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There are **287** NRICH Mathematical resources connected to **Addition and subtraction**, you may find related items under Calculations and numerical methods.

Problem
Primary curriculum
Secondary curriculum
### Sea Level

The picture shows a lighthouse and some underwater creatures. Can you work out the distances between some of the different creatures?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tug Harder!

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tug of War

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Negative Numbers

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Connect Three

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Difference Sudoku

Use the differences to find the solution to this Sudoku.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Caterpillars

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Longer, Making Shorter

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions Jigsaw

A jigsaw where pieces only go together if the fractions are equivalent.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cunning Card Trick

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Twelve Pointed Star Game

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Diagonal Sums

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?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Differences

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ring a Ring of Numbers

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carrying Cards

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Seven

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Robot Monsters

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Pyramids

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Deca Tree

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Square of Numbers

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cinema Problem

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 1, 2, 3 Magic Square

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Totality

This is an adding game for two players. Can you be the first to reach the target?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Egyptian Fractions

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubes Within Cubes

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?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Primes Make One Square

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One Wasn't Square

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Tomato and the Bean

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Watch the Clock

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prison Cells

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Daisy

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and Two

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Neighbours

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Have You Got It?

Can you explain the strategy for winning this game with any target?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Puzzling Sweet Shop

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Amazing Splitting Plant

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Coins

Ben has five coins in his pocket. How much money might he have?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plants

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Age 5 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Numbers

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

Age 7 to 14

Challenge Level