Can you each work out what shape you have part of on your card?
What will the rest of it look like?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This activity investigates how you might make squares and pentominoes from Polydron.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
These pictures show squares split into halves. Can you find other
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?
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
If you have ten counters numbered 1 to 10, how many can you put
into pairs that add to 10? Which ones do you have to leave out?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
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?
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
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
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
Make a spiral mobile.
Here is a version of the game 'Happy Families' for you to make and
What do these two triangles have in common? How are they related?
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?
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?
Ahmed is making rods using different numbers of cubes. Which rod is
twice the length of his first rod?
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?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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.
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 three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Move four sticks so there are exactly four triangles.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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 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 create more models that follow these rules?
A game in which players take it in turns to choose a number. Can you block your opponent?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
Explore the triangles that can be made with seven sticks of the
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