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.
This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?
Try this matching game which will help you recognise different ways of saying the same time interval.
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?
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.
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
Explore the different snakes that can be made using 5 cubes.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
This activity focuses on rounding to the nearest 10.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Can you fill in the empty boxes in the grid with the right shape and colour?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
How many different shapes can you make by putting four right- angled isosceles triangles together?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
My coat has three buttons. How many ways can you find to do up all the buttons?
Find all the numbers that can be made by adding the dots on two dice.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
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.
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 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.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
Can you find out in which order the children are standing in this line?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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 different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Find out what a "fault-free" rectangle is and try to make some of your own.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?
What two-digit numbers can you make with these two dice? What can't you make?
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.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?