What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
Is there an efficient way to work out how many factors a large number has?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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?
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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
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?
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.
Which set of numbers that add to 10 have the largest product?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Find the sum of the series.
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. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
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?
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 an efficient method to work out how many handshakes
there would be if hundreds of people met?
Can you maximise the area available to a grazing goat?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you find the area of a parallelogram defined by two vectors?
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?
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?
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
What is the same and what is different about these circle
questions? What connections can you make?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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. . . .
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 ?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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. . . .
Explore the effect of combining enlargements.
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Can you describe this route to infinity? Where will the arrows take you next?
Explore the effect of reflecting in two parallel mirror lines.
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?
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?
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?