Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
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?
Have a look at these photos of different fruit. How many do you see? How did you count?
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
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?
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,. . . .
Can you discover whether this is a fair game?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
Which of these dice are right-handed and which are left-handed?
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.
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 Mah Ling?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Can you make a 3x3 cube with these shapes made from small cubes?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
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.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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 looks at levels of geometric thinking and the types of activities required to develop this thinking.