[Closed] How many 10s in 868?

Crap!!

8 hundreds 6 tens 8 units

guess it depends on how the question is asked tho

Reminds me of the film Little Man Tate, when the eponymous character gets asked "which of the following numbers are divisible by 7?" and he replies - quite correctly - "all of them". The question is pitched and asked for a given audience, which means the answer might be nonsense to the "wrong" audience.

[i]8 hundreds 6 tens 8 units[/i]

But there are 80 10s in 8 hundreds..

86.8 is the answer I'd have given

6 is just some made up hippy bullshit

But there are 80 10s in 8 hundreds..

I was taught hundreds/tens/units at primary school, from the thread I assume it wasn't universal.

This is my point - especially in mathematics, you have to phrase questions properly, you should have to second-guess what the questioner was getting at. I would have said 86.8 too.

In the second example, the correct answer is apparently 10. Which again I can see how they get that, but it's a nonsense question.

It could also be 86 tens and 8 singles.

But in the context of teaching hundreds, tens and units, 6 is perfectly correct. Don't call it rubbish when you don't know the context.

IIRC hundreds, tens and units was taught before division. 86 or 86.8 is the answer to a division question, which presumably doesn't exist for these kids.

So if 868 were written in Hex (364) then that answer suggests it would have 6 sixteens but no 10s, whereas in decimal it has 6 tens and no 16s? But the number itself remains divisible by both 10 and 16 in exactly the same way regardless of how it's expressed. That's gotta confuse some kids.

or try writing it properly
eight hundred and sixty eight (aka eight hundreds, six tens and eight)

you wouldn't say
eighty sixty eight
or
eighty six tens and eight
would you?

86.8 is the answer to "what is 868 divided by ten?"

86 or 86.8 is the answer to a division question, which presumably doesn't exist for these kids.

It's mathematics - the correct answer shouldn't be different depending on the assumed knowledge of the student.

Some people would say eight sixty eight. A lot of people say things like 'twenty-six hundred' instead of 'two thousand six hundred' too.

Or it could be six gross and a third of a dozen.

It's mathematics - the correct answer shouldn't be different depending on the assumed knowledge of the student.

Its like these questions that are posed in facebook which go along the lines of 1 x 2 - 3 + 4 x 6 = ??? Which are nonsense without brackets.

A lot of people say things like

Which are nonsense without brackets.

don't most math science degrees begin with forget everything you've learned so far none of it is that simple.

I remember in my third year we finally proved that 1+1 = 2 😉 (first you need to define what zero is, then what 1 is and how your set of integers is constructed from that, then what + means and then you can get to the proof.)

doesn't make them right tho does it

I think technically, in English, it does 🙂

I remember a brilliantly phrased question from when I was at University. It read "Write down what you know about <subject>" I answered "Nothing". I reckon I should have got 100% for that answer.....!

Which are nonsense without brackets

No they're not. Maths operations have a specific order so even without brackets you know which parts to calculate first. Brackets are part of that specific order but aren't a necessity for the example you posted.

Look up BODMAS.

[EDIT - beaten to it by D0NK]

How many tens in 868?
At least three.

DrP

I had this with Jr a few years ago. It ties in with the methodology they are being taught for multiplication/division known as 'chunking'.

8 hundreds 6 tens 8 units

That's how I was taught at junior school. It's not a mathematics question, it's a numeracy question. It's part of teaching kids the significance of columns in numbers. (I remember at the time, one kid who would write two hundred and thirty seven as 200307...)

OPs question is only confusing because it is missing the context:

e.g. it is a test about "Place Values" not division.

http://www.mathsisfun.com/place-value.html

In the second example, the correct answer is apparently 10. Which again I can see how they get that, but it's a nonsense question.

?? 5 surely?

1.5 is 1 unit and 5 tenths.

But the number itself remains divisible by both 10 and 16 in exactly the same way regardless of how it's expressed. That's gotta confuse some kids.

By the time they move on to bases other than decimal, they'll have - no, they'll [i]need[/i] - a firm grasp of what the columns mean.

1.5 is 1 unit and 5 tenths.

The logic, apparently, is that if you divide 1.5 into 10ths, there are 10 10ths in 1.5.

Basically, the correct answer to "How many 10ths are there in xxxx" is always 10.

And yes, I can see where they're going with place values, but they're still assuming the knowledge level of the pupil - my 3-year-old can grasp place value.

I had this with Jr a few years ago. It ties in with the methodology they are being taught for multiplication/division known as 'chunking'.

My daughter's learning long division at the moment, and she uses a really weird method to do it, nothing like how I learnt it... I just go along with her, I really don't want to confuse her by doing it a different way.

