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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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?
Can you work out some different ways to balance this equation?
What two-digit numbers can you make with these two dice? What can't you make?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you find the chosen number from the grid using the clues?
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
What happens when you round these numbers to the nearest whole number?
Follow the clues to find the mystery number.
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?
This activity focuses on rounding to the nearest 10.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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?
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
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Can you find all the different ways of lining up these Cuisenaire
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
How many different triangles can you make on a circular pegboard that has nine pegs?
An investigation that gives you the opportunity to make and justify
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.
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?