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.
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?
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.
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?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
The pages of my calendar have got mixed up. Can you sort them out?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
In this matching game, you have to decide how long different events take.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
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?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
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?
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.?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Can you draw a square in which the perimeter is numerically equal to the area?
An investigation that gives you the opportunity to make and justify predictions.
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?
A Sudoku with a twist.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to 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?
How many different triangles can you make on a circular pegboard that has nine pegs?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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'.
Two sudokus in one. Challenge yourself to make the necessary connections.
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.
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?
Can you coach your rowing eight to win?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.