Ambiguity - Mathematics.

[Wizard19]

DD Y3 had a question.

How would you answer the question, How many tens in 100?
How many tens in 427?

DD who is very able mathematically answered the latter as 42.
Expected answer was 2.

If that is the correct answer, then it follows that there are zero tens in 100!

How would you mark that as a teacher, as children work in mixed abilities and one answer shows understanding beyond the basic place value?

guys:

though I take your point...and in now way doubt your abilities as mathematicians (Rafa/ LikeaSoul)...

What I think the parent (Wizard 19) was querying was why '2' was the correct answer for how many tens in 427.

I totally get the strange wording issues/ poorly phrased question & that there are many ways one can interpret that question

I totally get that you can divide 427 by 10 and indeed find that 'ten can go into 427 some 42 times'

But -

and I fear this is the point I'm trying to make

in a test situation

the 11+ or KS2 SATs

Most parents oddly enough want their child to do well on tests - to get into good schools/ to get into top sets/ etc.....

How many tens in XXX is pretty much 'standard format' - it's how in the present 'teaching maths' mindset - place value is discussed - How many hundreds in 9876? Not What is the digit in the hundreds column? What value does it have? (as I would have been taught - in a 2-step system at a similarly young age).

I get the points RAFA is making & LikeaSoul (a mathematician) is making - but both are using (as I do) language to describe mathematics which is 'out of step' with what is presently being used in many primaries or appears on DfE guidance (programmes of study/ best practice/ government research documents).

So - stepping back - and looking at this as a parent asking why is X answer correct and Y answer wrong. Why wasn't my child rewarded for Y answer - I think that shows real flair/ ability in maths?

I was trying to explain that the test was less about calculation (working out how many times ten can go into a particular number) - and more about number patterns (so the sequence question) and symbolism (the tens [column] questions). (the government is very big on this now - no bad thing - but probably not something that was consciously taught much in the past).

I suspect - like many schools - Today is Thursday and we're learning X - was the thinking behind it. It's a very compartmentalized approach - and one that implies teachers buying in teaching materials and teaching to the package. I don't totally fault the approach - as sometimes I think you need to stop calculation work and talk about wider concepts/ constructs. But as a parent - much like wizard19 - with no worked examples or clear instructions (this test is working on X issues & we use Y terminology now for that) - it can be really perplexing why '2' is correct for How many tens in 427.

I appreciate & respect your mathematical abilities/ experience/ and approaches but at core helping this parent understand why her child's answer was considered wrong was the issue.

This is primary school maths after all - it was a while ago - but I'm sure you can remember the tyranny of only one right answer and no credit for attempting something imaginative or novel.

People, I don't think you need to explain place value to the OP, she clearly understands the question and both possible answers.
OP I work in a mathematical area and agree your DD's response shows better understanding of number than the answer 2 would. It's like those questions that ask how many squares there are in the diagram isn't it? Weaker mathematicians only see the smallest squares, stronger ones count larger ones made up of 4 & 9 small squares too.

So yes I'd expect if the teacher had thought about it (s)he'd mark it correct. I think the PP who said the teacher was probably just ticking off against a list of correct answers has probably got the measure of the situation.

Badly written test altogether. 360 in figures is 360, as a previous poster has said! Unless it was a trick question.......

catkind I'm also wondering if the teacher/TA marked it on autopilot - not blaming them for that, they have so much to do!

Catkind

OP asked:

How would you answer the question, How many tens in 100?
How many tens in 427?

[deleted aside] Expected answer was 2.

If that is the correct answer, then it follows that there are zero tens in 100!

So that doesn't exactly sound to me like OP understood that 0 TENS (meaning the digit in the tens column is zero) was the correct answer.

I don't think it's helpful to imply that the child who answers 2 to the How many tens in 427 is a weaker mathematician. Understanding place value which is a stepping stone to understanding borrowing/ carrying is important and is of as much value as understanding the concept of multiplying/ dividing by ten - which in Birmingham (and I think we all know this city isn't particularly well known for its highly educated population) is Year 2 skill vs. place value/ borrowing carrying/ base 10/ binary numbers/ number pattern skills being Y4+. I think people miss that place value is the touch stone to these more complicated number pattern skills. Thus my spirited defence of place value as an important element in primary/ elementary maths/ math curriculum.

As we've all discussed - there are a myriad of ways to think through this poorly worded question - the point (as I see it at least) was to discuss why 2 is the right answer for how many tens in 427 and 0 is the right answer for how many tens in 100.

and yes LikeASoul -

I agree - a teacher just ticking right/ wrong and not explaining why a question's answer is wrong doesn't really help the pupil.

DD2 has changed schools and one of the things I totally adore about the school is when a question is wrong there's usually a little comment....

try working through this problem again - I think you'll see you made a simple addition error.

or

try thinking about this from the point of view of what you do know (for a missing value of an angle question) about how many degrees are in a straight line. It will help you solve the problem. Try again - if you can't solve it - let me know and I'll help in class.

HTH

PastSellByDate - yes, I think OP was making the point that most people would take how many 10s in 100 to be a division question. Just like you'd take how many 2s in 10 to be a division question.

