Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
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?
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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
What happens when you try and fit the triomino pieces into these two grids?
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?
A game for two players. You'll need some counters.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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,. . . .
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?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10.
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.
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.
Move just three of the circles so that the triangle faces in the opposite direction.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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.
Can you find a way of counting the spheres in these arrangements?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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?
Watch this animation. What do you see? Can you explain why this happens?
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?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
A game for two players on a large squared space.
Have a look at these photos of different fruit. How many do you see? How did you count?
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?
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?
Can you fit the tangram pieces into the outline of the sports car?
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Can you fit the tangram pieces into the outline of the dragon?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the rabbits?
Can you fit the tangram pieces into the outline of Granma T?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.