Math help
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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.
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.
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 intelligence-questions which prove high level processing skills as opposed to well-versed 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.
In the end the level of intelligence/attainment needed for any selective school will be based on number of applicants versus number of places.
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 cross-cancelling, 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 set-up is correct it will mean slightly less work and faster answers.
If they can be encouraged to set up fractions and cancel down, without necessarily 'doing the stages' independently, provided the set-up is correct it will mean slightly less work and faster answers.