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?

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

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

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

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

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

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 ...?

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?

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

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.

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

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

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?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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

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

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?

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

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

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

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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.

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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?

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?