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.
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. . . .
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.
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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 ?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Use the differences to find the solution to this Sudoku.
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
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.
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?
Can you find the area of a parallelogram defined by two vectors?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you describe this route to infinity? Where will the arrows take you next?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the 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?
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?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
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. . . .
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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?
Is there an efficient way to work out how many factors a large number has?
If a sum invested gains 10% each year how long before it has
doubled its value?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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...
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?