What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
An investigation that gives you the opportunity to make and justify
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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
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.?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
This activity investigates how you might make squares and pentominoes from Polydron.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you draw a square in which the perimeter is numerically equal
to the area?
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.
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.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
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?
In this matching game, you have to decide how long different events take.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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.
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?
The pages of my calendar have got mixed up. Can you sort them out?