Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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
If you have only four weights, where could you place them in order
to balance this equaliser?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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!
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?
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?
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?
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?
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.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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 complete this jigsaw of the multiplication square?
A card pairing game involving knowledge of simple ratio.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A generic circular pegboard resource.
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 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?
An interactive activity for one to experiment with a tricky tessellation
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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. . . .
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?
A train building game for 2 players.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Choose a symbol to put into the number sentence.
Use the interactivities to complete these Venn diagrams.
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?
Here is a chance to play a version of the classic Countdown Game.
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Using angular.js to bind inputs to outputs
Work out how to light up the single light. What's the rule?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
These interactive dominoes can be dragged around the screen.
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?
Exchange the positions of the two sets of counters in the least possible number of moves
How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
How many different triangles can you make on a circular pegboard
that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Choose the size of your pegboard and the shapes you can make. Can
you work out the strategies needed to block your opponent?