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.

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

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. . . .

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

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

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

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.

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?

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?

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

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?

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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?

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?

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?

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

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.

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

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 always true, sometimes true or never true?

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

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

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

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

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?

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

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...

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

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.

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

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

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?

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

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?