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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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. . . .
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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.
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?
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.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
A game for two players on a large squared space.
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 dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Watch this animation. What do you see? Can you explain why this happens?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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 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 make a 3x3 cube with these shapes made from small cubes?
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?
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.
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find a way of counting the spheres in these arrangements?
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?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Can you fit the tangram pieces into the outlines of the convex shapes?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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.
Which of these dice are right-handed and which are left-handed?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
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?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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!
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.