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
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Try this matching game which will help you recognise different ways of saying the same time interval.
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?
The pages of my calendar have got mixed up. Can you sort them out?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben has five coins in his pocket. How much money might he have?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
In this matching game, you have to decide how long different events take.
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.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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 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?
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?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
An investigation that gives you the opportunity to make and justify
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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?
Number problems at primary level that require careful consideration.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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 this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
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?
Can you find all the different ways of lining up these Cuisenaire
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?