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?

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

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?

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

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

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?

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?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

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

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.

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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

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?

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?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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?

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

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

Number problems at primary level that require careful consideration.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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

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

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?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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

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

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?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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