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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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.
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Find the sum of this series of surds.
Which set of numbers that add to 10 have the largest product?
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?
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.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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.
What is the same and what is different about these circle questions? What connections can you make?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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. . . .
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?
What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.
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?
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
How many different symmetrical shapes can you make by shading triangles or squares?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Use the differences to find the solution to this Sudoku.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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?
Is there an efficient way to work out how many factors a large number has?
Can you describe this route to infinity? Where will the arrows take you next?