problem
One Big Triangle
Age
5 to 7
Challenge level
Make one big triangle so the numbers that touch on the small triangles add to 10.
problem
Butterfly Flowers
Age
5 to 7
Challenge level
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?
problem
Same Length Trains
Age
5 to 7
Challenge level
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
problem
What's in a Name?
Age
5 to 7
Challenge level
What do you notice about these squares of numbers? What is the same? What is different?
problem
I'm Eight
Age
5 to 11
Challenge level
Find a great variety of ways of asking questions which make 8.
problem
Number match
Age
5 to 11
Challenge level
A task which depends on members of the group noticing the needs of others and responding.
problem
I Like ...
Age
5 to 7
Challenge level
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
problem
Even and odd
Age
5 to 7
Challenge level
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?
problem
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?
problem
Cuisenaire Counting
Age
5 to 7
Challenge level
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
problem
Domino Sorting
Age
5 to 7
Challenge level
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
problem
That number square
Age
5 to 11
Challenge level
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
problem
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 ...?
problem
Strike it Out
Age
5 to 11
Challenge level
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
problem
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?
problem
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?
problem
The add and take-away path
Age
5 to 7
Challenge level
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?
problem
Ordering cards
Age
5 to 11
Challenge level
This problem is designed to help children to learn, and to use, the two and three times tables.
problem
Digit Addition
Age
5 to 11
Challenge level
Try out this number trick. What happens with different starting numbers? What do you notice?
problem
Half Time
Age
5 to 11
Challenge level
What could the half time scores have been in these Olympic hockey matches?
problem
How Many?
Age
5 to 11
Challenge level
Have a look at these photos of different fruit. How many do you see? How did you count?
problem
Double or Halve?
Age
5 to 7
Challenge level
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
problem
Are you well Balanced?
Age
5 to 7
Challenge level
Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.
problem
Always, Sometimes or Never?
Age
5 to 11
Challenge level
Are these statements relating to odd and even numbers always true, sometimes true or never true?
problem
How do you see it?
Age
5 to 11
Challenge level
Here are some short problems for you to try. Talk to your friends about how you work them out.
problem
Birthday Sharing
Age
5 to 7
Challenge level
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?
problem
Growing Garlic
Age
5 to 11
Challenge level
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
problem
Tables Teaser
Age
5 to 7
Challenge level
How will you work out which numbers have been used to create this multiplication square?
problem
Arranging Additions and Sorting Subtractions
Age
5 to 7
Challenge level
Order these four calculations from easiest to hardest. How did you decide?
problem
Subtraction Slip
Age
5 to 7
Challenge level
Can you spot the mistake in this video? How would you work out the answer to this calculation?
problem
Biscuit Decorations
Age
5 to 7
Challenge level
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?
problem
Equivalent Pairs
Age
5 to 7
Challenge level
Can you match pairs of cards which show the same amount?
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?
problem
Fraction Match
Age
5 to 11
Challenge level
A task which depends on members of the group noticing the needs of others and responding.
problem
Robot Monsters
Age
5 to 7
Challenge level
Use these head, body and leg pieces to make Robot Monsters which are different heights.
problem
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?
problem
Secret Number
Age
5 to 7
Challenge level
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
problem
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.
problem
Ring a Ring of Numbers
Age
5 to 7
Challenge level
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
problem
6 Beads
Age
5 to 7
Challenge level
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?
problem
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?
problem
The Tall Tower
Age
5 to 7
Challenge level
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
Grouping Goodies
Age
5 to 7
Challenge level
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
problem
4 Dom
Age
5 to 11
Challenge level
Use these four dominoes to make a square that has the same number of dots on each side.
problem
Bryony's Triangle
Age
7 to 11
Challenge level
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?
problem
Number Differences
Age
7 to 11
Challenge level
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?
problem
Matching fractions
Age
7 to 11
Challenge level
Can you find different ways of showing the same fraction? Try this matching game and see.
problem
Tumbling Down
Age
7 to 11
Challenge level
Watch this animation. What do you see? Can you explain why this happens?
