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.
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 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?
A challenging activity focusing on finding all possible ways of stacking rods.
Use the clues about the symmetrical properties of these letters to place them on the grid.
How many different symmetrical shapes can you make by shading triangles or squares?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
The pages of my calendar have got mixed up. Can you sort them out?
In how many ways can you stack these rods, following the rules?
How long does it take to brush your teeth? Can you find the matching length of time?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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.?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
A Sudoku with clues as ratios.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
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....?
This activity investigates how you might make squares and pentominoes from Polydron.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
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.
An investigation that gives you the opportunity to make and justify predictions.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
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 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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
How many different differences can you make?
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.
Two sudokus in one. Challenge yourself to make the necessary connections.
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
How many different triangles can you make on a circular pegboard that has nine pegs?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
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?
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 numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?