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

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?

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

This challenge is about finding the difference between numbers which have the same tens digit.

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

What two-digit numbers can you make with these two dice? What can't you make?

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Can you find out in which order the children are standing in this line?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

My coat has three buttons. How many ways can you find to do up all the buttons?

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

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

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?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

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....?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

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 maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Find all the numbers that can be made by adding the dots on two dice.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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.