Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
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 move the tiles around, can you make squares with different coloured edges?
Can you maximise the area available to a grazing goat?
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?
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. . . .
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Here's a chance to work with large numbers...
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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.
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?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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.
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?
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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?
Explore the effect of combining enlargements.
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find the area of a parallelogram defined by two vectors?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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?
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. . . .
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Can all unit fractions be written as the sum of two unit fractions?
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
A jigsaw where pieces only go together if the fractions are equivalent.