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.
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.
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Can you find out in which order the children are standing in this line?
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?
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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.
In this matching game, you have to decide how long different events take.
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
This challenge is about finding the difference between numbers which have the same tens digit.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?