# Category Archives: Number Sense

## Line multiplication and the FOIL method

Line multiplication is a nice activity for teaching multiplication especially for more than one-digit numbers. The method is shown in the figure. The horizontal line represents the number 13 where the top line represents the tens digit and the lines below it represents the ones digit. The lines are grouped according to their place value.… Read More »

## Math Knowledge for Teaching Addition

This post is the second in the series of post about the Math Knowledge for Teaching (MKT) where I present task/lesson that teachers and interested readers of this blog can discuss. The first is about Tangents to Curves, a Year 12 lesson. This second post is for young learners. The task How many small cubes make up… Read More »

## What can the representations of numbers tell us?

Numbers can be represented in different ways. The kind of representation we choose can highlight or de-emphasise the properties of the numbers. Studies about understanding mathematics discuss about two kinds of representations of a mathematical idea: (1) transparent representations and (2) opaque representations. A transparent representation has no more and no less meaning than the represented idea(s)… Read More »

## What are fractions and what does it mean to understand them?

Negative numbers, the irrationals, and imaginary numbers are not that easy to make sense of for many students. But this is something understandable. One only needs to check-out the histories of these numbers. The mathematicians themselves took a long time to accept and make sense of them. But fractions? How can something so natural, useful,… Read More »