Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
What is the smallest number with exactly 14 divisors?
There are lots of different methods to find out what the shapes are worth - how many can you find?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
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 ?
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. . . .
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Explore the effect of combining enlargements.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
Explore the effect of reflecting in two parallel mirror lines.
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?
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?
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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
The Egyptians expressed all fractions as the sum of different unit
fractions. The Greedy Algorithm might provide us with an efficient
way of doing this.
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
A decorator can buy pink paint from two manufacturers. What is the
least number he would need of each type in order to produce
different shades of pink.
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?
A jigsaw where pieces only go together if the fractions are
Can you find the area of a parallelogram defined by two vectors?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Is it always possible to combine two paints made up in the ratios
1:x and 1:y and turn them into paint made up in the ratio a:b ? Can
you find an efficent way of doing this?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Here's a chance to work with large numbers...
Can all unit fractions be written as the sum of two unit fractions?
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?
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.
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?