Think of two whole numbers under 10. Take one of them and add 1.
Multiply by 5. Add 1 again. Double your answer. Subract 1. Add your
second number. Add 2. Double again. Subtract 8. Halve this. . . .
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?
Powers of numbers behave in surprising ways. Take a look at some of
these and try to explain why they are true.
Can you see how to build a harmonic triangle? Can you work out the
next two rows?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Which set of numbers that add to 10 have the largest product?
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?
Many numbers can be expressed as the difference of two perfect
squares. What do you notice about the numbers you CANNOT make?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
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?
Investigate how you can work out what day of the week your birthday
will be on next year, and the year after...
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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?
The clues for this Sudoku are the product of the numbers in
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. . . .
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
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
A circle is inscribed in a triangle which has side lengths of 8, 15
and 17 cm. What is the radius of the circle?
Can you find the area of a parallelogram defined by two vectors?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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 ?
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. . . .
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?
What is the same and what is different about these circle
questions? What connections can you make?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
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?
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?
Why does this fold create an angle of sixty degrees?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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. . . .
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?
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
Here are four tiles. They can be arranged in a 2 by 2 square so
that this large square has a green edge. If the tiles are moved
around, we can make a 2 by 2 square with a blue edge... Now try. . . .
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?