What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
Can you use the information to find out which cards I have used?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Number problems at primary level that require careful consideration.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What happens when you round these three-digit numbers to the nearest 100?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you substitute numbers for the letters in these sums?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you make square numbers by adding two prime numbers together?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Ben has five coins in his pocket. How much money might he have?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
An investigation that gives you the opportunity to make and justify
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This dice train has been made using specific rules. How many different trains can you make?
Have a go at balancing this equation. Can you find different ways of doing it?
What happens when you round these numbers to the nearest whole number?
Can you work out some different ways to balance this equation?