Monday, 27 July 2009

If the UK were a village of 100 people - or - How to embed adult numeracy / functional mathematics in vocational learning

Little Britain - Portrait of the nation as a neighbourhood appeared in last week's Independent (July 21st) along with a set of 11 wonderful illustrations from Laurent Taubin.
One quick glance and I immediately earmarked the entire 'Independent Life' pullout as an addition to my small but select stack of saved newspapers.

My stack includes: last month's flu graphic from The Times - which I fear will be gravely old hat before term starts (but I still think it's a great resource!); several newspapers from 9/11, 7/7, New Year's Day 2000, etc. I used to cut out just the relevant sections of newspapers / magazines but have discovered that it's a better idea to save the entire document. This gives the text real-life credibility and students get a much better idea of its source / purpose.

Anyway, to return to the UK Village report: I'm convinced it will come in handy next term for teaching percentages, fractions, data handling and goodness-knows-what.

The report has come in for quite a bit of flack from Independent readers (see the comments below the online version). OK, so the statistics might not be the most reliable (you could discuss this with your students) but I still think there's a lot of mileage in them.

There's an abundance of obvious links with vocational courses (and probably quite a few not-so-obvious ones).

If Britain were a village of 100 people:

  • Seventy-eight of the villagers would have a passport.
  • The people of the village would have made 107 trips abroad, spending £60, 055 between them.

Leisure, Travel and Tourism

  • Fifty-five would have a driving licence.
  • There would be 56 motor vehicles in the village, including 44 cars and two motorbikes.
  • Of the 42 households in the village, 18 would have one car, 13 would have two or more cars and 10 would not have a car at all.

Motor Vehicles

  • If Britain were a village of 100 people, 17 of the villagers would smoke, of whom 11 would like to give up.
  • Nineteen adults and three children would be classified as obese (that is they would have a Body Mass Index of 30 or greater).
  • Sixteen men and eight women would usually exceed the Government's daily sensible drinking benchmark (3-4 units per day for men; 2-3 units a day for women).
  • Eight men and four women would have taken an illicit drug in the past year.
  • One person would have dementia.
  • The village would welcome one new baby this year. The baby would expect to live for 76 years and six months (if it was a boy), or 81 years and seven months (if it was a girl).

Health and Social Care

  • Five villagers would be employed in the food industry.
  • Three of the villagers would be vegetarians and a further five would be partly vegetarian.
  • Between them, the villagers would spend £2,955 a week on food and non-alcoholic drinks. They would spend £1,154 a week on food eaten outside the home, of which £355 would go towards alcohol.


(If you look hard enough you'll also find statistics related to media, sport, animal care, and business studies.)

OK. So, we've got the links to vocational topics there for possible embedded teaching. What next?

Well, I like the idea of using the UK Village as a general introduction to percentages. It clearly demonstrates that 'percentage' means out of one hundred.

Then there's the possibility of simplifying all those percentages / fractions (and thus demonstrate that fractions and percentages are just alternative ways of expressing the same number).

E.g. What fraction of villagers / Britons have a driving licence?
55% - 55/100 - 11/20

Or, how about working out the average cost of a trip abroad?

Or, creating a pie chart (in Excel) depicting the ethnicity of the village? (You'll need to read the report to get these stats).

Or, for Entry 3 Numeracy (which now includes percentages) you could get students to come up with their own 'fun' statistics based on one of the illustrations.

This brings me on to a (vaguely) related topic: Functional Maths standards.

I am rather mystified by some of the Functional Maths standards (admittedly still in draft format). As I've just mentioned, someone has seen fit to introduce percentages at Entry 3 in the new online adult numeracy core curriculum curriculum (you'll need to register with the Excellence Gateway to get access). This seems a sensible idea to me - after all, percentages are very commonplace and knowing that 50% = 1/2 seems like a suitable Entry 3 skill.

