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
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Find the sum of all three-digit numbers each of whose digits is
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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?
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?
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?
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
Can you substitute numbers for the letters in these sums?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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.
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?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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.
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 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!
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Can you use the information to find out which cards I have used?
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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