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?

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?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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.

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

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

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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!

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

This dice train has been made using specific rules. How many different trains can you make?

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

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

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?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

Can you substitute numbers for the letters in these sums?

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.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Ben has five coins in his pocket. How much money might he have?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?