Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
How many triangles can you make on the 3 by 3 pegboard?
An activity making various patterns with 2 x 1 rectangular tiles.
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
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?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Here is a version of the game 'Happy Families' for you to make and
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
These pictures show squares split into halves. Can you find other ways?
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Can you create more models that follow these rules?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
A brief video looking at how you can sometimes use symmetry to
distinguish knots. Can you use this idea to investigate the
differences between the granny knot and the reef knot?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you make the birds from the egg tangram?
Explore the triangles that can be made with seven sticks of the
These practical challenges are all about making a 'tray' and covering it with paper.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How many models can you find which obey these rules?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?