Use the applet to explore the area of a parallelogram and how it relates to vectors.
Learn how to make a simple table using Excel.
Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
Learn how to use Excel to create triangular arrays.
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Can you make sense of these three proofs of Pythagoras' Theorem?
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
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.
If you take two integers and look at the difference between the square of each value, there is a nice relationship between the original numbers and that difference. Can you find the pattern using. . . .
Learn how to use advanced pasting techniques to create interactive spreadsheets.
Discover how Heron of Alexandria missed his chance to explore the unknown mathematical land of complex numbers.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
Be playful with graphs and networks, and see what theorems you can discover!
Use Excel to find sets of three numbers so that the sum of the squares of the first two is equal to the square of the third.
This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
Learn how to use logic tests to create interactive resources using Excel.
How good are you at finding the formula for a number pattern ?
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
One of the articles supporting STEM teaching in the classroom.
Show that all pentagonal numbers are one third of a triangular number.
Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?
Some of our experiences of discovering and using triangle numbers in a range of contexts.
Make the twizzle twist on its spot and so work out the hidden link.
In this article, Alan Parr shares his experiences of the motivating effect sport can have on the learning of mathematics.
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses. . . .
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.
Use an interactive Excel spreadsheet to explore number in this exciting game!
chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
Choose four numbers and make two fractions. Use an Excel spreadsheet to investigate their properties. Can you generalise?
Learn how to use conditional formatting to create attractive interactive spreadsheets in Excel.
Need some help getting started with solving and thinking about rich tasks? Read on for some friendly advice.
An article introducing the ideas of differentiation.
6: Introducing and developing STEM in the classroom.
Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?
How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...
Articles about mathematics for students
This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
In this article, Rachel Melrose describes what happens when she mixed mathematics with art.
The archive of our upper secondary student articles.