I get the feeling a lot of people on this thread haven't realised that maths teaching has moved on since they were kids! (Or that it can be taught in different ways).

[i]It's not a mathematics question, it's a numeracy question.[/i]

this the teaching of maths is very structured now.

If your child is still being taught about 100's, 10's and units then they won't expected to be in a position to also do the long division necessary to work out it's 86.8 10's.

If you try and get your child to do the 86.8 thing before they've firmly grasped place when working out tens and units you may cause problems.

If you have concerns I'd talk to the teacher about how the curriculum is being taught in your child's school.

I have some knowledge about English teaching of maths but not sure what differs in Scotland.

Most people don't remember how they were taught maths - I suspect we've all been through this process.

[edit] seen your most recent post - talk to them - they shoudl be differentiating work and have a specific learnign objective for each pupil in every lesson.

The logic, apparently, is that if you divide 1.5 into 10ths, there are 10 10ths in 1.5.

Eh???????

If it is [i]actually[/i] meant to be a division then surely there are 15 tenths in 1.5?

i.e. it could be written as the fraction 15/10 or as the words "fifteen tenths"

But if that question is from the same test as the first one then it is using the same language so [i]should[/i] also be referring to place value and the answer [i]should[/i] be 5.

The logic, apparently, is that if you divide 1.5 into 10ths, there are 10 10ths in 1.5.

Basically, the correct answer to "How many 10ths are there in xxxx" is always 10.

That is really crap. The how many tens thing I could accept but this?

By the time they move on to bases other than decimal, they'll have - no, they'll need - a firm grasp of what the columns mean.

Yep! Which is why it irks me that people teach kids to count from one to ten. We should teach them to count the units: ZERO to nine. Would save a lot of confusion IMO

The logic, apparently, is that if you divide 1.5 into 10ths, there are 10 10ths in 1.5.

Basically, the correct answer to "How many 10ths are there in xxxx" is always 10.

It really isn't. I think you must be mistaken, there's no logic whatsoever that would make that correct.

We should teach them to count the units: ZERO to nine. Would save a lot of confusion IMO

PS. I also presumed using place values the answer to the 1.5 tenths question was 5, you sure it's 10?

It really isn't. I think you must be mistaken, there's no logic whatsoever that would make that correct.

The full discussion is over on Mumsnet apparently - I just got it second-hand from the missus.

But I can see what the questioner is getting at. If you cut a cake into 10ths, it has 10 10ths. So if you asked "How many 10ths are there in a cake?" The answer would be 10. Substitute 1.5 for cake.

But it's a trick question really - like what's the difference between one quarter of a million dollars and one-quarter of a million dollars?

(The former is 25 cents, the latter is $250,000. Or maybe it's the other way around)

I would have guessed that dad got kid's homework wrong.

It is a method of teaching. It is not 'maths' the way a fully grown man would possibly understand it. Most people probably learned about numbers this way but have forgotten that this was a formative step en route to doing maths - it isn't maths, but it helps to teach it.

we also count on fingers, holding up your left thumb and saying "zero" is even more confusing shirley?

"zero" is "no fingers."

But I can see what the questioner is getting at. If you cut a cake into 10ths, it has 10 10ths. So if you asked "How many 10ths are there in a cake?" The answer would be 10. Substitute 1.5 for cake.

Yeah, but then you'd start with 1.5 cakes, so you'd have fifteen tenths.

And it's wrong anyway in the context of the first example, you've moved the goalposts. The first question is asking about units columns, the second (as you explain it) is a division question. Both are valid answers (ie, 5 or 15), but you can't just follow a units question with a mathematical division question without context, that's the sort of wooly unsolvable nonsense that ends up on Facebook. In the context of the first question, the answer to the second is "5," end of.

I'll say it again. Unless you're dealing in something other than decimal there is no way while I've got a hole in my arse that the correct answer to "how many tenths are there in 1.5" is "10."

Orbital mechanics (aka dead hard sums aka maths) allows us to plan the landing of a probe on a comet a bazillion miles away and works because maths is well-defined and not open to interpretation. Everything else is just bollocks.

But aswell as just reeling off the numbers 1 - 10 we also count on fingers, holding up your left thumb and saying "zero" is even more confusing shirley?

Just start with no fingers when you say zero.

(I'm doing this with my two kids because personally I think holding off on the concept of zero as some kind of "special thing" is anachronistic. Kids understand the concept of "none" - it's not hard).

Substitute 1.5 for cake.

Yeah.. but.. that only works because you have chose to substitute 1.5 (cakes) for 1 (cake).

