Can you maximise the area available to a grazing goat?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
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.
If you move the tiles around, can you make squares with different coloured edges?
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?
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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.
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?
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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?
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?
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 have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you describe this route to infinity? Where will the arrows take you next?
Explore the effect of reflecting in two parallel mirror lines.
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Which set of numbers that add to 10 have the largest product?
How many different symmetrical shapes can you make by shading triangles or squares?
Explore the effect of combining enlargements.
The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
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?
Here's a chance to work with large numbers...
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
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?
Can all unit fractions be written as the sum of two unit fractions?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find the area of a parallelogram defined by two vectors?
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
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...