Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
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?
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?
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 pictures show squares split into halves. Can you find other ways?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
An activity making various patterns with 2 x 1 rectangular tiles.
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.
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?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Here is a version of the game 'Happy Families' for you to make and play.
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.
NRICH December 2006 advent calendar - a new tangram for each 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 special way?
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?
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.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you create more models that follow these rules?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Explore the triangles that can be made with seven sticks of the same length.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Can you split each of the shapes below in half so that the two parts are exactly the same?
How many models can you find which obey these rules?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
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?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 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 child walking home from school?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these people?