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Phrasing maths questions correctly

Discussion in 'Mathematics' started by Sunlounger, Jun 28, 2020 at 5:09 PM.

  1. Sunlounger

    Sunlounger New commenter

    OK, I know this is basic stuff and some of us should really get life ... but I'd welcome comments on a 'simple' question in a maths test (S&S) that has opened up a can of worms.

    The question:
    • How many times smaller is 54 than 540
    The official answer:
    • They give the answer as: 10
    Given that 540 has ten lots of 54
    And that 54 has one lot of 54 ...
    54 is smaller than 540 by 9 lots of 54.
    So the correct answer is 9.​

    We can all see what S&S probably meant to ask but in the view of some of us their sloppy use of English is distorting a quite important mathematical point here and misleading students . Or is it?
    Last edited: Jun 28, 2020 at 5:14 PM
  2. UKExceED

    UKExceED New commenter

    This is a great point, and one that we discussed just a few months ago.

    The example we had was:

    David has 24 stickers. Evan has three times more than David. How many does Evan have?

    The answer was listed as 24x3=72.

    However this is technically incorrect. The wording of the questions is “three times more than”, which means he actually has four times as many as David.

    For the 72 to be correct it should be “three times as many as” or “two times more than”. It is so frustrating that our children are set questions by people who clearly have not actually thought through the implications of their wording.
  3. gainly

    gainly Star commenter

    I would interpret "10 times smaller" as meaning divide by 10, just as "10 times larger" would mean multiply by 10.

    If you interpret 54 as 9 times smaller than 540, you would say 30 is one times smaller than 60, which doesn't make much sense.
    Boardingmaster, Stiltskin and bonxie like this.
  4. adamcreen

    adamcreen Occasional commenter

    7 years ago there was a KS2 SATs question like this. About polar bears.
    "In a zoo, the adult polar bear weighs three times more than the baby elephant. Together they weigh 700 kilograms. How much does the polar bear weigh?"
    The "correct" answer was 525 kg. Students got no marks for 560 kg.
    And don't get me started on 54 being 10 times smaller. It's not even 9 times smaller, so you're wrong too, Sunlounger. It's ONE TENTH OF THE SIZE.
    Screenshot 2020-06-30 at 10.14.50.png
  5. UKExceED

    UKExceED New commenter

    Yep... should be 560Kg. Nasty question.
  6. gainly

    gainly Star commenter

    The problem is trying to ask maths questions using everyday language which is potentially ambiguous. It would be better to stick to proper mathematical language which is very precise.

    Some years ago I was going through a maths paper with a student. One question was, "What is the reciprocal of 7?" I told her the reciprocal meant one over the number. "Oh, so it's 8 then," she replied.
    bonxie likes this.
  7. Stiltskin

    Stiltskin Star commenter

    One tenth of the size = ten times smaller
    Ten times the size = ten times larger

    I agree the wording on the KS2 paper is poor. They should have said three times as much as a baby elephant, not three times more.
  8. adamcreen

    adamcreen Occasional commenter

    No, you can't have 10 times smaller. Multiplying by 10 makes it bigger. Writing smaller doesn't change the multiply into a divide. It's one tenth of the size.

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