the half time scores have been in these Olympic hockey matches?

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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 shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Investigate the different ways you could split up these rooms so that you have double the number.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?