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.

Catering

(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)
http://www.excellencegateway.org.uk/172329

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.

wiki How to draw an 'S' from straight lines

I use iGoogle as my home page (after being introduced to it by my youngest son about a year ago).

One of the things I enjoy about my current iGoogle desktop is the ‘How to for the day’ listing (see middle column on screen shot right).

Everyone knows about Wikipedia and Wiktionary - but it seems that wikiHow is not so well known (as an aside, I have just today discovered that although it is powered by MediaWiki, it isn’t actually part of the Wikimedia 'family' of projects).

I have no idea how long it’s been around for, but something on the daily ‘How to …’ listing often catches my eye. Yesterday it was How to Draw an S Made Entirely of Straight Lines. If you’re thinking the same as me - that it looks more like an 8 than an S - keep reading.

Now the trouble with being a basic skills tutor is that you tend to look at almost everything, especially texts, from the ‘can I use this in my classes’ or ‘would this make a good resource?’ point of view.

The answer is yes, and two ideas spring to mind.

For numeracy I would adapt the instructions to include measurement (e.g. Draw three parallel lines, each 2cm apart and 4cm long, etc.) and insist upon a ruler. I might even be generous and provide some 1cm squared paper!
Depending on the learner group, I would either read the instructions aloud, or display them on the board (with or without pictures). It makes a good crossover from ‘common measures’ to ‘shape and space’. MSS2/E1.2 Understand everyday positional vocabulary (e.g. between, inside or near to). MSS1/E2.5 Read, estimate, measure and compare length using common non-standard and standard units (g) know how to use a ruler to draw and measure lines to the nearest cm. MSS2/L1.2 draw 2-D shapes in different orientations using grids (e.g. in diagrams or plans). MSS2/L2.2 solve problems involving 2-D shapes and parallel lines.

For literacy the instructions would make good paired listening practice. You know the thing: students sit back to back, one reads and other attempts to draw (without being told the title of the piece). SLlr/E2.4 listen to and follow short, straightforward explanations and instructions.

Alternatively, I might read it to the whole group, see how they fare, then show them the picture. SLlr/E3.2 Listen for detail in explanations, instructions and narratives in different contexts

or, give the ‘speaker’ the finished S (or 8!) picture and ask them to make up and deliver their own instructions to their partner SLc/L1.3 Express clearly statements of fact and give short explanations, instructions, accounts and descriptions

or, compose, write down and edit their own instructions then swap and check carefully for ambiguity, conciseness, etc. Wt/L2.7 Proof-read and revise writing for accuracy and meaning (a) understand that, as well as checking for errors or spelling, grammar and general sense, proof-reading enable the writer to spot: unintended ambiguity (where meaning can be taken in more than one way); long-windedness or repetition (where the same point could be made more concisely); compression (where too many points are pushed into to few words and the sense is muddled).

or, you never know, I might just give out copies (or ask learners to go online) and use the text for some good old fashioned reading practice! Rt/E2.1 Trace and understand the main events of chronological and instructional texts.

Any or all of these is bound to lead to discussion of why a picture can be worth a thousand words. Rt/E3.9 relate an image to print and use it to obtain meaning Rt/E2.4 Use illustrations and captions to locate information (a) understand that illustrations contribute to meaning and can help locate and interpret information.

Of course, the thing about Wikis is that they are editable by all. This idea is itself a lesson in the power of group proof reading! Wt/L2.7 Proof-read and revise writing for accuracy and meaning b) understand that revising these might involve rewriting some sentences as well as adding or removing individual words.

I started writing this last night - this morning I noticed that the text in question had changed. There’s now an extra picture at the bottom showing how to draw transform the shape from an 8 to an S, and the introductory paragraph has also been changed to reflect this. So, I recommend that if you find a good wikiHow text that suits your learner group (or you), you make a copy of it because it might be completely different next time you look – or not even be there at all!

A final note. Just as I’m about to post this, what do I see on iGoogle?
A new “How To of the Day...”: How to Spell

If you have any teaching ideas that involve wikiHow – please share them via this Blog or email them to me from http://www.skillsworkshop.org/

Missing elements

I’m cock-a-hoop about numeracy elements today. At long last - after more than seven years - the site has complete coverage of every single adult numeracy element (Entry 1- Level 2).

Thanks must go to Jane Kay for providing two separate resources that between them cover the last three ‘missing elements’.

MSS1/E2.8 Read and compare positive temperatures in everyday situations such as weather charts (a) understand that temperature is a measure of heat (or cold) (b) understand that weather temperature is measured in degrees Celsius in the UK (but that different scales exist).
MSS1/E2.9 Read simple scales to the nearest labelled division (a) understand that scales measure in different units (b) understand labelled divisions on different scales.
MSS1/E3.9 Read, measure and compare temperature using common units and instruments (a) know how to read a thermometer (b) understand that temperature can be measured on different scales, but that Celsius is the standard scale in the UK.

It wasn’t pure chance of course. Everyone who has contributed to the site receives a monthly newsletter which now includes a ‘wanted’ list. This month it was emailed to more than 150 contributors. The number of contributors now increases by about 8-10 per month although that will doubtlessly slow down over the summer break.

The monthly site stats are always updated just before the email is sent out and this sly tactic provokes friendly competition between some contributors (you know you are!).

For those of you that are not contributors - I have summarised this month's wish list (having first joyfully omitted the now redundant list of 'missing numeracy elements').

WANTED!
We now have resources for most elements of the adult literacy and numeracy curricula. However, elements that are not covered (or only covered briefly) include:
preEntry milestones 6, 7 (many literacy and numeracy elements)
Entry 2 listening, speaking and discussion resources. Especially:
SLlr/E2.1 listen for and follow the gist of explanations, instructions and narratives.
SLd/E2.1 follow the gist of discussions.
SLlr/E2.5 listen to and identify simply expressed feelings and opinions.
SLlr/E2.3 listen for and identify the main points of short explanations or presentations.
Level 2 speaking and discussion resources. Especially:
SLc/L2.2 make requests and ask questions to obtain detailed information in familiar and unfamiliar circumstances.
SLd all discussion elements i.e.
SLd/L2.1 make relevant contributions and help to move discussions forward.
SLd/L2.2 adapt contributions to discussions to suit audience, context, purpose and situation.
SLd/L2.3 use appropriate phrases for interruption and change of topic.
SLd/L2.4 support opinions and arguments with evidence.
SLd/L2.5 use strategies intended to reassure, e.g. body language and appropriate phraseology.
Level 2 reading
Rt/L2.4 Read an argument and identify the points of view.
Rt/L2.5 Read critically to evaluate information and compare information, ideas and opinions from different sources.
Rt/L2.8 summarise information from longer documents.
Handwriting resources for higher levels. Produce legible text Ww/E3.3 L1.1 L2.1.

So - there's no cause for me to rest on my laurels just yet!

In fact, I have a funny feeling that even if complete coverage was ever achieved - that glorious day would be instantly followed by the swapover to Functional Skills with a whole bunch of new curriculum elements describing the same old basic skills we all know and love...

I'll finish with the final, less-daunting section of this month's wish list.

Topical resources also needed for:
Beijing Olympics or general Olympics
General spring/summer resources e.g. camping, beaches, air flights, barbecues, swimming, etc.
Contextual resources for any vocational areas. E.g. beauty therapy, construction, motor vehicles, catering, hairdressing, care, plumbing, etc.
Any help with any of these (or any other) topics is always VERY MUCH appreciated