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?

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 the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

These two group activities use mathematical reasoning - one is numerical, one geometric.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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.

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?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

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

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.

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!

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

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?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

This challenge is about finding the difference between numbers which have the same tens digit.

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?

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

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!

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?

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

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?