When we teach that the multiplication of two negatives always produces a positive, we need to prove to pupils that this is so always and we don’t really want them taking our word for it without a good reason to back up…

# Algebra

## Factorising quadratics without trial and improvement.

How do you teach GCSE students how to factorise an expression like; I was taught to solve through a very time consuming trial and improvement method with no reason given as to how it and why it worked. Since…

## Factorising challenging algebraic expressions

Last night I had a request on my Twitter account to help someone in South Africa with a factorisation problem that he in turn was trying to help his younger brother with. He followed up by sending a photo of…

## Factorisation and expansion [2]

In the previous blog we considered how the teaching of expansion and factorisation might be better taught simultaneously. Looking at whole numbers only. In this blog we will continue by looking at different specific linear algebraic expressions. The first expression…

## What comes first expansion or factorisation?

My answer to the title question is expansion followed instantly by factorisation in order to make the links immediately between the two. As with all mathematics let us start with a simple case of expansion over brackets. 2(3+4) This example gives…

## Teaching, questioning but not telling. Angle at circumference of a semi-circle.

I wrote an earlier blog on this subject but thought it might be useful to break it down into a series of teacher to student questions and instructions to get a more active learning experience in the classroom. This can…

## Commutativity and fraction problems

In this short blog we will look at how, by using the commutative property of multiplication it is possible to solve complex looking fraction multiplication problems mentally. Previously we looked at concrete approaches to conceptualising the process of multiplication of…

## The angle inscribed in a semi-circle is a right angle.

Take any semi-circle, join two straight lines from each end of the diameter at an apex on the circumference and this angle will always be a right angle. This is one of the more accessible of the circle theorems to…

## The formulae for the area of a triangle. (Part 3 – Scalene.)

In the previous blogs we have seen that the area for any right-triangle and any isosceles triangle (to include the special equilateral triangle) has given up the formula area = bh/2. We should now move on to the next type…

## The difference of two squares – what is really happening.

A specific problem Both 4x – 3y and 4x + 3y from the outset should be seen as non specific values, in other words numbers that will provide a product. The terms given in this problem are slightly more complex…