Find your way through the grid starting at 2 and following these operations. What number do you end on?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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?
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 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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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 is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
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?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Can you make a 3x3 cube with these shapes made from small cubes?
Move just three of the circles so that the triangle faces in the opposite direction.
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
How many different triangles can you make on a circular pegboard that has nine pegs?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
Have a go at this 3D extension to the Pebbles problem.
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 find ways of joining cubes together so that 28 faces are visible?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?