A 3rd grade Western math question

[WarpSpeed]

Susento you may like his answer but you didn't post any better solution prior..

[sustento]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

[wolf5370]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

[WarpSpeed]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

No, props to your admission, we did the same thing, I just didn't like the way my question and I was being poked at without anyone understanding I was looking for the simplicity we all seem to have overlooked.

Edited April 26, 2014 by WarpSpeed

[nidieunimaitre]

OK, here we go, straight from a Greek island, and non-algebraic, so that even 3rd grade educated westerners that hate modern teaching can understand it.

64 has to be divided into 3 parts, of wich 2 are equal, 1 is 8 down.

Let us say the answer is 27 / 27 / 10

This is not correct, since the difference is not 8

Let us say the answer is 26 / 26 / 12

This is not correct, since the difference is not 8

So we try 25 / 25 / 14

.

Next try 24 / 24 / 16

Halelujah! We found the answer!

And without algebra!

That seems a winner! Why did it seem so complicated? I guess it was how you began to get to those numbers? What did you use as a starting point for example? Why 27? Or any number between 1 and 64?

Of course you could have started just about anywhere, as long as you have 2 same numbers, 1 down, and all 3 adding up to 64.

To shorten the search, you need to start from something more or less "realistic".

Or start from any numbers, but then judge how far you are off, and estimate accordingly.

Learning to judge what is "realistic", and acting accordingly would be a far more important skill then just answering this particular question - not unlike using a calculator to add up several amounts, but at the same time making an estimate of the sum.

[WarpSpeed]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

Excellent!You also accounted for the 8 missing miles I insisted correctly was there, well done!!

[nidieunimaitre]

OK, here we go, straight from a Greek island, and non-algebraic, so that even 3rd grade educated westerners that hate modern teaching can understand it.

64 has to be divided into 3 parts, of wich 2 are equal, 1 is 8 down.

Let us say the answer is 27 / 27 / 10

This is not correct, since the difference is not 8

Let us say the answer is 26 / 26 / 12

This is not correct, since the difference is not 8

So we try 25 / 25 / 14

.

Next try 24 / 24 / 16

Halelujah! We found the answer!

And without algebra!

That seems a winner! Why did it seem so complicated? I guess it was how you began to get to those numbers? What did you use as a starting point for example? Why 27? Or any number between 1 and 64?

Of course you could have started just about anywhere, as long as you have 2 same numbers, 1 down, and all 3 adding up to 64.

To shorten the search, you need to start from something more or less "realistic".

Or start from any numbers, but then judge how far you are off, and estimate accordingly.

Learning to judge what is "realistic", and acting accordingly would be a far more important skill then just answering this particular question - not unlike using a calculator to add up several amounts, but at the same time making an estimate of the sum.

[wolf5370]

OK, here we go, straight from a Greek island, and non-algebraic, so that even 3rd grade educated westerners that hate modern teaching can understand it.

64 has to be divided into 3 parts, of wich 2 are equal, 1 is 8 down.

Let us say the answer is 27 / 27 / 10

This is not correct, since the difference is not 8

Let us say the answer is 26 / 26 / 12

This is not correct, since the difference is not 8

So we try 25 / 25 / 14

.

Next try 24 / 24 / 16

Halelujah! We found the answer!

And without algebra!

That seems a winner! Props, obviously I wasn't the only fooled. Why did it seem so complicated? I guess it was how you began to get to those numbers? What did you use as a starting point for example? Why 27? Or any number between 1 and 64?Never mind, now after the fact it is logical to have started with some combination of numbers that essentially splits with an uneven balance left and count from there.

This is a method sometimes termed as "estimating and refining". The easiest starting point is to roughly divide the total by 3 and add it from the difference by 3 for the 2 high numbers and subtract it from the third (you know it ill not be correct - but as it yields an easy starting point) 64/3 ~= 21 and 8/3 ~= 3 - so first try is (21+3) | (21+3) | (21-3) = 24 | 24 | 18 (24 - 18 = 6 - so move along) 26 | 26 | 18 (26 - 18 = 8, but 26 + 26 + 8 = 60 - so move along) 25 | 25 | (25 - 8 = 17) = 67 (move along) 24 | 24 | (24 - 8 = 16) = 64 Bingo!

