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 Post subject: Tricky questions - help!
PostPosted: Tue Jan 03, 2006 5:46 pm 
Hi all.

Can anyone shed some light on the best way to tackle the following 3 questions that crop up in Nfer papers. The first (‘scale type’) question is a particular pain.

1. A map of Ireland is drawn to a scale of 1:325,000. How many cm on the map would show 65km?

2. A water tank has a volume of 1 cubic metre. Find (a) its volume in cm cubed b) the mass of the water in kg.

Is the best/quickest way to tackle the following ‘best buy’ question to calculate 1kg first?

3. Which is the better buy per kg and by how much?

Y a-5kg pack costing 75p
Z a 1250-g pack costing 20p.

Many thanks!

PostPosted: Wed Jan 04, 2006 12:15 pm 
1. 1cm on the map shows 325 000 cm on the ground - this is what the map scale means.

so you need to find out how many cm on the map would show 6500 000 cm on the ground (this is what 65km is in cm).

This is 6500 000 divided by 325 000 which is 20. So 20cm on the map would represent 65km on the ground.

2. 1 cubic metre is a cube with each side 1m long. The volume of a cube with sides of 1m needs to be worked out in cubic centimetres. One metre is 100cm so it is 100 x 100 x 100 cubic centimetres which equals 1000 000 cubic centimetres.

One cubic centimetre of water weighs one gramme. So 1 cubic metre weighs 1 000 000 grammes. Divide by 1000 to convert this to kilogrammes. The answer is 1000 kg.

3. The best way to tackle this question is by the method you find easiest as the exam is very soon!! As long as you can do the question I would not worry about the method. Can you do it or are you asking for help on this one too?

 Post subject:
PostPosted: Wed Jan 04, 2006 1:34 pm 
Thanks heaps for your quick response and well explained help with these questions answermachine (interesting name!). For no.3 - I would divide cost price/weight. Please suggest a method if I'm on the wrong track (or a long track!). Thanks!!!

 Post subject: difficult questions
PostPosted: Wed Jan 04, 2006 7:37 pm 
Is the best/quickest way to tackle the following ‘best buy’ question to calculate 1kg first?

Y a-5kg pack costing 75p
Z a 1250-g pack costing 20p.

Yes I would first of all find out much 1kg would cost as it is the price per kg you are being asked to compare. As in the map question they are trying to make the question more difficult for you by using different units for different bits of the question (in this one g and kg, in the other one, cm and km).

If 5kg of Y costs 75p, 1kg must cost 75p divided by 5 which is 15p.

for Z, we are told that 1250 grammes cost 20p. 1250 grammes equals 1.25 kg. So 1kg of Z just cost 20p divided by 1.25 which is 16p (are you OK dividing 20p by 1.25 without a calculator?).

So Y is better value for money, and is 1pence per kg cheaper than Z.

Good luck. When are you sitting your maths paper and which area of the country?

 Post subject:
PostPosted: Thu Jan 05, 2006 2:23 pm 
You’re so right, map questions are often worded to make them seem more difficult. It’s a bother, especially if you’re not sure which conversation factor to use (e.g. times/divide by 100, 10 .....). Adding an extra 0 or two is a common/frustrating mistake. What do you make of the questions below? 2 and 3 are reversed *rolls eyes*.

1. A road map measured 4.5 cm, which represented a distance of 45km. What distance does 1mm on the map represent?

2. A road shown on a map measures 50mm, which represents an actual distance of 1km. Find the scale to which the map is drawn.

3. A line 8cm long represents a distance of 3.2m. The scale to which the line is drawn is 1m to ? cm.


PostPosted: Fri Jan 06, 2006 9:20 am 
The important principle to get across is for the child to think about simple metric conversion. In particular 10mm = 1 cm, 100cm = 1m, and 1000m = 1km. So for the various questions:-

1. For 4.5 cm representing 45 km, the scale conversion factor is 100 x 1000 (5 zeros or 5 decimal places).
Hence the scale is 4.5: 45 x 100,000 = 4.5:4,500,000. Dividing both sides by 4.5 we get 1: 1,000,000. Counting 5 zeros on the right means that on this scale 1cm represents 10km or 1mm represents 1km.

2. 50mm represents 1km is equivalent to a scale of 50: 1,000,000 (6 zeros). Div by 50 gives 1: 20,000

3. Only a simple scale division required, just have to work out 8 div 3.2 = 2.5 Therefore the scale of the line is 1m represented by 2.5cm.

Hope this helps

 Post subject:
PostPosted: Fri Jan 06, 2006 12:55 pm 
We struggled with this one for a while until my Father (retired maths teacher) pointed me in the same direction as KenR has just described.
However, we did find for my daughter that memory of just how many zeros she needed when converting mm/km etc was a huge problem. We cracked this by encouraging her to write a quick metric scale as follows before answering any conversion questions:

mm x10 = cm
cm x100 = m
M x1000 =km

Just writing these downwards was enough to make sure she didn't miss a few zeros in conversion.

 Post subject:
PostPosted: Fri Jan 06, 2006 1:10 pm 
Thanks to everyone above, you've been so helpful.

PostPosted: Fri Jan 06, 2006 1:45 pm 
would suggest that if a child has difficulties remembering how many mm in a cm, how many cm in a metre etc, that you give them some practical measuring tasks with a 30cm ruler, and a much longer steel tape measure. this will help reinforce the learning of mm, cm, and metres.

harder for km -------- but to encourage the child to measure their stride in metres and work out how many strides they would have to make for a kilometre - this might help. Also compare km with miles if a mile has some mearning for them.

 Post subject:
PostPosted: Sat Jan 07, 2006 12:28 am 
Re Post from answermachine,

Thanks for the extra tip for remembering mm/cm etc. This is the approach that our school followed - I guess to ensure that children understand the concept of relativity of measurements. This was also recommended in some of the maths revision books we used.

We certainly re-inforced this method at home but unfortunately found it to be totally useless for our daughter who is dyslexic. She understood the concepts perfectly but even if she could remember this the following day, a week later would have difficulty remembering just how many how mm were in a km etc (failure to consolidate information into her long term memory - common problem with dyslexia). She is certainly not thick (IQ top 2%, as per Ed Psych Assessment), so we hit upon the method I described in my post above following advice from a maths teacher (ok so he's my Dad so I'm biased) that the metric system, unlike the old imperial system, is based upon multiples of 10.

We also followed this method for units of weight g/kg and volumes of liquid ml/l. In doing so we solved 2 years of difficulty remembering weights and measures.

Thought this might help when all else fails.


P.S. Are you a teacher?

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