This article for primary teachers suggests ways in which to help children become better at working systematically.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 three-digit numbers to the nearest 100?
What two-digit numbers can you make with these two dice? What can't you make?
Can you work out some different ways to balance this equation?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
What happens when you round these numbers to the nearest whole number?
This challenge extends the Plants investigation so now four or more children are involved.
Follow the clues to find the mystery number.
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?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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?
Number problems at primary level that require careful consideration.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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 activity focuses on rounding to the nearest 10.
Can you find the chosen number from the grid using the clues?
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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
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.
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'.
How many different triangles can you make on a circular pegboard that has nine pegs?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 possible answers?