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?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Find the sum of the series.
There are lots of different methods to find out what the shapes are worth - how many can you find?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Which set of numbers that add to 10 have the largest product?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
If you move the tiles around, can you make squares with different coloured edges?
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?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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.
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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.
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?
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.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
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 find rectangles where the value of the area is the same as the value of the perimeter?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Can you find the area of a parallelogram defined by two vectors?
Can you maximise the area available to a grazing goat?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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. . . .
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can all unit fractions be written as the sum of two unit fractions?
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?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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.
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.