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.…

# KS2

## 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.…

## Fraction multiplication – Making sense of multiplying improper fractions.

In the last blog we looked at why multiplication of proper fractions can be fluently completed by multiplying numerators then doing the same with denominators. At this stage learners will have begun to understand this procedure and the truth of it…

## Fraction multiplication – a concrete approach

Why is the following statement true? For those of us in the know we might be tempted to say on the left hand side if we multiply numerators by each other and do likewise with denominators we will…

## Reasoning behind the shortcuts 1: Angles in any triangle sum to 180˚

Angles in any triangle sum to 180˚ I remember being given this piece of information at school and I have always remembered it. I was never told why it was true for all triangles however, I was simply required to…

## Mental multiplication of odd numbers by 5

There are some very interesting, magical (initially) tricks used in mental mathematics which once practiced can serve you well. Once I am over the apparent magical quality of a procedure I cannot help myself but try to fathom out why…

## Problems with ambiguous labelling

This SATs question was recently brought to my attention (there were two of them hence the wording of the question.) Calculate the perimeter of these rectilinear shapes. This replica diagram is faithful to the original but the length labelled 2…