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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
An environment which simulates working with Cuisenaire rods.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different ways of lining up these Cuisenaire
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Can you explain the strategy for winning this game with any target?
Here is a chance to play a version of the classic Countdown Game.
How many different triangles can you make on a circular pegboard that has nine pegs?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
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!
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you complete this jigsaw of the multiplication square?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
A train building game for 2 players.
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.
Work out the fractions to match the cards with the same amount of
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
A card pairing game involving knowledge of simple ratio.
Work out how to light up the single light. What's the rule?
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?
A generic circular pegboard resource.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?