What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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?
An investigation that gives you the opportunity to make and justify
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
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 could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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?
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?
Can you use the information to find out which cards I have used?
Can you substitute numbers for the letters in these sums?
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
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
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.
Ben has five coins in his pocket. How much money might he have?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What happens when you round these three-digit numbers to the nearest 100?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 happens when you add three numbers together? Will your answer be odd or even? How do you know?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Can you make square numbers by adding two prime numbers together?
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 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?
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.
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as 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?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?