Can you describe this route to infinity? Where will the arrows take you next?
Can you find the area of a parallelogram defined by two vectors?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
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?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
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?
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.
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
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?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
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 to. . . .
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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 maximise the area available to a grazing goat?
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 ?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can all unit fractions be written as the sum of two unit fractions?
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?
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.
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?
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
If a sum invested gains 10% each year how long before it has
doubled its value?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
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?
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?