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fractions question

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1. Hi
Sorry to trouble you all with what will probably be an insignificant question when you've probably got much better things to do...

I'm a primary school teacher and, to cut a long story short, one of the questions on this year's arithmetic test, was 140 x 2/5.

The demands of this year's test are so much that I told my less able ones just to give the quickest answer they could do and move on (they have 36 questions in 30 minutes) so I'd imagine most of them gave an answer of 280/5.

My more able kids would have converted it to 56.

The instructions specifically say that answers to such questions can be given as common fractions and nowhere does it say answers have to be converted into mixed fractions or whole numbers.

Anyway, the mark scheme has been published and only gives 56 as the answer. In most other questions, alternative answers are given.

So, regardless of how vulgar 280/5 is, is it 100% correct to say that one of the answers to 140 x 2/5 is 280/5?

2. That's really only doing half the work. Fractions aren't really acceptable as answers when they can be cancelled down to a whole number.

Fair enough about simplifying to the smallest denominator or mixed numbers, but they should be able to recognise that 280 is divisible by 5 and complete the step.
3. (Original post by Barry Girtles)
So, regardless of how vulgar 280/5 is, is it 100% correct to say that one of the answers to 140 x 2/5 is 280/5?

Yes, certainly.
4. (Original post by Barry Girtles)
Hi
Sorry to trouble you all with what will probably be an insignificant question when you've probably got much better things to do...

I'm a primary school teacher and, to cut a long story short, one of the questions on this year's arithmetic test, was 140 x 2/5.

The demands of this year's test are so much that I told my less able ones just to give the quickest answer they could do and move on (they have 36 questions in 30 minutes) so I'd imagine most of them gave an answer of 280/5.

My more able kids would have converted it to 56.

The instructions specifically say that answers to such questions can be given as common fractions and nowhere does it say answers have to be converted into mixed fractions or whole numbers.

Anyway, the mark scheme has been published and only gives 56 as the answer. In most other questions, alternative answers are given.

So, regardless of how vulgar 280/5 is, is it 100% correct to say that one of the answers to 140 x 2/5 is 280/5?

If the instructions explicitly say that there is no requirement to simplify or convert, then 280/5 is a perfectly valid answer - it's simply an improper fraction that hasn't been simplified as much as it could be. Is it definitely the case that the instructions don't state "Please give answers in their simplest form"?

In terms of building up confidence with numbers, I would hope that you'd be encouraging students to recognize that 140 = 14 x 10 and therefore 140 x 1/5 = 14 x 10 / 5 = 14 x 2 = 28, so the answer has to be 28 x 2 = 56, i.e. there's no need to create a numerator as big as 280 in this case.

(My immediate - and cynical - reaction to questions like this is usually: "What's the point?" i.e. what is it that the question is trying to test? If you just expect students to give the answer as 280/5 then you might as well ask them what 140 x 2 is and not bother introducing a denominator because you're not really making use of the extra information contained in it - it's redundant! Thankfully I'm not involved in education professionally, so I don't have to worry about the reasoning behind setting questions like this )
5. Thanks for the answers. I'll list the replies if that's ok.

1. There is a new curriculum that the children have had to get their heads around in very little time.

2. A lot of the fractions work has never been tested before.

3. As in a lot of primary classes, there is a gulf between the children's abilities. Some are probably ready for GCSE work; others still struggle with the basics (for a variety of reasons).

4. Despite this, they all have to do the same test and the school is judged on the results.

5. For some of the less able ones, this has been incredibly difficult as they've not "lived" the new curriculum from day one i.e. Reception class; rather, it's been foisted upon them this year and last.

6. While we've practised converting and simplifying, in a test situation, you're looking for a quick and acceptable answer which is why the less able ones would've given a vulgar fraction while the more confident would have given the whole number answer.

7.There is a lot of politics in primary education at the moment. I'll leave it there.

Thanks.

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