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.
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A challenging activity focusing on finding all possible ways of stacking rods.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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....?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Use the clues to colour each square.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This challenge extends the Plants investigation so now four or more children are involved.
How many trains can you make which are the same length as Matt's, using rods that are identical?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you find all the different ways of lining up these Cuisenaire
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find out what a "fault-free" rectangle is and try to make some of
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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. . . .
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you find all the different triangles on these peg boards, and
find their angles?
How many different rhythms can you make by putting two drums on the
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.