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?
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
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Can you make the birds from the egg tangram?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
Here is a version of the game 'Happy Families' for you to make and
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
These pictures show squares split into halves. Can you find other ways?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How many triangles can you make on the 3 by 3 pegboard?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Explore the triangles that can be made with seven sticks of the
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
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.
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 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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many models can you find which obey these rules?
Can you create more models that follow these rules?
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
What do these two triangles have in common? How are they related?
Exploring and predicting folding, cutting and punching holes and