List

Being Collaborative - Primary Number

Dicey Array
game
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Dicey Array

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

I'm Eight
problem
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I'm Eight

Age
5 to 11
Challenge level
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Find a great variety of ways of asking questions which make 8.
Domino Sequences
problem
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Domino Sequences

Age
5 to 7
Challenge level
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Find the next two dominoes in these sequences.
Robot Monsters
problem
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Robot Monsters

Age
5 to 7
Challenge level
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Use these head, body and leg pieces to make Robot Monsters which are different heights.
Cuisenaire Counting
problem
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Cuisenaire Counting

Age
5 to 7
Challenge level
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Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
Same Length Trains
problem
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Same Length Trains

Age
5 to 7
Challenge level
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How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Domino Sorting
problem
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Domino Sorting

Age
5 to 7
Challenge level
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Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
Strike it out
problem
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Strike it Out

Age
5 to 11
Challenge level
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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Sort them out (1)
problem
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Sort them out (1)

Age
5 to 7
Challenge level
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Can you each work out the number on your card? What do you notice? How could you sort the cards?
Number match
problem
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Number match

Age
5 to 11
Challenge level
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A task which depends on members of the group noticing the needs of others and responding.

The add and take-away path
problem
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The add and take-away path

Age
5 to 7
Challenge level
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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
I Like ...
problem
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I Like ...

Age
5 to 7
Challenge level
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Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Half Time
problem
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Half Time

Age
5 to 11
Challenge level
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What could the half time scores have been in these Olympic hockey matches?
Even and odd
problem
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Even and odd

Age
5 to 7
Challenge level
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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?
All Change
problem
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All Change

Age
5 to 7
Challenge level
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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?
How do you see it?
problem
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How do you see it?

Age
5 to 11
Challenge level
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Here are some short problems for you to try. Talk to your friends about how you work them out.

Are you well Balanced?
problem
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Are you well Balanced?

Age
5 to 7
Challenge level
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Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.
Ip Dip
problem
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Ip Dip

Age
5 to 11
Challenge level
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"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 ...?

That number square
problem
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That number square

Age
5 to 11
Challenge level
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Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Dicey Addition
problem
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Dicey Addition

Age
5 to 11
Challenge level
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Who said that adding couldn't be fun?
Growing Garlic
problem
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Growing Garlic

Age
5 to 11
Challenge level
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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Ordering cards
problem
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Ordering cards

Age
5 to 11
Challenge level
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This problem is designed to help children to learn, and to use, the two and three times tables.
Eightness of Eight
problem
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Eightness of Eight

Age
5 to 7
Challenge level
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What do you see as you watch this video? Can you create a similar video for the number 12?
Digit Addition
problem
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Digit Addition

Age
5 to 11
Challenge level
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Try out this number trick. What happens with different starting numbers? What do you notice?

Double or Halve?
problem
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Double or Halve?

Age
5 to 7
Challenge level
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Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
How Many?
problem
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How Many?

Age
5 to 11
Challenge level
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Have a look at these photos of different fruit. How many do you see? How did you count?
Subtraction Slip
problem
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Subtraction Slip

Age
5 to 7
Challenge level
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Can you spot the mistake in this video? How would you work out the answer to this calculation?
Equivalent Pairs
problem
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Equivalent Pairs

Age
5 to 7
Challenge level
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Can you match pairs of cards which show the same amount?
Always, Sometimes or Never?
problem
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Always, Sometimes or Never?

Age
5 to 11
Challenge level
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Are these statements relating to odd and even numbers always true, sometimes true or never true?

Placeholder: several colourful numbers
project

How Many?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Birthday Sharing
problem
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Birthday Sharing

Age
5 to 7
Challenge level
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It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?
Tables Teaser
problem
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Tables Teaser

Age
5 to 7
Challenge level
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How will you work out which numbers have been used to create this multiplication square?
Fraction Match
problem
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Fraction Match

Age
5 to 11
Challenge level
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A task which depends on members of the group noticing the needs of others and responding.

One Big Triangle
problem
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One Big Triangle

Age
5 to 7
Challenge level
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Make one big triangle so the numbers that touch on the small triangles add to 10.

Two flowers with the numbers 15 and 16 on them
problem
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Butterfly Flowers

Age
5 to 7
Challenge level
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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?

Biscuit Decorations
problem
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Biscuit Decorations

Age
5 to 7
Challenge level
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Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
What's in a Name?
problem
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What's in a Name?

Age
5 to 7
Challenge level
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What do you notice about these squares of numbers? What is the same? What is different?
Next Domino
problem
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Next Domino

Age
5 to 7
Challenge level
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Which comes next in each pattern of dominoes?
Making Sticks
problem
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Making Sticks

Age
5 to 7
Challenge level
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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?
Secret Number
problem
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Secret Number

Age
5 to 7
Challenge level
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Annie and Ben are playing a game with a calculator. What was Annie's secret number?
Jumping squares
problem
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Jumping squares

Age
5 to 7
Challenge level
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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.
Ring a Ring of Numbers
problem
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Ring a Ring of Numbers

Age
5 to 7
Challenge level
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Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
6 Beads
problem
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6 Beads

Age
5 to 7
Challenge level
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If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Birthday Cakes
problem
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Birthday Cakes

Age
5 to 7
Challenge level
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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?
Grouping Goodies
problem
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Grouping Goodies

Age
5 to 7
Challenge level
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Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

The Tall Tower
problem
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The Tall Tower

Age
5 to 7
Challenge level
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As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
4 Dom
problem
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4 Dom

