Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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!
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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 is an adding game for two players.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
If you have only four weights, where could you place them in order
to balance this equaliser?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Who said that adding couldn't be fun?
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.
Can you substitute numbers for the letters in these sums?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
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?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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!
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
A game for 2 players. Practises subtraction or other maths
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Ben has five coins in his pocket. How much money might he have?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
This task follows on from Build it Up and takes the ideas into three dimensions!