Different combinations of the weights available allow you to make different totals. Which totals can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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?
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 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 different symmetrical shapes can you make by shading triangles or squares?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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. . . .
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Use the differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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 work out the dimensions of the three cubes?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
Can you maximise the area available to a grazing goat?
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
If you move the tiles around, can you make squares with different coloured edges?
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
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...
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?
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?
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?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Explore the effect of reflecting in two parallel mirror lines.
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Explore the effect of combining enlargements.
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
Is there an efficient way to work out how many factors a large number has?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?