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…

## 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…

## 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…

## 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…

## Calculating areas of polygons with (x, y) coordinate vertices.

Calculating the area of a triangle is a straight forward task. We simply multiply the base length by its vertical height and then divide it all by 2. All very well if we are given the base and vertical height…

## Teaching trigonometry – calculating unknown angles

The last blog that looked at trigonometry focused on how to calculate an unknown side. This blog post will look at how we can use trigonometry to calculate an unknown angle in a right-triangle. This type of calculation is best…

## 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…

## 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…