List

Being collaborative - Primary number

I Like ...
problem
Favourite

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?

Are you well Balanced?
problem
Favourite

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.

How do you see it?
problem
Favourite

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.

Even and odd
problem
Favourite

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
Favourite

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?

Growing Garlic
problem
Favourite

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?

That number square
problem
Favourite

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
Favourite

Dicey addition

Age
5 to 11
Challenge level
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In these addition games, you'll need to think strategically to get closest to the target.

Ip Dip
problem
Favourite

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 ...?

Subtraction Slip
problem
Favourite

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?

Eightness of Eight
problem
Favourite

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?

Equivalent Pairs
problem
Favourite

Equivalent pairs

Age
5 to 7
Challenge level
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Can you match pairs of cards which show the same amount?

Digit Addition
problem
Favourite

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?

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?

Ordering cards
problem
Favourite

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.

How Many?
problem
Favourite

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?

Double or Halve?
problem
Favourite

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?

Always, Sometimes or Never?
problem
Favourite

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?

Fraction Match
problem
Favourite

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
Favourite

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.

Birthday Sharing
problem
Favourite

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?

Two flowers with the numbers 15 and 16 on them
problem
Favourite

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?

Tables Teaser
problem
Favourite

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?

What's in a Name?
problem
Favourite

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?

Dicey Array
game
Favourite

Dicey array

Age
5 to 11
Challenge level
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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
Favourite

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.

Biscuit Decorations
problem
Favourite

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?

Next Domino
problem
Favourite

Next domino

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

Domino Sequences
problem
Favourite

Domino sequences

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

Cuisenaire Counting
problem
Favourite

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?

problem
Favourite

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.

Domino Sorting
problem
Favourite

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?

Same Length Trains
problem
Favourite

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?

Strike it out
problem
Favourite

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
Favourite

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?

The add and take-away path
problem
Favourite

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?

Half Time
problem
Favourite

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?

Number match
problem
Favourite

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.

Ring a Ring of Numbers
problem
Favourite

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.

problem
Favourite

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?

6 Beads
problem
Favourite

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?

Making Sticks
problem
Favourite

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
Favourite

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
Favourite

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.

4 Dom
problem
Favourite

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.

problem
Favourite

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
Favourite

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?

problem
Favourite

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?

Which symbol?
problem
Favourite

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
Favourite

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?

Planning a School Trip
problem
Favourite

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.

How do you do it?
problem
Favourite

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.

Take three numbers
problem
Favourite

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
Favourite

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
Favourite

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.

Let us divide!
problem
Favourite

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
Favourite

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
Favourite

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.

Bryony's Triangle
problem
Favourite

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
Favourite

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
Favourite

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?

Picture Your Method
problem
Favourite

Picture your method

Age
7 to 11
Challenge level
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Can you match these calculation methods to their visual representations?
Factors and Multiples Game
game
Favourite

Factors and multiples game

Age
7 to 16
Challenge level
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A game in which players take it in turns to choose a number. Can you block your opponent?

Compare the Calculations
problem
Favourite

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?

problem
Favourite

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
Favourite

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.

problem
Favourite

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?

The Deca Tree
problem
Favourite

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.

problem
Favourite

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.

Number Differences
problem
Favourite

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
Favourite

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?

Trebling
problem
Favourite

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?

Magic Vs
problem
Favourite

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?

Carrying Cards
problem
Favourite

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?

Coded hundred square
problem
Favourite

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?

An Easy Way to Multiply by 10?
problem
Favourite

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?

Shape Times Shape
problem
Favourite

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?

Three neighbours
problem
Favourite

Three neighbours

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

Multiples Grid
problem
Favourite

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?

problem
Favourite

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?

Six Numbered Cubes
problem
Favourite

Six numbered cubes

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

Table patterns go wild!
problem
Favourite

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.

problem
Favourite

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?

Number Lines in Disguise
problem
Favourite

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?

Forgot the Numbers
problem
Favourite

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
Favourite

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.

Chocolate
problem
Favourite

Chocolate

Age
7 to 14
Challenge level
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There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Roll these Dice
problem
Favourite

Roll these dice

Age
7 to 11
Challenge level
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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?

Pumpkin Pie Problem
problem
Favourite

Pumpkin pie problem

Age
7 to 11
Challenge level
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Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

problem
Favourite

Maze 100

Age
7 to 11
Challenge level
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Can you go through this maze so that the numbers you pass add to exactly 100?

Fractions in a Box
problem
Favourite

Fractions in a box

Age
7 to 11
Challenge level
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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Domino Square
problem
Favourite

Domino square

Age
7 to 11
Challenge level
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Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Twenty Divided into Six
problem
Favourite

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?

problem
Favourite

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
Favourite

Sealed solution

Age
7 to 14
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
Favourite

Got it

Age
7 to 14
Challenge level
filled star filled star empty star

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
Favourite

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
Favourite

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?