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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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?
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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.
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?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Explore the effect of reflecting in two parallel mirror lines.
Can you find the area of a parallelogram defined by two vectors?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
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?
Explore the effect of combining enlargements.
What is the smallest number with exactly 14 divisors?
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 ?
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.
Can all unit fractions be written as the sum of two unit fractions?
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?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting 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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
A jigsaw where pieces only go together if the fractions are
How many solutions can you find to this sum? Each of the different letters stands for a different number.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?