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.

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

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?

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

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.

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

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

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?

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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?

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.

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

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?

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?

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?

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?

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?

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?

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?

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?

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?

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.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

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

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

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?