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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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 opposite direction.
A variant on the game Alquerque
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 two players. You'll need some counters.
What is the best way to shunt these carriages so that each train can continue its journey?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
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?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
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.
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?
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,. . . .
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
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?
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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. . . .
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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 Little Ming and Little Fung dancing?
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 fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
What can you see? What do you notice? What questions can you ask?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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.
Have a go at this 3D extension to the Pebbles problem.
Make a cube out of straws and have a go at this practical challenge.