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Broad Topics > Numbers and the Number System > Counting

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Eightness of Eight

Age 5 to 7 Challenge Level:

What do you see as you watch this video? Can you create a similar video for the number 12?

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Count the Crayons

Age 5 to 7 Challenge Level:

How could you estimate the number of pencils/pens in these pictures?

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Five Steps to 50

Age 5 to 7 Challenge Level:

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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Incey Wincey Spider

Age 5 to 7 Challenge Level:

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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Snail One Hundred

Age 5 to 11 Challenge Level:

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

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How Would We Count?

Age 5 to 11 Challenge Level:

An activity centred around observations of dots and how we visualise number arrangement patterns.

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All Change

Age 5 to 7 Challenge Level:

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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Jumping Squares

Age 5 to 7 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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Dotty Six

Age 5 to 11 Challenge Level:

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

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Count the Digits

Age 5 to 11 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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Pairs of Numbers

Age 5 to 7 Challenge Level:

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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How Odd

Age 5 to 7 Challenge Level:

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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Ip Dip

Age 5 to 11 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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Sort Them Out (1)

Age 5 to 7 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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Lots of Biscuits!

Age 5 to 7 Challenge Level:

Help share out the biscuits the children have made.

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Tug Harder!

Age 7 to 11 Challenge Level:

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

Age 5 to 7 Challenge Level:

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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KS2 Teacher Playing with Dice Collection

Age 7 to 11 Challenge Level:

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Swimming Pool

Age 5 to 11 Challenge Level:

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

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Picture a Pyramid ...

Age 7 to 11 Challenge Level:

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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100 Square Jigsaw

Age 5 to 7 Challenge Level:

Can you complete this jigsaw of the 100 square?

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Cunning Card Trick

Age 11 to 14 Challenge Level:

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

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Diagonal Sums Sudoku

Age 7 to 16 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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Ladybird Count

Age 5 to 7 Challenge Level:

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

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Amazing Card Trick

Age 11 to 14 Challenge Level:

How is it possible to predict the card?

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Counting Cards

Age 7 to 11 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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Which Is Quicker?

Age 7 to 11 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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Neighbours

Age 7 to 11 Challenge Level:

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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Birthday Cakes

Age 5 to 7 Challenge Level:

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?

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Making Sticks

Age 5 to 7 Challenge Level:

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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A Bowl of Fruit

Age 5 to 7 Challenge Level:

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?

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Buzzy Bee

Age 5 to 7 Challenge Level:

Buzzy Bee was building a honeycomb. She decided to decorate the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

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Next Domino

Age 5 to 7 Challenge Level:

Which comes next in each pattern of dominoes?

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Writing Digits

Age 5 to 7 Challenge Level:

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

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Noah

Age 5 to 7 Challenge Level:

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

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Birthday Cake Candles

Age 7 to 11 Challenge Level:

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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Dotty Six for Two

Age 5 to 11 Challenge Level:

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

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Incey Wincey Spider for Two

Age 5 to 7 Challenge Level:

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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Nim-7 for Two

Age 5 to 11 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

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Some Secret Codes

Age 7 to 11 Challenge Level:

Can you follow the rule to decode the messages?

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Pairs of Legs

Age 5 to 7 Challenge Level:

How many legs do each of these creatures have? How many pairs is that?

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Cube Bricks and Daisy Chains

Age 5 to 7 Challenge Level:

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

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Fingers and Hands

Age 7 to 11 Challenge Level:

How would you count the number of fingers in these pictures?

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Alien Counting

Age 7 to 11 Challenge Level:

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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Making Maths: Happy Families

Age 5 to 11 Challenge Level:

Here is a version of the game 'Happy Families' for you to make and play.

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Building Patterns

Age 7 to 11 Challenge Level:

Can you deduce the pattern that has been used to lay out these bottle tops?

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Binary Sequences

Age 16 to 18 Challenge Level:

Show that the infinite set of finite (or terminating) binary sequences can be written as an ordered list whereas the infinite set of all infinite binary sequences cannot.

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Adding with the Abacus

Age 5 to 16

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

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Natural Born Mathematicians

Age 5 to 7

Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.