N2/E3.2 Recognise and use equivalent forms

  • Understand that equivalent fractions look different but have the same value, e.g. 5/10 = 1/2
  • Understand that when the top and bottom number of a fraction are the same, this is equivalent to 1
  • Understand common simple percentages in familiar context, e.g. 25% and 50%
  • Understand common fraction/decimal/percentage equivalencies, e.g. 1/2 and 1/4 are equivalent to 50% and 25% respectively

Activities and examples

  • Circle equivalent fractions in a list e.g. 1/2 5/10 50/100
  • Investigation - look for a pattern in fractions equivalent to 1/2 e.g. 2/4 3/6 4/8 5/10 10/20 50/100 Write more fractions equivalent to 1/2.
  • Circle fractions in a list equal to 1.
  • Recognise relationships in the context of measure, e.g. that 5mm is half a centimetre, 50cm is half a metre, 500g is half a kilo, 500ml is half a litre.
  • In the context of money, recognise that 50p is half of £1 and appears on the calculator as 0.5.
  • Use the table function in Word to split cells to make a fraction wall and demonstrate equivalent fractions

Online Adult Numeracy Curriculum, Entry 3 Numeracy - N2/E3.2. (You need to register with the Excellence Gateway to access this link)

Interestingly, the Functional Maths standards seem to have gone the other way.The Amplified FS Standards make no mention of percentages until Level 1 where it briefly states:

Understand and use equivalencies between common fractions, decimals and percentages
• Read, write, order and compare common fractions, including mixed numbers, decimals with up to three decimal places and percentages.
(p.66, Amplified Functional Skills Standards, Level 1 Maths)

Now I fully take on board the fact that

'The level of demand of mathematical activities increases when it is contextualised in 'real life' scenarios. For this reason, the mathematical skills and techniques that are expected to be utilised and applied in functional skills activities are slightly lower than the usual band equivalences in the national curriculum levels.' (p53, Amplified Functional Skills Standards)

but it still seems strange that percentages are not actually 'used' until Level 2 FS Maths where the standards state:

Understand and use equivalencies between fractions, decimals and percentages
• Understand that fractions, decimals and percentages are different ways of expressing the same thing.

Use fractions, decimals and percentages to order and compare amounts or quantities and to solve practical problems. For example, what decimal must I multiply by to find the cost after a reduction of 25%? Choose to use a fraction, decimal or percentage to work out VAT.
• Know how to change fractions to equivalent fractions with a common denominator.
• Identify equivalences between fractions, decimals and percentages.
• Evaluate one number as a fraction or percentage of another.
• Understand that quantities must be in the same units to evaluate and compare.

Add and subtract fractions; add, subtract, multiply and divide decimals and percentages
• Add and subtract using halves, thirds, quarters, fifths and tenths.
• Add, subtract, multiply and divide decimals up to three places and check answers in the context of measurements and money, for example a bill for £32.67 shared equally among three people.

(pp.70-71, Amplified Functional Skills Standards, Level 2 Maths)

Seems like a big jump to me? And not at all clear exactly what is expected at L1 and what at Level 2?

I'll finish with one more statistic from the UK village:

'One person in the village would be illiterate'.

I'm not going to get into a discussion about what 'illiterate' means. You'll have to read my post of last July, What is complete illiteracy?.

If you have any further idea on using the UK Village in embedded teaching do share! Likewise, if you have any ideas for using it in literacy classes.


annec said...

Hi Maggie,

What a brilliant article! I am so pleased you alerted us to it.

Cheers, Anne

Cazz said...

Hi Maggie - great ideas for using print resources. Have you finished your level 5 course yet?

Maggie said...

Yes I have! Thanks for asking Cazz.

It was a lot of hard work but I have learned a lot - not just about numeracy teaching but teaching in general. Notably evidence based teaching and effect sizes (I am addicted to Geoff Petty's Evidence Based Teaching book - version 2).

I can't believe how much things have changed in the 5 years since I did my PGCE. One reason why, I guess, CPD is so important.

But, saying that, I intend to take it very easy next academic year. No major CPD, I am simply aiming to keep my IfL (Institute for Learning) Reflect area up to date.

I also intend to spend a lot of time updating my badly neglected web site. The list of things to do is endless but includes:

Removing old resources and dead links
Adding, editing and cataloging the 140+ resources in my email queue
Updating all the curriculum elements to reflect the new online adult literacy and numeracy curricula
Cross linking to Functional Mathematics and Functional English standards

I feel quite worn out just thinking about it but it will make a pleasant change from writing essays, reviews and case studies.