Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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.
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?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
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?
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
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!
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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
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 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 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?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Ben has five coins in his pocket. How much money might he have?
These two group activities use mathematical reasoning - one is
numerical, one geometric.