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?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Move just three of the circles so that the triangle faces in the
A variant on the game Alquerque
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A game for two players on a large squared space.
An activity centred around observations of dots and how we visualise number arrangement patterns.
How many different triangles can you make on a circular pegboard that has nine pegs?
Exchange the positions of the two sets of counters in the least possible number of moves
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
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.
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.
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,. . . .
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
What happens when you try and fit the triomino pieces into these
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you cover the camel with these pieces?
A game for two players. You'll need some counters.
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the chairs?
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 this brazier for roasting chestnuts?
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 Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these people?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of Granma T?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you fit the tangram pieces into the outlines of the workmen?