Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
What is the best way to shunt these carriages so that each train can continue its journey?
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 Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
Can you fit the tangram pieces into the outlines of these people?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of these convex shapes?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the rocket?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Try this interactive strategy game for 2
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you cut up a square in the way shown and make the pieces into a triangle?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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 these rabbits?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
Can you fit the tangram pieces into the outlines of the candle and sundial?
Reasoning about the number of matches needed to build squares that share their sides.
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
Make a cube out of straws and have a go at this practical challenge.
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?