We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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?

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you find all the different triangles on these peg boards, and find their angles?

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.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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.

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

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.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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

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

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

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

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

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

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?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Try this matching game which will help you recognise different ways of saying the same time interval.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.