Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Find a great variety of ways of asking questions which make 8.

How can we help students make sense of addition and subtraction of negative numbers?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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.

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

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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?

This article for teachers suggests ideas for activities built around 10 and 2010.

There are nasty versions of this dice game but we'll start with the nice ones...

Find out about Magic Squares in this article written for students. Why are they magic?!

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Use these four dominoes to make a square that has the same number of dots on each side.

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

In this game for two players, the aim is to make a row of four coins which total one dollar.

Are these statements always true, sometimes true or never true?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Investigate the different distances of these car journeys and find out how long they take.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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!