This article suggests some ways of making sense of calculations involving positive and negative numbers.

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

Here is a chance to play a version of the classic Countdown Game.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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

Delight your friends with this cunning trick! Can you explain how it works?

An environment which simulates working with Cuisenaire rods.

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make square numbers by adding two prime numbers together?

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.

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.

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?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

This dice train has been made using specific rules. How many different trains can you make?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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

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