Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
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?
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?
If the answer's 2010, what could the question be?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
This task follows on from Build it Up and takes the ideas into three dimensions!
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
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 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!
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.
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?
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?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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 hang weights in the right place to make the equaliser
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
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
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 make square numbers by adding two prime numbers together?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Can you substitute numbers for the letters in these sums?