Yet Another Cycling Forum
Random Musings => Miscellany => Kidstuff => Topic started by: Tim Hall on 17 October, 2012, 10:06:53 pm
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How's this for a year 4 (I think) maths homework question?
Which is the odd one out and why?
10 21 18 61 25
I was helping a Small Person I know with this. I suggested she check her list of times tables to see if any of the numbers weren't in it (having spotted that 61 is prime). Some minutes later the Small Person declared that 61 wasn't in it, so wrote that as the answer.
I saw her again today. The answer the teacher gave was 25, as it was the only number that didn't feature the digit 1. A valid response, just as valid as the Small Person's, which got marked wrongly.
Giving it a bit more thought, 10 is the odd one out because it has no "units". 21 because it's the only multiple of 7, 18 the only multiple of 9, 25 because it's a perfect square.
I (and the Small Person's mother) explained that we though her answer was right and the book the teacher got the question from wasn't very well thought out. This week's puzzle had a number square with a mistake in it.
Should the mother do anything else? Are there any other reasons any of the numbers are the odd one out?
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Learning to shrug and move on when faced with being told you're wrong because of this kind of narrow-mindedness / intelligence level mismatch is one of the most important lessons that primary school teaches you, surely?
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Working at a school, I have learnt that teachers are not always right. :-\
Unfortunately, both text books and exam papers are usually written by teachers. ::-)
Only today, I pointed out a mis-spelled word on a worksheet, only to be shown the text book that also spelled the word incorrectly. :facepalm:
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Odd one out questions should always be marked correct if the student can give a valid reason. They should be always marked incorrect if there is no valid reason given.
I hate them. They are the spawn of the devil and officially deprecated in any assessment course I have attended.
The smart answer would be to give five valid reasons whay each of the five should be considered the odd one out.
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IME quite a lot of homework is phrased in a way that probably makes sense in the context of a lesson but by the time the child gets home they've forgotten exactly what the context was, and of course when they ask mum and dad for help, they've never had any context whatsoever.
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I've seen questions where there is no correct answer, especially in maths.
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TLD had some homework, last year that asked a question but there was no way of working out the answer from the data given (it was Maths).
She looked at it, spent ages trying to work it out, then asked me.
I told her to write "Unable to give answer due to information not given" or words to that effect.
She got full marks for that homework, the teacher altered the wording then asked her to redo it, for which she got full marks again :)
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Yesterday's problem was fill in a "magic square" using the digits 2-10, such that each row, column and diagonal added up to 18. Taking Cudzo's point I hope there was some context given in the lesson, as it was v. hard. Presumably at that level (aged 8 ) it is about number patterns and simple adding up. A swift google found a method, so I filled in 2 of the 9 squares,leaving the Small Person to complete the rest. Is there an algorithm for these? (goes off to google it more)
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TLD had some homework, last year that asked a question but there was no way of working out the answer from the data given (it was Maths).
She looked at it, spent ages trying to work it out, then asked me.
I told her to write "Unable to give answer due to information not given" or words to that effect.
She got full marks for that homework, the teacher altered the wording then asked her to redo it, for which she got full marks again :)
That's a bit mean!
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Yesterday's problem was fill in a "magic square" using the digits 2-10, such that each row, column and diagonal added up to 18. Taking Cudzo's point I hope there was some context given in the lesson, as it was v. hard. Presumably at that level (aged 8 ) it is about number patterns and simple adding up. A swift google found a method, so I filled in 2 of the 9 squares,leaving the Small Person to complete the rest. Is there an algorithm for these? (goes off to google it more)
rule of thumb, stick the middle number in the center, in this case 6.
e.g.
7 2 9
8 6 4
3 10 5
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One of my S-i-Ls once asked for my help with a long worksheet she'd been given by her science teacher and she didn't have a clue. It was clear the teacher had written all the questions without recourse to a text book and as they were a bit "clever-clever" the teacher was probably very pleased with himself.
Unfortunately every single question on the sheet contained errors or were wildly ambiguous. Luckily it was clear what answer the teacher expected. So for each one I explained how to get the right answer, and explained what answer the teacher probably wanted. She asked which answer she should put. Given the comment above, I asked whether the teacher would appreciate having their work criticised.
She got full marks.
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I've seen questions where there is no correct answer, especially in maths.
I did an awful lot of maths homework where there was no correct answer, but that wasn't because of the questions. :-[
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I've seen questions where there is no correct answer, especially in maths.
