MathsConf18 (Part 4)

4. Changing Units (Jo Morgan)

So here it is the highly anticipated fourth blog post on MathsConf18! This blogging thing really requires you to not be swamped by work & in the mood to do it, phew! (PS sorry for lying about this being written two days ago)

So the fourth session I visited was hosted by the esteemed Jo Morgan of resourceaholic fame. I have followed Jo for quite some time but as of late Jo has been delving into the annals of history through the medium of the text book which has really piqued my interest.

As a bit of an opener Jo posed the following question:

How did you solve it?
I went with the tried & tested ratio table with a mix of multiplications & divisions as necessary.

So why should we worry about Unit Conversion? Well it appears to be one of those topics that we, as teachers, seem to expect our students to be able to complete quite well but if we look at past exam questions they don’t.

Is it because it’s a topic that’s not covered in depth early in the students’ progression? Is it because there is pre-requisite knowledge that isn’t taught effectively?

Students first come across metric units of measure in year 3

They are then introduced to the concept of converting between different units in year 4…

…and again in years 5 & 6

So why do students struggle to convert units when they get to GCSE? Do we, as secondary teachers, ‘unteach’ them? Do we try & rigorously impose a deliberate & abstract methodology that removes the students’ conceptual understanding? Perhaps we need to rethink the way we teach this particular topic.

It’s certainly a topic that needs to be covered if you intend for your students to fully access the new GCSE as it seems to be a popular choice for exam writers to assess. Looking at the last two years worth of exam questions Unit Conversion appeared 10 times on Edexcel papers & 8 times on AQA.

So what are the barriers to learning? (Steps to success)

  1. Multiplying & dividing by powers of 10
  2. Memorising the Unit Conversions
  3. Performing the conversions

With these as our basis we can ensure that our students are more confident with converting units. Jo didn’t cover multiplying & dividing by powers of 10 & neither will I as this would really be teaching you how to suck eggs. Instead we should concentrate on perhaps the thing students struggle the most, the memorisation of the Unit Conversions themselves.

All the conversions your students will need to know

So how can we embed these?

Well there is the tried & tested tabulated prefixes linked to the multipliers.

Will this be enough? We can take a leaf out of one of Jo’s old text books & discuss what the metric system is, the next example is from a book that predates the widespread use (& legal recognition of it as the UK’s official unit of measure) of the metric system!

Before every child grew up knowing of the metric system it had to be described & spoken about in great detail, perhaps if we went back to doing this it would help to embed the understanding of it. Interestingly, did you know that all the multiples of a unit have Greek prefixes & the Divisions of a unit have Latin prefixes?!

We can also bring it to life using video, Jo has suggested that we take a look at the following YouTube video.

Don’t forget we have some excellent concrete manipulatives available to us within the classroom!

So now we have explored the idea of memorisation of the key facts, we need to look at the actual performance of the conversion. There are many options available to us in this regard, it is purely a personal choice as to which way you use, but Jo wanted to show us a way that she was exploring, namely “Last Man Standing”.

So the Last Man Standing technique relies upon your students understanding the concept of ‘cancelling’ (cough cough, excuse me, did I just say that word?!)

We also need to be able to write the number one in different ways, namely using conversion factors, which are widely used in science

So this takes a little practice. Lets say we wanted to 128m into cm. We’d need to choose the factor that had both cm & m in it, we’d also need to ensure that they were arranged in a way that enabled the metres to be (ahem) cancelled.

This would lead us to multiply by 100 giving us 12 800cm.

Let’s try another:

This can also be used with compound units as well:

Now, I’m glad it took me so long to write this blog, as it has meant that I have been able to trial this technique on my students. They were a little confused the first time we tried it, but the more we looked into the different aspects of it the more comfortable they became with it. They have also given feedback on it compared to some of the other techniques they have used; because of the way in which the calculation is constructed they feel more comfortable with why we do what we do when converting.

I’m hoping to get my last blog on MathsConf18 out by the end of the week so pleae, keep watching this space.

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