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?
Can you complete this jigsaw of the multiplication square?
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?
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?
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
Can you hang weights in the right place to make the equaliser
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
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!
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you complete this jigsaw of the 100 square?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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 number weights to find different ways of balancing the equaliser.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Exchange the positions of the two sets of counters in the least possible number of moves
How many different rhythms can you make by putting two drums on the
An interactive activity for one to experiment with a tricky tessellation
Use the clues to colour each square.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Twenty four games for 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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Move just three of the circles so that the triangle faces in the
Can you find all the different triangles on these peg boards, and
find their angles?
How many different triangles can you make on a circular pegboard
that has nine pegs?
Use the interactivities to complete these Venn diagrams.
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?
Use the sightings of the lion to guess the location of its lair.
A variant on the game Alquerque
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
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?
These interactive dominoes can be dragged around the screen.