Sunday, August 26, 2012

Map Scale

This inquiry on map scale inwards AQA's 2018 Foundation tier GCSE newspaper was answered actually badly:
Most students had no idea. In fact, they would withdraw maintain done improve if they'd but guessed. The most mutual reply given was 1:1000.

The inquiry requires students to sympathise ii things:
  1. how to convert from cm to km. 
  2. how to translate a map scale given every bit a ratio with no units (eg knowing that 1:100000 agency that 1cm on the map represents 100,000cm inwards existent life). 
I think that metric conversions are relatively tardily to memorise (most students know that at that spot are a hundred centimetres inwards a metre from their familiarity with a metre ruler together with the prefix cent, together with they should live on aware that kilo agency thousand). So this leads me to believe that the principal difficulty with this inquiry was a lack of familiarity with map scales given every bit a ratio. 

I withdraw maintain a feeling that this topic is sometimes skipped over past times maths teachers. Some students may solely meet i maths lesson on map scale inwards their entire fourth dimension at secondary school. It gets buried inwards alongside other topics on schemes of travel (it's usually inwards with either ratio or with bearings together with scale drawings, though I withdraw maintain seen it inwards with similarity too). I think it sometimes goes unnoticed together with doesn't acquire the fourth dimension it deserves. Perhaps this is because it rarely comes upwards inwards GCSE exams. 

Curriculum
You may live on wondering if the powerfulness to purpose a map scale of the shape 1:50000 comes upwards inwards geography. In the geography GCSE syllabus it says that students must "use together with translate OS maps at a gain of scales, including 1:50 000 together with 1:25 000 together with other maps appropriate to the topic". It doesn't specifically say that students withdraw maintain to mensurate together with convert distances, though this is implied. I institute this on a geography revision website:
"The scale set out on an OS map indicates how many centimetres on the soil are represented past times a centimetre on the map. On a 1:100,000 scale map, i centimetre on the map represents 100,000 cm on the ground, inwards other words, i centimetre on the map represents i kilometre inwards reality. H5N1 scale of 1:5,000 so agency that a centimetre on the map represents a distance inwards existent life of 5,000 centimetres (50 metres). This method of representing the scale of a map is called the fractional method, but yous volition also meet graphical representations or written representations similar 2 cm = 1 km."
I wasn't aware that the method of representing map scale inwards the shape 1:50000 is called the fractional method. I similar knowing proper names for things. Though I'm non certain whether this term is used consistently - I've seen other sites refer to it as a ratio scale or a fractional scale or a representative fraction.

Wikipedia lists dissimilar types of map scale including lexical (ie expressed inwards words - also known every bit verbal or stated scales), linear or graphical scales (represented every bit a bar), ratio scales, together with fractional scales. It points out that a lexical scale inwards a linguistic communication known to the user may live on easier to visualise than a ratio, but lexical scales may crusade problems if expressed inwards a linguistic communication that the user does non sympathise or inwards obsolete or ill-defined units (eg i inch to a furlong or i pouce to i league). So ratio scales withdraw maintain pros together with cons. When I read this I right away away sentiment that at that spot could live on roughly actually prissy opportunities for enrichment inwards this topic - I'd beloved to beak to my students virtually antiquated units of measurement!

Anyway, it looks similar 'map skills' inwards GCSE geography focuses mainly on recognising symbols together with using grid references. I haven't institute many geography resources on ratio scale, other than a brace of PowerPoints on TES that run through it real quickly. So it seems that measuring lengths on maps together with performing unit of measurement conversions using ratio scales isn't something they pass much fourth dimension on inwards the GCSE geography course.
We definitely create demand to pass roughly fourth dimension on it inwards maths lessons, together with it fits good at both Key Stage 3 together with 4. The maths GCSE specification says (in both the ratio together with geometry sections) that students should know how to purpose scale diagrams together with maps. AQA's Teaching Guidance helpfully provides additional clarification: "Scale could live on given every bit a ratio (for event 1:500 000) or every bit a commutation (for event 1cm represents v km)."  

