Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you draw a square in which the perimeter is numerically equal to the area?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 jugs.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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!
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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 substitute numbers for the letters in these sums?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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.
Ben has five coins in his pocket. How much money might he have?
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?
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 predictions.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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 use the information to find out which cards I have used?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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 possibilities that could come up?
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?
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 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.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
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?