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?
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...
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
If a sum invested gains 10% each year how long before it has
doubled its value?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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.
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
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Powers of numbers behave in surprising ways. Take a look at some of
these and try to explain why they are true.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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 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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you describe this route to infinity? Where will the arrows take you next?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Many numbers can be expressed as the difference of two perfect
squares. What do you notice about the numbers you CANNOT make?
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.
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?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
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 ?
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
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?
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. . . .
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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.
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. . . .
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 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?
The clues for this Sudoku are the product of the numbers in
What is the smallest number with exactly 14 divisors?
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 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?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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?
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?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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. . . .
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
A circle is inscribed in a triangle which has side lengths of 8, 15
and 17 cm. What is the radius of the circle?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?