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guest23

Posted: Mon Oct 15, 2007 10:43 am 


if 1km is equivalent to 5/8 mile and one gallon equates 4.5litres. How many Km/litre is 30miles per gallon?


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fm

Posted: Mon Oct 15, 2007 11:20 am 


Do it in stages.
1. Change 30 miles to km first. Tell the child Km are smaller so you will have more of them so you will mulitplying by 8 and dividing by 5
i.e. 30 x 8 = 240 then 240/5 = 48. You know have 48 km travelled to 1 gallon.
2. 1 gallon = 4.5 litres so you have a fuel consumption of 48km to 4.5 litres.
3. If you can do 48 km with 4.5 litres of fuel, then you will do with 1 litre of fuel 48km / 4.5.
4. Tell the child that 48km divided by 4.5 is easier done by 96 divided by 9 which will result in 10 rem 6 or 10 and 6/9 which is 10 2/3 which is 10.6666666.
5. So you can get 10.66km travelled on 1 litre of petrol.
OR
1. 30 miles to gallon is 30 miles to 4.5 litres.
2. Which is 30/4.5 to 1 litre which is 60/9 which is 6 6/9 which is 6 2/3 miles to 1 litre.
3. 6 2/3 miles is 6 2/3 x 8/5 km which is 20/3 x 8/5 which is 160/15 which is 10 10/15 which is 10 2/3 which is 10.66 which thankfully is the same as the answer above.
I think the first explanation is probably easier for a child as most are a bit hit and miss when it comes to fractions. In fact, I'm not sure many children would manage the above other than very top end ones.
Hope this is helpful.


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guest23

Posted: Mon Oct 15, 2007 11:30 am 


Thank you.
How do they expect an 11year old to do this?


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fm

Posted: Mon Oct 15, 2007 11:34 am 


I don't think most 11plus exams do expect this. I don't think any of the children I am tutoring this year would manage to execute the whole of this correctly yet many of these children are going to win grammar school places.
In which paper did you find this?


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guest23

Posted: Mon Oct 15, 2007 11:38 am 


This was given to my child by his tutor, apparently it is a past question from one of the independent schools.


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fm

Posted: Mon Oct 15, 2007 12:50 pm 


I think independent schools are a different ball game to state grammars. Our local independent (KE) is searching for children who have already reached a very good standard and their test is designed to draw these out; they also pose a few beyond difficult questions in order to select scholarship candidates. Our local state grammar (KE foundation) pose questions that don't necessarily rely on a superior primary school education but do rely on a lot of native intelligencequestions which prove high level processing skills as opposed to wellversed competence.
In the end the level of intelligence/attainment needed for any selective school will be based on number of applicants versus number of places.


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Guest

Posted: Mon Nov 12, 2007 10:00 am 


You might find some of the brighter children are able to appreciate how those stages can be distilled into an initial sum of 30/1 x 8/5 x 2/9 (easier than 1/4.5) which, after crosscancelling, becomes 2/1 x 8/1 x 2/3 = 32/3 = 10 2/3 = 10.67km/l.
If they can be encouraged to set up fractions and cancel down, without necessarily 'doing the stages' independently, provided the setup is correct it will mean slightly less work and faster answers.


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Guest55

Posted: Mon Nov 12, 2007 7:33 pm 

Joined: Mon Feb 12, 2007 1:21 pm Posts: 11956

PLEASE do not teach crosscancelling  it causes problems with fractional equations later in Secondary ...


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