You can't hold up one and half cakes and say you have one cake.

It's like saying "How many 427 sheep do I have in that field?"
"That's right I have one 427 sheep."

Edit: Cougar is clearly on my wavelength and [s]has less work to do[/s] [i]is a faster typist[/i]. 😉

"zero" is "no fingers."

0-9 may make sense for properly counting Tens, just not sure how it would work - I guess I'm probably tied to the decimal = count on [s]fingers[/s] digits concept.

D0NK: you can put your thumb up to count ten, but then, importantly, LEAVE it up as you count up to 19 😀

(Oh and make it your left thumb, tens go on the left!)

Did cross my mind but what about after 19?
sorry not trying to shoot it down just want to get my head around it
Would also teaching kids binary help with this sort of thing aswell? stop thinking purely in decimal and concentrate on the units/values? or just confuse matters further? the option to count upto a 1023 on your hands has geek appeal 🙂

Did cross my mind but what about after 19?

Nobody likes a clever dick.

Ultimately I think it is flawed either way D0NK (really having ten fingers means that we [i]should[/i] theoretically use a base 11 counting system 😀 )

I think the important thing is to get kids used to the idea of zero as the starting number, rather than introducing it as some magically thing that appears as "a placeholder" at ten - and then reintroducing it as a proper number when they get to number lines etc.

(Note: I am not a teacher, just a parent. And a programmer)

I did see that coming cougar (fnar fnar) but thought no-one would be base (10) enough to say it

graham fair enough. May start doing 0 1 2 3 4 5 6 7 8 9 *pause* ten start again! or something
IMO it's 10-19 that screw it up, especially 11 and 12, after that you've got proper sets twenty thirty etc, why do we have eleven instead of "onety one" or "oneteen"?

The full discussion is over on Mumsnet apparently

http://www.mumsnet.com/Talk/_chat/a1988081-How-many-tenths-in-1-5

[i]One thousand posts[/i] 😯

Eh. I must be thick as the answer is 86 (.8). How is the answer 6?

hora: it's not about division:

See> http://www.mathsisfun.com/place-value.html <

IMO it's 10-19 that screw it up, especially 11 and 12, after that you've got proper sets twenty thirty etc, why do we have eleven instead of "onety one" or "oneteen"?

A man after my own heart 😀

It's amazing how many of these [i]universally-accepted-yet-weird[/i] things you notice when you have kids and they start asking "Why?" 😀

English is just as fickle: e.g. drink, drunk, drank.. wtf?

Really odd when I thunk about it properly.

I was Mr thicky McThick at Maths but having read the posts even I get it. OP it's not hard, really it isnt.

After looking at the first page of Mumsnet there I see where they were going with this now.

10. There are always 10 tenths of a whole whether the whole be 15 or 370. Each tenth is 1.5.

The "logic" here is you have "something", you divide it by ten, how many parts do you have? Ten!

It's flawed logic though. If your "whole" is six oranges, you'd end up with ten tenths of six oranges, which is nonsensical.

The thread says it's a badly worded question. It's not, it's just out of context. The kid learns about units all day - hundreds, tens, units, tenths, hundredths - then comes home and goes "mum, how many tenths are there in 1.5?", mum then posts to Mumsnet and chaos ensues because they've not been given sufficient information to solve the question in the manner being tested for.

Orbital mechanics (aka dead hard sums aka maths) allows us to plan the landing of a probe on a comet a bazillion miles away

if you have difficulty with hundreds tens and units don't look at [url= http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/representingdata2rev4.shtml ]leaf diagrams[/url]

And the truth is revealed.

That question is from a different sheet.

I was right about moving goalposts. They're two different examples from two different question sheets (potentially) testing two different things. No wonder it ran to a thousand posts.

Mumsnet... It's flawed logic though

Quite!

(Maybe that could be their tagline?)

Eh. I must be thick as the answer is 86 (.8). How is the answer 6?

868

8 'hundreds'
6 'tens'
8 'units'

DONK I just tried

[img] [/img]

[s]mum[/s] Hora then posts to Mumsnet and chaos ensues

if you have difficulty with hundreds tens and units don't look at leaf diagrams

Easy enough to understand, I just wonder [i]why[/i] you would want to set your data out like that?

It's a histogram for people without Excel. 🙂

(and better than a histogram in one respect, as it leaves the original data intact).

That Mumsnet page just keeps on giving. "I have a maths degree!" - yes, but this is Key Stage 2. Your average junior school kid isn't going to be doing differential calculus, they're going to be learning what it means when you move a digit one to the left.

"I have a maths degree!"

