In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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 cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
What shapes can you make by folding an A4 piece of paper?
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
How many triangles can you make on the 3 by 3 pegboard?
Can you visualise what shape this piece of paper will make when it is folded?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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 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?
What do these two triangles have in common? How are they related?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
These practical challenges are all about making a 'tray' and covering it with paper.
What shape and size of drinks mat is best for flipping and catching?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Here's a simple way to make a Tangram without any measuring or
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Can you fit the tangram pieces into the outline of this junk?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of this telephone?
Can you make the birds from the egg tangram?
Ideas for practical ways of representing data such as Venn and
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up your own.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Make a cube out of straws and have a go at this practical
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
You could use just coloured pencils and paper to create this
design, but it will be more eye-catching if you can get hold of
hammer, nails and string.
Can you deduce the pattern that has been used to lay out these