These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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.
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 many triangles can you make on the 3 by 3 pegboard?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
How many models can you find which obey these rules?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
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 predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
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
This activity investigates how you might make squares and pentominoes from Polydron.
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
What do these two triangles have in common? How are they related?
Can you make the birds from the egg tangram?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Here is a version of the game 'Happy Families' for you to make and
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you create more models that follow these rules?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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 Granma T?
This practical activity involves measuring length/distance.
How do you know if your set of dominoes is complete?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Here's a simple way to make a Tangram without any measuring or
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?