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 practical activity involves measuring length/distance.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
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?
These pictures show squares split into halves. Can you find other ways?
Here is a version of the game 'Happy Families' for you to make and
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.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
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
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
Can you make the birds from the egg tangram?
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?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
An activity making various patterns with 2 x 1 rectangular tiles.
How many triangles can you make on the 3 by 3 pegboard?
Can you put these shapes in order of size? Start with the smallest.
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
What do these two triangles have in common? How are they related?
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?
A game to make and play based on the number line.
A game in which players take it in turns to choose a number. Can you block your opponent?
How many models can you find which obey these rules?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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.
Can you create more models that follow these rules?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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 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?
Explore the triangles that can be made with seven sticks of the
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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