If you have only four weights, where could you place them in order
to balance this equaliser?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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!
An environment which simulates working with Cuisenaire rods.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you complete this jigsaw of the multiplication square?
Here is a chance to play a version of the classic Countdown Game.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Work out how to light up the single light. What's the rule?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
A train building game for 2 players.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Train game for an adult and child. Who will be the first to make the train?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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. . . .
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Using angular.js to bind inputs to outputs
A card pairing game involving knowledge of simple ratio.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
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?
An interactive activity for one to experiment with a tricky tessellation
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
A generic circular pegboard resource.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
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....?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Can you find all the different ways of lining up these Cuisenaire
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.