Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

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!

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.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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!

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

How would you count the number of fingers in these pictures?

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

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

There were 22 legs creeping across the web. How many flies? How many spiders?

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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?

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?