What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Which set of numbers that add to 10 have the largest product?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
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?
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.
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
Is there an efficient way to work out how many factors a large number has?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
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?
Find the sum of the series.
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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?
Why does this fold create an angle of sixty degrees?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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. . . .
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Can all unit fractions be written as the sum of two unit fractions?
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find the decimal equivalents of the fractions one ninth, one ninety
ninth, one nine hundred and ninety ninth etc. Explain the pattern
you get and generalise.
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?
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?
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
Can you find the area of a parallelogram defined by two vectors?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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 ?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
What is the same and what is different about these circle
questions? What connections can you make?
Can you maximise the area available to a grazing goat?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Use the differences to find the solution to this Sudoku.
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?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?