Can you lay out the pictures of the drinks in the way described by the clue cards?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Exploring and predicting folding, cutting and punching holes and
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
Here's a simple way to make a Tangram without any measuring or
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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?
Make a cube out of straws and have a go at this practical
What do these two triangles have in common? How are they related?
Ideas for practical ways of representing data such as Venn and
An activity making various patterns with 2 x 1 rectangular tiles.
Have you ever noticed the patterns in car wheel trims? These
questions will make you look at car wheels in a different way!
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?
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?
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?
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?
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 telephone?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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?
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?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
What shape is made when you fold using this crease pattern? Can you make a ring design?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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?
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
How many models can you find which obey these rules?
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?
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Can you create more models that follow these rules?
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?