Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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....?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
An environment which simulates working with Cuisenaire rods.
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?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Can you find all the different ways of lining up these Cuisenaire
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
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!
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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!
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?
A variant on the game Alquerque
How many different rhythms can you make by putting two drums on the
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
An odd version of tic tac toe
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Here is a chance to play a version of the classic Countdown Game.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use the clues to colour each square.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Sort the houses in my street into different groups. Can you do it in any other ways?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.