Can someone do this Y4 maths question for me please?

[cantdomaths]

Brain is muddled...

There are 170 people in a hall.
There are 6 times as many girls as boys.
There are 6 more boys than teachers.
How many teachers are there?

I have Maths A level...but have also been drinking wine....

I asked my ds to do Arkadia's question, without using algebra. He used trial and error method. And figured out right answer in about 10 minutes.
So, definitely doable with only primary maths knowledge.

Yes, with trial and error you can solve a lot of problems, but it defeats the purpose of the problem, doesn't it? Besides I can give you the same probelm with big numbers or with a solution not within N, in which case it would be near to impossible to do it or at least it would require a VERY long time.

But the purpose of these question is to stretch your brain, to think the way to solve it, understand what's needed to answer, figure out what to do to achieve the solution and enthusiasm to do it without giving up thinking it's too complicated.
Once they hit secondary, they will use algebra. But using bar method, trial error etc definitely benefit the children.

with trial and error you can solve a lot of problems, but it defeats the purpose of the problem

I don't fully agree, if you know a methodology, then just applying it is no more defeating the purpose than using your knowledge of maths to trial and error it quickly. I'm sure irvineoneohone's DS wasn't going

1, no, 2, no, 3, no …

but using some solid estimation techniques to get close and then test. Having the number knowledge to estimate well is at least as significant a skill as knowing some technique to answer it - especially when the technique seems to be a stop-gap until algebra.

Of course as you're suggesting having the maths knowledge to enable you to recognise which of the techniques you know can be used is also important, but I don't think it nullifies trial and error completely.

Well, trial and error is usually brute force. The bar modelling technique allows you to see patterns and find solutions which are valid for any number.

I was googling trying to understand when one must use trial and error and instead have come across this one:

John has some money, Mary has 50% less. If John gives Mary £15, she will have 40% less than John.
What was the amount of money they started off with?

I didn't know how to do it, so I tried trial and error, but couldn't use that either :D

John: £240
Mary: £120

£240 - £15 = £225
£120 + £15 = £135

£130 / £ 225 = 0.6

I think it's the right answer.
I have shown ds the question before he went to bed last night. Done it in his head, in bed, using trial and error, told me the answer this morning,

This is maths for Year 4?!

I had no idea how to do it and to be honest am not even sure I understand even with the explanation.

@thatmustbenigelwiththebrie, ad I was saying upthread, it is perfectly doable by a Y4 (or y3), assuming he has been taught in the past the right technique problem solving. It is a bit like asking whether one can do 332x759 without ever having seen a long moltiplicati on or a times table. It would require an awful long time :D

Arkadia, I think grade/year 4 in Singapore is not same age as yr4 in English/Scottish system. So slightly older. But I agree, it's difference between knowing the method or not.

And to be quite efficient in using trial and error, you only need a good basic grasp of maths, so you don't need to go through tedious try, and can be able to do a educated guess at what numbers to start with. Because primary maths wouldn't be likely to give them a ridiculously big numbers to work with.

My experience with the bar models is limited to what I've read on here, mostly from Arkadia.

I attempted the chicken problem by using bars and worked it out pretty quickly, less than 15 minutes.

Must be some kind of genius, me ;)

Usually I would just throw algebra at any sort of problem with unknowns and would never even stop to think. Algebra for me does not involve thinking, just applying technique, whereas the bar model is much more elegant but requires me to actually think about what I'm doing.

The way I solved it with bars was:
One long bar, original chickens
half that length, original ducks
cut off 16 withing original ducks bar, to make final ducks. Do that twice to show that final ducks +16 + final ducks + 16 = original chickens.
Now within that long bar, cut the final ducks in half to make final chickens (again, do that twice)
So now my bar looks like this:
Final chickens + final chickens + 16 + final chickens + final chickens + 16 = long bar for original chickens.
Final chickens is original chickens -272
So if I take one 'final chickens' off my bar, the rest adds up to 272
So my sum is
final chickens + 16 + final chickens + final chickens + 16 = 272
3xfinal chickens +32 = 272
3x final chickens = 240
final chickens = 80

Arkadia, may I ask, if I were going to teach DS (a young Y4, fairly able in maths) to use the bar method, can you suggest any resources, online and off?

ah, this thread's popped up again. I mentioned my son's use of 2s and 7s upthread. I think that's a good example of "intelligent" trial and error - he has a real understanding of his times tables and beyond, and could apply that in a meaningful way to reduce the number of trials massively. I don't think him doing that question was pointless or "just brute force", I think he enjoyed it and he used his learning. If they find their own, original, ways of solving the problem, isn't that the point?

The trial & error vs taught method debate is an interesting point. They are meant to stretch and engage (or keep busy!) the quickest ones in a class, who've finished the rest of the worksheet. I'm a bit dubious about the value of setting any trial and error question for the sake of it, but OTOH just giving them a method and asking them to follow it would stop it being the "stretching" thing it's meant to be. They'd just be following another taught method, albeit a funky one.

I'm not sure what the answer is. My son seems to spend a lot of time in class doing sudoku, or those sums where each letter stands for a different number, or fully enumerating 64 different combinations of coins. But it's hard to keep thinking up new ideas, at school or home. My old maths teacher used to bring in the Sunday Times brainteaser, and we often ended up with a bit of trial and error doing that, even as double maths A level students with knowledge of algebra.

