A game in which players take it in turns to choose a number. Can you block your opponent?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
How good are you at estimating angles?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the interactivities to complete these Venn diagrams.
Can you fit the tangram pieces into the outline of Little Ming?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Work out the fractions to match the cards with the same amount of money.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
If you have only four weights, where could you place them in order to balance this equaliser?
Use the interactivities to complete these Venn diagrams.
A generic circular pegboard resource.
A card pairing game involving knowledge of simple ratio.
Can you complete this jigsaw of the multiplication square?
An environment which simulates working with Cuisenaire rods.
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Investigate how logic gates work in circuits.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
A train building game for 2 players.
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?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
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....?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.