This challenge invites you to create your own picture using just
straight lines. Can you identify shapes with the same number of
sides and decorate them in the same way?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
What shapes can you make by folding an A4 piece of paper?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Watch this "Notes on a Triangle" film. Can you recreate parts of
the film using cut-out triangles?
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
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.
Have you ever noticed the patterns in car wheel trims? These
questions will make you look at car wheels in a different way!
Explore the triangles that can be made with seven sticks of the
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
For this activity which explores capacity, you will need to collect some bottles and jars.
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?
You'll need a collection of cups for this activity.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
This practical activity involves measuring length/distance.
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?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in 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?
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.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Ideas for practical ways of representing data such as Venn and
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or
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.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this telephone?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
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
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?