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.
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.
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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 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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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.
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
If a sum invested gains 10% each year how long before it has
doubled its value?
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Can you find the area of a parallelogram defined by two vectors?
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 ?
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 explain the surprising results Jo found when she calculated
the difference between square numbers?
Is there an efficient way to work out how many factors a large number has?
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?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
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.
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?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Explore the effect of combining enlargements.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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
Explore the effect of reflecting in two parallel mirror lines.
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?
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. . . .
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Use the differences to find the solution to this Sudoku.