What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Number problems at primary level that require careful consideration.
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
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you replace the letters with numbers? Is there only one solution in each case?
Can you substitute numbers for the letters in these sums?
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!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
Find out what a "fault-free" rectangle is and try to make some of
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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!
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
An investigation that gives you the opportunity to make and justify
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Follow the clues to find the mystery number.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?