Approach together with Resources
Without audio cognition of both place value and metric unit of measurement conversions nosotros can't fifty-fifty acquire started on this topic. So that's the start thing nosotros demand to check. I recollect i time giving my gain laid Year 10 a uncomplicated starter holler for them to set these lengths inwards ascending order:
It took way longer than expected.

If metric conversions demand teaching, at that spot are loads of practiced resources for this, including:
Students who scrap with uncomplicated unit of measurement conversions powerfulness honour it helpful to depict out a ratio tabular array each time, writing their known fact at the gain together with using multiplicative reasoning to fill upwards inwards the gap:
Once students are fluent inwards unit of measurement conversions, it would live on sensible to remind them of how ratios travel earlier moving onto map scale. There are lots of dandy resources available for this broad ranging topic (see my post on ratio), but the focus hither is simplifying ratios with mixed units (ie converting the antecedent together with consequent to the same units), together with on expressing ratios inwards the format 1:n. Useful resources include:

Now nosotros but demand to combine these ideas to sympathise map scale.

If a map has scale 1:50000, how create nosotros travel out what 6cm on the map represents inwards km on the ground? The ii steps involved (the unit of measurement conversion together with the criterion conversion) tin live on done inwards either order. I'd propose something similar this:
Here I've start past times writing the ratio scale with units - whatsoever units travel but cm is usually preferable. Instead of writing 1cm = 50,000cm (which is a horrible purpose of the equals sign!) I've used a table.

I did my unit of measurement conversion inwards ii steps, going via metres every bit the base of operations unit.

Using a similar approach to reply the question: "If 4cm on a map represents 100km on the ground, what's the ratio scale?", nosotros withdraw maintain the next process:
So the reply is 1:2500000.

Of course of written report at that spot are lots of dissimilar ways to laid the workings out hither - the tabular array is optional.

Most resources I've seen online for ratio scales skip through it real chop-chop - it's frequently covered inwards a brace of slides at the destination of a related lesson. Teaching it properly - inwards depth - should likely withdraw maintain ii or 3 dedicated lessons. The CIMT cloth 'KS3 Scale Drawing' is real useful, every bit are the Boss Maths lessons 'Using scale diagrams together with maps' and 'Scale drawings'. Corbett Maths has roughly examine manner questions on this topic.

I am eagerly awaiting something on variationtheory.com on all this!

Once students are fluent inwards metric unit of measurement conversions together with working with ratio scales, they powerfulness relish a flake of map travel to consolidate their learning. MathsPad withdraw maintain a free online map scale tool which is helpful for demonstrating map skills on the board. The Mapzone website shows what dissimilar OS map scales facial expression similar - this is non on the maths curriculum but powerfulness live on of involvement to students. This Reading Map Scales Activity from emtay on TES gives students the peril to practise using a ratio scale on a map of Europe.

No dubiety mortal volition tell me that when teaching this topic I *must* give my students total size OS maps together with ship them exterior on roughly big orienteering project! Hmm. I'm non certain that's practical on a principal route inwards Croydon... I also believe that although they may recollect the activity, it likely won't manage them either sympathise or recollect the maths. So I'll likely skip that.
Since we've all at nowadays got sat nav on our phones this topic isn't every bit much of a 'life skill' every bit it i time was. That's ok though. Thankfully nosotros don't instruct mathematics for its utility.

What's practiced virtually this topic is that every bit good every bit sewing together ii commutation areas of schoolhouse maths (ratio together with metric units), nosotros acquire the peril to come upwards dorsum to it when nosotros instruct bearings, together with i time again when nosotros create expanse together with book scale constituent with questions similar this:
A map has a scale of 1:50 000. H5N1 commons is shown on the map every bit a rectangle measuring 6cm past times 4.2cm . What is the actual expanse of the park?
The Boss Maths lesson 'Converting betwixt metric units of measures of expanse together with volume' covers this.

I'm involved inwards the London Thames Maths Hub workgroup on Challenging GCSE Topics inwards which I promise to facial expression at unit of measurement conversions together with ratio. Do arrive acquit on if yous desire to acquire involved inwards developing roughly resources for this topic.

In the meantime - let's all brand certain that map scale gets the fourth dimension it deserves inwards maths!




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