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.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
How many models can you find which obey these rules?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
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?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
These practical challenges are all about making a 'tray' and covering it with paper.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
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 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?
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
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?
Here is a version of the game 'Happy Families' for you to make and
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of this goat and giraffe?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Exploring and predicting folding, cutting and punching holes and
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
Make a cube out of straws and have a go at this practical
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.