Just asked my 5 year old and (maths grad) husband both questions and both also said 10 and 42, as would I have (maths PhD). Not sure what that proves about sophistication, but certainly suggests that to those who haven't just been drilled in Hundreds Tens and Units this is not obviously a place value question.

I get the points RAFA is making & LikeaSoul (a mathematician) is making - but both are using (as I do) language to describe mathematics which is 'out of step' with what is presently being used in many primaries or appears on DfE guidance (programmes of study/ best practice/ government research documents).

I'm not sure where you've got the idea that this is out of step from. The new curriculum mentions this when talking about using place value to help calculate. The additional guidance suggests children in KS1 should be able to partition numbers such as 23 not only into 20+3, but also 10+13 for use in calculation. Best practice would suggest that in order to do that they need to understand what ones, tens and hundreds are and how they relate to each other. I'm pretty sure that similar skills were taught under the 2006 and 1999 frameworks as well.

Is this not another case of St Mediocre missing out large chunks of the maths curriculum?

Montessori materials are really very good at demonstrating this.

The montessori bead system demonstrates that once you have 10 '10 beads', you have 100. The 10 '10 beads' are then exchanged for 1 'hundred square'. Once you have that hundred square, you can't take any away from it - it's a complete square, bonded together. The only way you can take a 10 from it, or count a 10 within it, is to break it back into 10 '10 beads', by exchanging the 100 square for 10 '10 beads'. They use a place value mat to lay the items on, so it's very visual.

Similarly, the stamp game - if you need a 10, you have to 'cash in' a 100 for ten 10s, then you can use them as you require.

So a question asking 'how many tens are there....' would be very obviously answered, because only the 10 beads would be available for counting in the 10's column.

Because we use the same digits (0-9) to convey hundreds, tens and units, relying on their place to signify what value they have, it is easy to see them as 'the same' and equally available.

I made my own montessori beads and they've been so very helpful.

I have been marking maths assessments today. Very similar question...how many tens in a number - infact, may have been the very same number.

I marked 42 as the correct answer. The mark scheme also said to allow 2.

This was a general maths assessment covering lots of maths areas, not just focusing on place value or division.

Infact the other questions sound very similar. These were the first 4 or 5 questions and designed to be mental maths style - read aloud to the child. So the "write 204 in figures" means exactly that - write it using the actual digits or numerals. Not write it in words. The same assessment asks for the latter later on.

www.wiganschoolsonline.net/curriculum/maths/docs/Assessment/Y2%20Block%201%20Questions.pdf

Page 9

Though it is meant to be a year 2 autumn term assessment. FWIW, though, we find this assessments rather generous.

I am fucked when my kid starts bringing maths homework home.

You guys will still be here, right?

Don't worry, we'll still be here.

Probably still arguing about place value, ambiguous questions and BIDMAS

Look guys - I totally take your points and I'm not saying your way of looking at it is wrong or that the question was well written....

I'm saying that the teacher was justified to see there was only one solution to those questions:

How many tens in 427 - answer 2
How many tens in 100 - answer 0

they were asking about place value

Lovely to debate merits of other answers - but in a test situation (KS2 SATs or 11+) - answering 42 or 10 (treating the above questions respectively as divisions) would just be incorrect.

Putting it to you rhetorically - if you were to ask a pupil

How many tens go into 427 - and they wrote 2 - would you mark that correct? For your logic to work - you'd have to allow two answers for what is a division question but could be interpreted by some as a place value question.

Does it help the parent or more importantly her DC to see there are multiple answers to this test question? Or does it help to discuss what the question was looking for and why 'the expected' answers were correct. I respect it's ambiguous - and maybe that needs to be raised with the teacher in terms of how to prepare children to distinguish division word problems from place value word problems on standard tests.

Can you link to standard test with this phrasing, because in my experience it isn't that common? Most of the resource books I have here use a different wording and I can't at the moment find anything online that uses that wording either, although I'm sue there probably is some stuff out there?

I would mark 2 wrong for 'how many tens go into 427?' wrong because it is wrong. There is no different interpretation for it. That question is not ambiguous it has one answer.

Appallingly worded question. Totally muddles up integer division with ideas of place value. Tell the teacher to do better or use different materials. Your child's answer was fine. Tell the teacher to correct her mark and use better Q&A materials.

But it is a standard wording for a division question. In fact it sounds like in hula's markscheme to the same quiz, 42 was the intended answer but 2 was also accepted.

To be fair this type of question wouldn't be written like this in real SATs. They are less ambiguous.

It may well be that it is now standard practice in primary maths to ask questions about place value like this - the confusion is coming because in real life and in primary maths when doing division, you also ask 'how many tens in 427' and expect to get 42, 42 remainder 7 or 42.7 as your answer depending on their sophistication at maths.

Asked ds1 this earlier (y5) and he's given me all 4 answers straight off saying 'well depends what sort of maths you are doing' explained each of the 4 answers to me so even he at Y5 (albeit good at maths for his age) can recognise it's a badly worded maths question!

Well I saw lots of extended family over the weekend so I asked them. Round the table were four retired primary teachers, a couple of maths grads, couple of other relatives plus three primary aged children.

They all gave the same answer: 42. Well apart from the one in year 6 who said 42.7

Oh and even after I then explained the alternative interpretation of the question, the teachers were unanimous in agreeing that marking the answer 42 as wrong would be totally wrong.