These practical challenges are all about making a 'tray' and covering it with paper.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many triangles can you make on the 3 by 3 pegboard?
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?
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 practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
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
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
What do these two triangles have in common? How are they related?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
How do you know if your set of dominoes is complete?
Can you create more models that follow these rules?
Can you make the birds from the egg tangram?
Here is a version of the game 'Happy Families' for you to make and
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
What shape is made when you fold using this crease pattern? Can you make a ring design?
How can you make a curve from straight strips of paper?
Can you fit the tangram pieces into the outline of this junk?
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 outlines of the lobster, yacht and cyclist?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?