Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Is there an efficient way to work out how many factors a large number has?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
Explore the effect of reflecting in two parallel mirror lines.
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Can you maximise the area available to a grazing goat?
If you move the tiles around, can you make squares with different coloured edges?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
Can you describe this route to infinity? Where will the arrows take you next?
Explore the effect of combining enlargements.
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?
A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
Can all unit fractions be written as the sum of two unit fractions?