In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
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 two-digit numbers can you make with these two dice? What can't you make?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Have a go at balancing this equation. Can you find different ways of doing it?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
This activity focuses on rounding to the nearest 10.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you work out some different ways to balance this equation?
What happens when you round these numbers to the nearest whole number?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one solution in each case?
This challenge extends the Plants investigation so now four or more children are involved.
Number problems at primary level that require careful consideration.
Follow the clues to find the mystery 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 town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you find the chosen number from the grid using the clues?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you substitute numbers for the letters in these sums?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
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
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
How many different triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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.
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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
An investigation that gives you the opportunity to make and justify
Find out what a "fault-free" rectangle is and try to make some of
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?