How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Use the clues about the symmetrical properties of these letters to place them on the grid.
In this matching game, you have to decide how long different events take.
In how many ways can you stack these rods, following the rules?
A challenging activity focusing on finding all possible ways of stacking rods.
Ben has five coins in his pocket. How much money might he have?
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.?
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?
The pages of my calendar have got mixed up. Can you sort them out?
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.
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?
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 took.
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?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Number problems at primary level that require careful consideration.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
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?
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!
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've 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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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 jugs.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you make square numbers by adding two prime numbers together?
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?
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?