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
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
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
This activity investigates how you might make squares and pentominoes from Polydron.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find out what a "fault-free" rectangle is and try to make some of
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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...
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
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.
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.
Can you draw a square in which the perimeter is numerically equal
to the area?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
This challenge extends the Plants investigation so now four or more children are involved.
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.?
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?
What happens when you round these numbers to the nearest whole number?
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?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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?