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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A jigsaw where pieces only go together if the fractions are equivalent.
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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: 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.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
Explore the effect of reflecting in two parallel mirror lines.
Explore the effect of combining enlargements.
Can you describe this route to infinity? Where will the arrows take you next?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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. . . .
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.
Can you maximise the area available to a grazing goat?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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.