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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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

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.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

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?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

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

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

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

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....?

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

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.

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

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?

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?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

If you had 36 cubes, what different cuboids could you make?

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Can you find the chosen number from the grid using the clues?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

What happens when you try and fit the triomino pieces into these two grids?

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?