Like the pilots and aircraft engineers that show up on the airplane/conveyor belt thread.. and get it wrong. 😀

My wife has a Master Degree in how the under 7's learn mathematical concepts.

It's sometimes quite counter-intuitive for those of us who already understand it.

Gods, someone's talking about Base 1 now. WTF is base 1? A numerical system where a digit can have [i]one[/i] value?

"Count after me, children:
1,
11,
111,
1111,
..."

"Miss, what's 1 minus 1?"

"Don't be clever, Henry."

Its like these questions that are posed in facebook which go along the lines of 1 x 2 - 3 + 4 x 6 = ??? Which are nonsense without brackets.

Firstly:

It's like the questions which are posted on Facebook, which go along the lines of 1 x 2 - 3 + 4 x 6 = ? , which are nonsense without brackets.

No brackets, not nonsense:
1 x 2 - 3 + 4 x 6 = 2 - 3 + 24 = 23

On the original question, division by ten and "how many tens?" on a place value exercise are very different.

[i] A numerical system where a digit can have one value? [/i]

I'm all for base 0.

It's a histogram for people without Excel.

My first thought was why bother doing it like that, when you could just use a spreadsheet 🙂

TBH, I think I'd rather my kids learned to use a spreadsheet than learning about leaf diagrams, seems more useful. Although I'm willing to admit I could be missing something, do these diagrams lead on to something more interesting?

I'm a qualified primary school teacher, who now teaches GCSE maths and A level physics. Am I correct in thinking I'll get annoyed if I look at the Mumsnet thead?

Unless you're dealing in something other than decimal there is no way while I've got a hole in my arse that the correct answer to "how many tenths are there in 1.5" is "10."

I think when teaching kids they just leave out a bit of context that we as grown ups need due to our extra knowledge of division. The question would be better phrased as...

"How many tenths [b][i]of 1.5[/i][/b] are there in 1.5?"

That makes the answer obviously 10. They are trying to test that the puplil knows that "tenths" = spilt into ten lumps.

A similar question could be...

"How many eighths (of 763) are there in 763?" with the answer being 8.

Its not intuative but then I'm not 8. I may have to take a course when my kids are old enough to go to school!

I think I'd rather my kids learned to use a spreadsheet than learning about leaf diagrams

It's not one or the other.

(Although, I'd never even heard of a stem and leaf plot until I taught it for the first time, and I'm still non-the-wiser on when they'd be used. They do make it easier to find the mode and median values when working by hand.)

No brackets, not nonsense:

Again, it is a nonsensical without context. You're correct according to operator precedence, but would primary school children be learning BODMAS?

That's the mistake some of the Mumsnet lot are making, all degrees and no common sense.

would primary school children be learning BODMAS?

Yes.

Fair enough then (-: It was actually a genuine question, you answered before I edited the post to say so.

"How many eighths (of 763) are there in 763?" with the answer being 8.

I find it hard to believe that this is the sort of question that would be asked in a school maths lesson. A Christmas cracker, maybe.

It's not one or the other.

(Although, I'd never even heard of a stem and leaf plot until I taught it for the first time, and I'm still non-the-wiser on when they'd be used. They do make it easier to find the mode and median values when working by hand.)

I appreciate you could teach both, but I'm still thinking that leaf diagrams are a bit of a waste of time, and given that time is limited it would be better spent on learning how to get Excel to do the hard work for you. (With appropriate theory taught first of course, not just plugging the numbers in and getting the answer!)

ten tenths of six oranges

BOOM!

I teach stem and leaf diagrams because they're on the exam, not because I think they're useful 🙂

"How many tenths of 1.5 are there in 1.5?"

That makes the answer obviously 10.

No that makes it WAAAY less obvious.

a "tenth of 1.5" is 0.15

So "How many tenths of 1.5 are there in 1.5?" means "How many 0.15 are there in 1.5"

They are trying to test that the puplil knows that "tenths" = spilt into ten lumps.

They're not. Mumsnet has it wrong.

They are either testing division skills (possibly) or they are testing knowledge about place values (most likely).

If they wanted to test splitting whole things into ten parts as the definition of "tenth" then the question would have been "What is a tenth of 1.5?"

I appreciate you could teach both, but I'm still thinking that leaf diagrams are a bit of a waste of time, and given that time is limited it would be better spent on learning how to get Excel to do the hard work for you.

Same argument as [i]"Why teach kids to multiply or divide when in reality they'll just use a calculator."[/i]

Same argument as "Why teach kids to multiply or divide when in reality they'll just use a calculator."

Not sure it is, a leaf diagram seems to have little or no use in real life, beyond passing your GCSE maths exam.

Whereas long division... 😉