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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .
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?
Which set of numbers that add to 10 have the largest product?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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.
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.
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you maximise the area available to a grazing goat?
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?
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?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you move the tiles around, can you make squares with different coloured edges?
Explore the effect of combining enlargements.
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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. . . .
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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 there an efficient way to work out how many factors a large number has?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The clues for this Sudoku are the product of the numbers in adjacent squares.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?