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?
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.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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.
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?
In this matching game, you have to decide how long different events take.
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
The pages of my calendar have got mixed up. Can you sort them out?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
An investigation that gives you the opportunity to make and justify predictions.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
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?
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?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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 find all the different ways of lining up these Cuisenaire rods?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Find out about Magic Squares in this article written for students. Why are they magic?!
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....?
Number problems at primary level that require careful consideration.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
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?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.