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Broad Topics > Calculations and Numerical Methods > Addition & subtraction

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Double or Halve?

Stage: 1 Challenge Level: Challenge Level:1

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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Five Steps to 50

Stage: 1 Challenge Level: Challenge Level:1

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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Dotty Six

Stage: 1 and 2 Challenge Level: Challenge Level:1

Dotty Six is a simple dice game that you can adapt in many ways.

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Follow the Numbers

Stage: 2 Challenge Level: Challenge Level:1

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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How Do You Do It?

Stage: 2 Challenge Level: Challenge Level:1

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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Even and Odd

Stage: 1 Challenge Level: Challenge Level:1

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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Which Symbol?

Stage: 2 Challenge Level: Challenge Level:1

Choose a symbol to put into the number sentence.

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Nice or Nasty

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Countdown

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Magic Vs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Shut the Box

Stage: 1 Challenge Level: Challenge Level:1

An old game but lots of arithmetic!

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Oh! Harry!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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How Much Did it Cost?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Sea Level

Stage: 2 Challenge Level: Challenge Level:1

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?

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Tug Harder!

Stage: 2 Challenge Level: Challenge Level:1

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?

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Tug of War

Stage: 1 Challenge Level: Challenge Level:1

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

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First Connect Three

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Caterpillars

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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More Carroll Diagrams

Stage: 2 Challenge Level: Challenge Level:1

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

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Carroll Diagrams

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Balance of Halves

Stage: 2 Challenge Level: Challenge Level:1

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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Making Longer, Making Shorter

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Domino Pick

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Are these domino games fair? Can you explain why or why not?

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The Twelve Pointed Star Game

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Number Differences

Stage: 2 Challenge Level: Challenge Level:1

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?

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Ring a Ring of Numbers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Carrying Cards

Stage: 2 Challenge Level: Challenge Level:1

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?

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Robot Monsters

Stage: 1 Challenge Level: Challenge Level:1

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

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A Mixed-up Clock

Stage: 2 Challenge Level: Challenge Level:1

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?

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The Deca Tree

Stage: 2 Challenge Level: Challenge Level:1

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.

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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1, 2, 3 Magic Square

Stage: 2 Challenge Level: Challenge Level:1

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

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Cubes Within Cubes

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Two Primes Make One Square

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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One Wasn't Square

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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The Tomato and the Bean

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Abundant Numbers

Stage: 2 Challenge Level: Challenge Level:1

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?

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Zios and Zepts

Stage: 2 Challenge Level: Challenge Level:1

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?

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Watch the Clock

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Neighbours

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Puzzling Sweet Shop

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Amazing Splitting Plant

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Five Coins

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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I'm Eight

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Plants

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Always, Sometimes or Never? KS1

Stage: 1 Challenge Level: Challenge Level:1

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

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Open Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?