problem
First Connect Three
Age
7 to 11
Challenge level
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?
problem
Magic Vs
Age
7 to 11
Challenge level
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
problem
Sweets in a box
Age
7 to 11
Challenge level
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?
problem
Coded hundred square
Age
7 to 11
Challenge level
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
problem
Highest and Lowest
Age
7 to 11
Challenge level
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
problem
The Moons of Vuvv
Age
7 to 11
Challenge level
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
problem
Times Tables Shifts
Age
7 to 11
Challenge level
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
problem
Planning a School Trip
Age
7 to 11
Challenge level
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.
problem
Multiplication Squares
Age
7 to 11
Challenge level
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.
problem
How do you do it?
Age
7 to 11
Challenge level
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
problem
Take three numbers
Age
7 to 11
Challenge level
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
problem
Representing Numbers
Age
7 to 11
Challenge level
Find as many different ways of representing this number of dots as you can.
problem
Trebling
Age
7 to 11
Challenge level
Can you replace the letters with numbers? Is there only one solution in each case?
problem
Journeys in Numberland
Age
7 to 11
Challenge level
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
problem
Carrying Cards
Age
7 to 11
Challenge level
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?
problem
An Easy Way to Multiply by 10?
Age
7 to 11
Challenge level
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
problem
Let us divide!
Age
7 to 11
Challenge level
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?
problem
Less is More
Age
7 to 11
Challenge level
Use your knowledge of place value to try to win this game. How will you maximise your score?
problem
Fifteen cards
Age
7 to 11
Challenge level
Can you use the information to find out which cards I have used?
problem
Always, Sometimes or Never? Number
Age
7 to 11
Challenge level
Are these statements always true, sometimes true or never true?
problem
Shape Times Shape
Age
7 to 11
Challenge level
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
problem
Picture Your Method
Age
7 to 11
Challenge level
Can you match these calculation methods to their visual representations?
problem
Compare the Calculations
Age
7 to 11
Challenge level
Can you put these four calculations into order of difficulty? How did you decide?
problem
Space distances
Age
7 to 11
Challenge level
This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.
problem
Fractional Triangles
Age
7 to 11
Challenge level
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
problem
The Deca Tree
Age
7 to 11
Challenge level
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
Twenty Divided into Six
Age
7 to 11
Challenge level
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
Reach 100
Age
7 to 11
Challenge level
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.
problem
Sealed Solution
Age
7 to 11
Challenge level
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?
problem
Got It
Age
7 to 14
Challenge level
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.
problem
Mystery Matrix
Age
7 to 11
Challenge level
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
problem
All the Digits
Age
7 to 11
Challenge level
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?
problem
Factor Lines
Age
7 to 14
Challenge level
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
problem
Table patterns go wild!
Age
7 to 11
Challenge level
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
Three neighbours
Age
7 to 14
Challenge level
Take three consecutive numbers and add them together. What do you notice?
problem
Counting Cogs
Age
7 to 14
Challenge level
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
problem
Two Primes Make One Square
Age
7 to 11
Challenge level
Can you make square numbers by adding two prime numbers together?
problem
Remainders
Age
7 to 14
Challenge level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
problem
Number Lines in Disguise
Age
7 to 14
Challenge level
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
problem
Multiples Grid
Age
7 to 11
Challenge level
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
Factor-Multiple Chains
Age
7 to 11
Challenge level
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
problem
Six Numbered Cubes
Age
7 to 11
Challenge level
This task combines spatial awareness with addition and multiplication.
problem
What Distance?
Age
7 to 11
Challenge level
Can you use addition and subtraction to answer these questions about real-life distances?
problem
Forgot the Numbers
Age
7 to 11
Challenge level
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?
problem
Doughnut percents
Age
7 to 14
Challenge level
A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.
problem
Chocolate
Age
7 to 14
Challenge level
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?
problem
Roll these Dice
Age
7 to 11
Challenge level
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?
problem
Pumpkin Pie Problem
Age
7 to 11
Challenge level
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?