Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
An activity making various patterns with 2 x 1 rectangular tiles.
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 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?
How many triangles can you make on the 3 by 3 pegboard?
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?
How many models can you find which obey these rules?
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 it up?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
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.
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Delight your friends with this cunning trick! Can you explain how it works?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
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 the chairs?
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 shape. How would you describe it?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this plaque design?
Exploring and predicting folding, cutting and punching holes and making spirals.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of this telephone?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you fit the tangram pieces into the outline of Granma T?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.