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? Why?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many triangles can you make on the 3 by 3 pegboard?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
Here is a version of the game 'Happy Families' for you to make and
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?
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?
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?
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?
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 smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
These practical challenges are all about making a 'tray' and covering it with paper.
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 each work out the number on your card? What do you notice?
How could you sort the cards?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you make the birds from the egg tangram?
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 the workmen?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
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 lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?