What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these numbers to the nearest whole number?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

Number problems at primary level that require careful consideration.

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

An investigation that gives you the opportunity to make and justify predictions.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Can you replace the letters with numbers? Is there only one solution in each case?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Can you find all the ways to get 15 at the top of this triangle of numbers?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This task follows on from Build it Up and takes the ideas into three dimensions!

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

An activity making various patterns with 2 x 1 rectangular tiles.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

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

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?