I did an awful lot of maths homework where there was no correct answer, but that wasn't because of the questions. :-[
;D
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Which is the odd one out and why?
10 21 18 61 25
I was helping a Small Person I know with this. I suggested she check her list of times tables to see if any of the numbers weren't in it (having spotted that 61 is prime). Some minutes later the Small Person declared that 61 wasn't in it, so wrote that as the answer.
I saw her again today. The answer the teacher gave was 25, as it was the only number that didn't feature the digit 1. A valid response, just as valid as the Small Person's, which got marked wrongly.
I think we saw primes in year 5, and you'd want a child to be very familiar indeed with the concept before trying a question like this on them without context. For 11+ / Common Entrance or higher levels, Small Person's answer is the best.
If you have to answer 25, then "it's the only square number" is reasonably year-4-friendly and mathematically cogent. "Not featuring the digit 1" is a really stupid reason, largely because a 1 in the tens column and a 1 in the units column mean different things, so it's counterproductive to suggest to a learner that this is a pattern to be looking for.
To finish off the challenge with successively less plausible answers, 21 is the only Fibonacci number in the set; and 18 is the only abundant number (it's less than the sum of all its proper factors 9+6+3+2+1 = 21)
Ten is just not very special. It's the only number in the set which isn't special in any really mathematical way. That makes it the odd one out, of course.
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21 is the only Fibonnaci number in the set
Nice. Fibonacci numbers came up in conversation elsewhere the other day. I met a trader (currency, I think) who uses some Fibonacci thing to determine when to get in or out of a trade. I boggled. A lot.
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The only Fibonacci (thanks for the spelling correction) phenomenon I've ever thought I've seen in the markets was during a period in the early 90s when the pound was trading around $1.62. Far more often than you'd expect, the reported price was very close to £1 = $1.6180 --- or equivalently, $1 = £0.6180.
My conjecture was that the telephone quotes common at the time were being given without the leading figures, and with the price just there a quote given the wrong way up (pounds per dollar instead of dollars per pound) would also sound sensible. A very small number of misunderstandings could lead to the market being sticky at the Golden Ratio price.
Re magic squares: constructing one can be a fiddly task with no particular purpose or rules, though some hobbyists seem to enjoy the game. Knight's moves tend to feature. But if you've got one it's easy to find another: the Small Person will have seen a square using the numbers 1-9, and she can just add one to each entry to get a square using 2-10. The total of each row will go up by 3, of course.
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But if you've got one it's easy to find another: the Small Person will have seen a square using the numbers 1-9, and she can just add one to each entry to get a square using 2-10. The total of each row will go up by 3, of course.
<smacks own head> That's blindingly obvious now you mention it. Still a bit of a step for an 8 year old perhaps.
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Middle child came home with an astronomy worksheet with constellations to tick off when they saw them.
So we ticked off the plough and cassiopeia and orion. But next to Leo I had to write a note. 'This week Leo is not visible in the night sky until 2am. As I am unwilling to let XXX stay up this late on a school night he has been unable to complete his homework'
Maybe it was just there to catch out the ones who were cheating..
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what time does Leo set? could it be more appropriately witnessed at say 7am before the journey to school?
However I recognise this may also not be a practical option for some kids who "don't do mornings"
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Not dark at that time. This is Scotland..
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It's dark here at 7am, honest.
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Depends on the time of year. Wait a week and it will be light at 7am.
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Which is the odd one out and why?
10 21 18 61 25
61. I've been all the rest.
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61 is the only prime.
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Helping Miss Dan the Elder with some maths terms homework ... definitions provided include:
angle - distance between two lines (no mention that the units might not be cm, nor of circles or crossing lines or rotation)
diameter - distance across a circle (no mention of the center)
measure - cm, m, km, grams, litres etc (they have other alternative words but not "units" and no suggestion that measure might be a verb)
rhombus - squashed square (there is talk of side length, angles, parallel elsewhere - I cannot help thinking that I've squashed it by sitting on it)
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Which is the odd one out and why?
10 21 18 61 25
Reordering them as 10, 18, 21, 25, 61 and converting to their alphabetic equivalents, and allowing for rollovers (A=1, 27, 53, etc.), the set becomes J, R, U, Y, I. If you look at the frequency distribution of these letters in Scrabble, you find that the only odd occurence is the letter I, of which there are nine in the game. Therefore 61 must be the odd one out.