Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
What do these two triangles have in common? How are they related?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you put these shapes in order of size? Start with the smallest.
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
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?
These pictures show squares split into halves. Can you find other
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
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?
Can you make five differently sized squares from the tangram
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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 fit the tangram pieces into the outline of this junk?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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.
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?
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 outlines of the lobster, yacht and cyclist?
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 the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this telephone?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 Little Fung at the table?
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?
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?
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 challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
This practical activity challenges you to create symmetrical
designs by cutting a square into strips.
Can you lay out the pictures of the drinks in the way described by
the clue cards?
Can you each work out what shape you have part of on your card?
What will the rest of it look like?
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?