# New approach for converting between fractions, decimals and percentages?

I have always found converting between fractions, decimals and percentages a challenging topic to teach when you’ve got pupils who have difficulty with mental and written arithmetic. Quite often you seem to get bogged down in the arithmetic of the calculation, and the pupils lose sight of why we are doing it in the first place.

Rather than plod on with numerical calculations: ‘divide by 100’, ‘divide numerator by denominator’, ‘use equivalent fractions to make denominator 100 then read off numerator’ etc I’ve been trying to think of alternative ways into the topic. Sometimes pupils who struggle with numerical calculations are good at spotting patterns and so I thought if I could create some kind of diagram that pupils could do FDP conversions with and look for patterns within it that it might be another way in to develop their understanding.

I’m a big fan of fraction walls for introducing the idea of equivalent fractions; the idea being that a pupil puts their ruler vertically on the fraction wall and can read off equivalent fractions. It occurred to me, why couldn’t we just put a decimal and percentage number line above the fraction wall? That way, when pupils put their ruler down on 3/4, not only can they see this is equivalent to 6/8, but also 0.75 and 75%?

Here’s the completed FDP converter:

To use it pupils place their ruler vertically at the appropriate point on the page and can read off the other scales.

I wonder, if over time and with plenty of practice using the diagram and identifying links and patterns within it, if some pupils will be able to make the step of not needing the diagram? Could they visualise it in their heads, even if just from a conceptual point of view? I’m going to give it a go with some of my classes to find out! If you have a go I’d love to hear your feedback in the comments section.

I have found a card sort helpful

row one fraction cards

row two their equivalent percentage

row three their equivalent decimal.

I group the fractions half quarter eighth three quarters / one third two thirds / one tenth one fifth four fifiths

Most pupils will get the half 50% 0.5 column.

thanks for the ideas they have been a great help

Great addition to the fraction wall. What do you think of rotating the diagram so that 0% is at the bottom and 100% at the top to relate these equivalences to notion of fullness?

Why do we still teach fractions in this declimal/digital age. I have sufferd along with the kids, should the torture end now?