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…

## 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…

## Understanding operations with negative numbers [2]. Subtracting a positive.

In the last blog we looked at how ‘zero’ is the border that separates negative and positive numbers on a number line and that adding positive values is seen as a journey along the line to the right, the destination being the solution.…

## 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…

## Mastery at greater depth in Year 6

Let me ask you to forgive the indulgence in this blog to publicise my latest book on mastery of mathematics. It is published by Harper Collins (ISBN 9780008207069) “Maths Mastery with Greater Depth – Year 6” and includes a challenge…

## Understanding operations with negative numbers [1]. Introduction.

By the end of year 6 pupils are required to be able to solve problems with negative numbers. Negative numbers, conceptually are more difficult to visualise than their positive cousins or have fewer possibilities available to them should I say.…

## 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…

## Multiplying two improper fractions.

In this the third blog in the series of multiplying fractions we shall look at what is happening when two improper fractions are being multiplied. What we should not do at this stage is assume that what has been true…