This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
A Sudoku with clues given as sums of entries.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Try this matching game which will help you recognise different ways of saying the same time interval.
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different triangles can you make on a circular pegboard that has nine pegs?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This challenge extends the Plants investigation so now four or more children are involved.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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?
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.
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.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
How many models can you find which obey these rules?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you find all the different ways of lining up these Cuisenaire rods?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
What happens when you try and fit the triomino pieces into these two grids?
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.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?