Age
5 to 11
Challenge level
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Use these four dominoes to make a square that has the same number of dots on each side.
Sweets in a box
problem
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Sweets in a box

Age
7 to 11
Challenge level
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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Highest and Lowest
problem
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Highest and Lowest

Age
7 to 11
Challenge level
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Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The Deca Tree
problem
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The Deca Tree

Age
7 to 11
Challenge level
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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.
The Moons of Vuvv
problem
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The Moons of Vuvv

Age
7 to 11
Challenge level
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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Number Differences
problem
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Number Differences

Age
7 to 11
Challenge level
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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?
First Connect Three
problem
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First Connect Three

Age
7 to 11
Challenge level
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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?
Multiplication Squares
problem
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Multiplication Squares

Age
7 to 11
Challenge level
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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Magic Vs
problem
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Magic Vs

Age
7 to 11
Challenge level
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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Shape Times Shape
problem
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Shape Times Shape

Age
7 to 11
Challenge level
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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Coded hundred square
problem
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Coded hundred square

Age
7 to 11
Challenge level
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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Which symbol?
problem
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Which symbol?

Age
7 to 11
Challenge level
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Choose a symbol to put into the number sentence.
Times Tables Shifts
problem
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Times Tables Shifts

Age
7 to 11
Challenge level
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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Trebling
problem
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Trebling

Age
7 to 11
Challenge level
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Can you replace the letters with numbers? Is there only one solution in each case?
Planning a School Trip
problem
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Planning a School Trip

Age
7 to 11
Challenge level
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You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.
Carrying Cards
problem
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Carrying Cards

Age
7 to 11
Challenge level
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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?
How do you do it?
problem
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How do you do it?

Age
7 to 11
Challenge level
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This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Fifteen cards
problem
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Fifteen cards

Age
7 to 11
Challenge level
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Can you use the information to find out which cards I have used?
An Easy Way to Multiply by 10?
problem
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An Easy Way to Multiply by 10?

Age
7 to 11
Challenge level
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Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
Take three numbers
problem
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Take three numbers

Age
7 to 11
Challenge level
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What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Representing Numbers
problem
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Representing Numbers

Age
7 to 11
Challenge level
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Find as many different ways of representing this number of dots as you can.
Journeys in Numberland
problem
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Journeys in Numberland

Age
7 to 11
Challenge level
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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Space distances
problem
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Space distances

Age
7 to 11
Challenge level
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This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.
Let us divide!
problem
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Let us divide!

Age
7 to 11
Challenge level
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Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
Less is More
problem
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Less is More

Age
7 to 11
Challenge level
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Use your knowledge of place value to try to win this game. How will you maximise your score?
Fractional Triangles
problem
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Fractional Triangles

Age
7 to 11
Challenge level
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Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Picture Your Method
problem
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Picture Your Method

Age
7 to 11
Challenge level
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Can you match these calculation methods to their visual representations?
Compare the Calculations
problem
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Compare the Calculations

Age
7 to 11
Challenge level
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Can you put these four calculations into order of difficulty? How did you decide?
Bryony's Triangle
problem
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Bryony's Triangle

Age
7 to 11
Challenge level
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Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Matching fractions
problem
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Matching fractions

Age
7 to 11
Challenge level
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Can you find different ways of showing the same fraction? Try this matching game and see.

Tumbling Down
problem
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Tumbling Down

Age
7 to 11
Challenge level
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Watch this animation. What do you see? Can you explain why this happens?

Factors and Multiples Game
game
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Factors and Multiples Game

A game in which players take it in turns to choose a number. Can you block your opponent?

Twenty Divided into Six
problem
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Twenty Divided into Six

Age
7 to 11
Challenge level
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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?
Reach 100
problem
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Reach 100

Age
7 to 11
Challenge level
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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.

Sealed Solution
problem
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Sealed Solution

Age
7 to 11
Challenge level
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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?
Got It
problem
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Got It

Age
7 to 14
Challenge level
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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.

Mystery Matrix
problem
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Mystery Matrix

Age
7 to 11
Challenge level
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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
All the Digits
problem
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All the Digits

Age
7 to 11
Challenge level
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This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Factor Lines
problem
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Factor Lines

Age
7 to 14
Challenge level
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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Two Primes Make One Square
problem
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Two Primes Make One Square

Age
7 to 11
Challenge level
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Can you make square numbers by adding two prime numbers together?
Remainders
problem
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Remainders

Age
7 to 14
Challenge level
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I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Table patterns go wild!
problem
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Table patterns go wild!

Age
7 to 11
Challenge level
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Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Counting Cogs
problem
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Counting Cogs

Age
7 to 14
Challenge level
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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Three neighbours
problem
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Three neighbours

Age
7 to 14
Challenge level
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Take three consecutive numbers and add them together. What do you notice?
Six Numbered Cubes
problem
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Six Numbered Cubes

Age
7 to 11
Challenge level
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This task combines spatial awareness with addition and multiplication.
Multiples Grid
problem
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Multiples Grid

Age
7 to 11
Challenge level
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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Factor-Multiple Chains
problem
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Factor-Multiple Chains

Age
7 to 11
Challenge level
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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Number Lines in Disguise
problem
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Number Lines in Disguise

Age
7 to 14
Challenge level
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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
What Distance?
problem
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What Distance?

Age
7 to 11
Challenge level
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Can you use addition and subtraction to answer these questions about real-life distances?

Forgot the Numbers
problem
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Forgot the Numbers

Age
7 to 11
Challenge level
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On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Doughnut percents
problem
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Doughnut percents

Age
7 to 14
Challenge level
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A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.