Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Find all the numbers that can be made by adding the dots on two dice.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
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?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
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?
Number problems at primary level that require careful consideration.
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?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
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.
If the answer's 2010, what could the question be?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
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?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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?
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?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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