Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
A game in which players take it in turns to choose a number. Can you block your opponent?
Our 2008 Advent Calendar has a 'Making Maths' activity for every 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.
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?
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?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Here is a version of the game 'Happy Families' for you to make and play.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
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?
How many models can you find which obey these rules?
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?
Can you fit the tangram pieces into the outline of this telephone?
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
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?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you fit the tangram pieces into the outline of this goat and giraffe?
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 outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of this plaque design?
A game to make and play based on the number line.