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?
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 if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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. . . .
Find the sum of the series.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
Can you maximise the area available to a grazing goat?
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.
Can you find rectangles where the value of the area is the same as the value of the perimeter?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
There are lots of different methods to find out what the shapes are worth - how many can you find?
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.
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
A jigsaw where pieces only go together if the fractions are
Can you find the area of a parallelogram defined by two vectors?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
What is the same and what is different about these circle
questions? What connections can you make?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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. . . .
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Explore the effect of combining enlargements.
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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Here's a chance to work with large numbers...
Can all unit fractions be written as the sum of two unit fractions?