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?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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 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.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
If you move the tiles around, can you make squares with different coloured edges?
Which set of numbers that add to 10 have the largest product?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
A jigsaw where pieces only go together if the fractions are equivalent.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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 is the same and what is different about these circle questions? What connections can you make?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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.
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. . . .
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 golden ratio.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
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?
Explore the effect of combining enlargements.
How many different symmetrical shapes can you make by shading triangles or squares?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
Is there an efficient way to work out how many factors a large number has?
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?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Can you maximise the area available to a grazing goat?
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. . . .
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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?
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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...