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There are **336** NRICH Mathematical resources connected to **Addition and subtraction**, you may find related items under Calculations and numerical methods.

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
### The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Eggs in Baskets

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Make 37

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

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
### Ladybirds in the Garden

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Got It

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.

Age 7 to 14

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
### Sealed Solution

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?

Age 7 to 11

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
### Reach 100

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.

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
### Four Goodness Sake

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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
### Super Shapes

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

Age 7 to 11

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Amy's Dominoes

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Make 100

Find at least one way to put in some operation signs to make these digits come to 100.

Age 7 to 11

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
### 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
### Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Age 7 to 11

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
### Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Age 5 to 7

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
Live 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 7 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
### Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Butterfly Flowers

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Age 5 to 7

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
### One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Buying a Balloon

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2, 4, 6, 8

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Age 5 to 7

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
### Two Dice

Find all the numbers that can be made by adding the dots on two dice.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Square

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

Age 7 to 11

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
### Noah

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Age 5 to 7

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
### Roll These Dice

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 possible answers?

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