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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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!

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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?

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

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.

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

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

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.

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.

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?

Investigate what happens when you add house numbers along a street in different ways.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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

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

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?

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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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.

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

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?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

It starts quite simple but great opportunities for number discoveries and patterns!

A challenging activity focusing on finding all possible ways of stacking rods.

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.