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?

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?

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?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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.

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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

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?

Place the numbers 1 to 10 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.

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?

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?

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

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?

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?

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?

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

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

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?

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

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?

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?

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?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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?

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

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

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

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?

This task combines spatial awareness with addition and multiplication.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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

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

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?

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?

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

This task follows on from Build it Up and takes the ideas into three dimensions!