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.
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
The pages of my calendar have got mixed up. Can you sort them out?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Can you draw a square in which the perimeter is numerically equal to the area?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
In this matching game, you have to decide how long different events take.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
An investigation that gives you the opportunity to make and justify predictions.
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.?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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?
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?
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.
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?
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 many possible necklaces can you find? And how do you know you've found them all?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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....?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Find out what a "fault-free" rectangle is and try to make some of your own.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can you find all the different ways of lining up these Cuisenaire rods?