Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you find the area of a parallelogram defined by two vectors?
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?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
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?
Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Which set of numbers that add to 10 have the largest product?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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 ?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
If you move the tiles around, can you make squares with different coloured edges?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
If a sum invested gains 10% each year how long before it has doubled its value?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
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?
A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .
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?
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
How many different symmetrical shapes can you make by shading triangles or squares?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .
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 find an efficient method to work out how many handshakes there would be if hundreds of people met?
Explore the effect of combining enlargements.
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?
Can you describe this route to infinity? Where will the arrows take you next?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Can you maximise the area available to a grazing goat?