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

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.

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.

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.

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

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

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

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

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

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.

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?

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

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?

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?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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?

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

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

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.

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?

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?

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?

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

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

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

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

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?

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?

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?

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

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

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

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

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?

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

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

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?

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?

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

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.