I don't recall doing stuff like this in Year 4! I don't even think I knew what algebra was until secondary school

Quote proud of myself - haven't looked at the other answers :- x = teachers. Step 1: x + x + 6 + 6(x+6) = 170: Step2: 2x +6 + 6x +36 = 170: Step 2: 8x +42 = 170: Step 3: 8x = 128: Step 4 x = 16 (teachers); boys 16 +6 = 22 ; Girls 22 x 6 = 132. 16+22+132 = 170!

@brilliotic, sorry, I have just seen your reply. We use the Singapore Maths, i.e. these books: amzn.to/2zsnnLP. Probably you want to start from that one (Level 3, Grade 4) as level 2 is probably too easy. It took me a while to understand what was going on and what was the point of this "Singapore maths", but after the penny dropped I was all ooohhhs and aaahhhs. BEar in mind, the book is American, so it is all inches and dollars, but that is not a problem as the unit of measurements are never an issue (you are not asked to convert quarts into pints and dimes into dollars :D ).

@mydietstartsmonday, indeed, but that's algebra :D

@IStillDrinkCava, yes, your method was quite insightful, but still relies on certain patterns and numbers behaving. The goal should be to find a method that could be applied given any number, even large ones or not behaving ones.
In addition there is stuff to be learned from it. Take for example this problem: Amy has 3 books and 2 pens and they cost £8, while John has 5 books and 4 pens and they cost £15 (random numbers). My DD couldn't do it... She could do the one with both John and Amy having 4 pens, but not the one where the numebr of pens was different.
That generated a discussion on WHY she could do one problem and not the other, WHAT she would have liked the numbers to be like and HOW she could solve the new problem. In the end the peny dropped and I though that was a worthwhile excercise, though exhausting in the end :D This was pretty much a pre-algebra kind of problem.

Arkadia, why are you so focused on these questions?
Yes it's great if you have a tool to do this, and some children benefit massively by being taught how to think. Singapore maths is great, but only if it's taught properly. I wouldn't teach my ds because I don't have the skill to teach him. And it will be just one of the method among many, especially after secondary. There are many challenging problem solving questions on sites like nrich, which can stretch children in many ways, not just this kind of questions.

Thanks Arkadia.

irvine I can't speak for Arkadia obviously. But in my case the situation is that school is focusing wholly on arithmetics and (up to now at least) has done only VERY basic problem solving.
My DS is strong at applying the techniques he has learnt, and has a good understanding of numbers and how they work together, and can even do some algebra, but confront him with a problem where he has to think and he does not know where to start.

nrich problems (in the past, haven't looked for a while I admit) were like that for him. Left him completely stumped.
So the bar modelling thing for me is an attempt to teach him a way to approach problems where it isn't immediately obvious which operations you need to apply. I hope it will teach him 'where to start' - i.e. draw a 'model' (which is something even degree level mathematicians do - needing to visualise the problem is not a sign of mathematical weakness). Once he has learned a strategy to approach such problems, I think he will be happier/more able to do nrich type problems too.

To me what these problems teach is how to model a problem, which is something, like in brilliotic's case, is never done at school. To be able to draw a problem in such a way you can isolate what is relevant from what is not is a lifelong skill that you will never forget, a bit like being able to swim or to ride a bicycle.
However, the most important bit is that they are FUN! ;)

brilliotic, have your ds tried parallel.org.uk/ ?

My ds's school is no good at all at extending. All the teachers introduced to him, he already knew for a start. I did work really hard to look for something different all these years, and occasionally asking on MN and people like noble responded.

Tbh, when I have shown him these questions on this thread, I wasn't sure my ds was up for it. And I wasn't going to force him if he wasn't interested. But he has shown interest. He is capable of using algebra, but I gave him specific instruction not to. I feel like what I have been doing all these years have paid off. He has learned to use his knowledge, but also learned not to give up easily.

Arkadia, my ds has no knowledge of bar method, but when he tried the chicken question, first thing he has done was draw something similar to bar model. So, I think children with strong understanding of maths concept, they do use it, taught or not. But with John and Mary question, it wasn't necessary, he said, numbers were more straight forward.

Parallel seems to be quite interesting this year, my ds is getting better results for yr9 question than yr7 ones. Anyways, it only allowed you to do the level nearest to your age last year, but you can try all the questions this year. He learned what is googol squared, which is totally new for him!

Thanks for suggesting Parallel, irvine, I hadn't heard of it but now we're all signed up, will see how it goes.

Arkadia, I went for it and ordered that Singapore Maths book. It arrived today and the initial problems seem very straightforward - DS didn't see the point in drawing any bars as he could see what needed to be done, and calculate the answer mentally. I assume they get a bit harder further on, so will continue experimenting.

If there were 6 more people you'd simply divide by 8. 176 divided by 8 = 22. Easy when you think of it but probably not for a year 4. Might pass this by my colleagues tomorrow for a bit of fun.
(If there were 6 more teachers, b + g + t =176. Divide by 8 - 6 lots of girls, one of boys, one of teachers. Each group is 22. Take 6 off for the teachers you added). Sadly can't bar model on here

Becauseif you add on 6, you have the same number of teachers as boys, and 6 times as many girls as boys making 8 lots altogether so you can divide 176 by 8

Parallel was introduced by Noblegiraff. Its related site mathigon is great too.

@brilliotic, yes, that is true (and that was my feeling too :) ) things will start to change from about problem 12.