Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you draw a square in which the perimeter is numerically equal to the area?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
An investigation that gives you the opportunity to make and justify predictions.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
What could the half time scores have been in these Olympic hockey matches?
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.
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?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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 nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
An activity making various patterns with 2 x 1 rectangular tiles.
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.