Can you complete this jigsaw of the multiplication square?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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....?
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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?
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?
An environment which simulates working with Cuisenaire rods.
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?
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!
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?
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?
Use the interactivities to complete these Venn diagrams.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Here is a chance to play a version of the classic Countdown Game.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
How many different triangles can you make on a circular pegboard
that has nine pegs?
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
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you find all the different triangles on these peg boards, and
find their angles?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
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.
Find out what a "fault-free" rectangle is and try to make some of
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. . . .
Can you find all the different ways of lining up these Cuisenaire
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 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?
Can you fit the tangram pieces into the outline of these convex shapes?