It works, but is very slow for such a question. See my logic method 6 minutes ago (#41) - no algebra

//EDIT: Added in post number - doesn't show it when your are replying

Edited April 26, 2014 by wolf5370

[Tywais]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

I think that is what the problem was for several of us myself included. Algebra, advanced algebra in high school, college level algebra and all the advanced math courses starts clouding the 'simplistic' approaches to a problem and instinct goes for the most common approach we have trained in for years. I vaguely remember these types of questions but that has been many decades ago.

[wolf5370]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

Excellent!You also accounted for the 8 missing miles I insisted correctly was there, well done!!

No worries Years of home schooling (and maths tutoring back home in the UK) - most kids need to be shown why as well as how - algebra is great, but it can cause maths blindness when kids do not understand why and are just told how. This can be really hard to correct later - so I think it is good that you are doing just that so you can walk your kid through. Puzzle questions like these can be fun for the kids if they understand how to attempt them without the pressure - and it opens the mind up for other logic problems. There are some good maths puzzle books out that are aimed at 10 years (and made more fun - like a normal puzzle book) - well worth the tiny investment I feel - can be fun for dads too

Incidentally - I found an old maths booklet from the 1940s. It is filled with O Level (16 year old) past maths papers from the pre war era. No calculators (some allow slide rules !) - but I really struggled on some of those questions myself (and I have a Masters!) - maths has definitely got easier over the years (especially as its all decimals and none of this guinies, pounds, shillings and halfpennies) - either that or my brain has gone more than I thought.

[nidieunimaitre]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

I think that is what the problem was for several of us myself included. Algebra, advanced algebra in high school, college level algebra and all the advanced math courses starts clouding the 'simplistic' approaches to a problem and instinct goes for the most common approach we have trained in for years. I vaguely remember these types of questions but that has been many decades ago.

edited because something wrong with the quotes

Yes indeed!

This now brings back memories....

I was 11 years old, and had to do a test for a scholarship for secondary school.

2 trains heading towards one another, at different speeds, where will they meet and when?

I easily solved the problem using algebra, only to be told by the priest "yes with algebra it is of course very easy"

I did get my scholarship for a state school though....

Edited April 26, 2014 by Tywais
Fixed quotes

[wolf5370]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

I think that is what the problem was for several of us myself included. Algebra, advanced algebra in high school, college level algebra and all the advanced math courses starts clouding the 'simplistic' approaches to a problem and instinct goes for the most common approach we have trained in for years. I vaguely remember these types of questions but that has been many decades ago.

I agree. I went through to post grad and into IT in the days of mainframes and 370 assembler language/PLi/COBOL etc. When I first started private tutoring for maths, initially for friends' kids and family, it was hard to explain how to solve things at their level and not to jumps half a dozen steps as it seems obvious. It is a real skill to master in itself, being able to grade down to their level, but still teach them. I take my hat off to those guys doing this day in and day out in primary/elementary/Pratong!

I home school my kids and sometimes I have to lookup ways to work things out in a more simplistic manor - just to remind myself and give me a way to explain what seems apparent.

[muchogra]

Partington and susteno are both correct. There is no missing or extra mile that you mention or fractions. Just reverse the procedure and plug the numbers in and they work correctly.

J = M = 24 (They ran the same distance)

J + M = 48

(J + M) + S = 64

48 + S = 64

S = 64 - 48 = 16

So M+J+S = 24 + 24 + 16 = 64

As for 3rd grade, depends on if it is Prathom 1-6 (the lower grades) or Maythom 1-6 (the upper grades). But sounds like the OP is referring to Prathom 3.

Now have to figure it out in the perspective of a 9 year old.

Your way is a way a non-scientific person would do

You obviously don't know very much about Tywais

Yeah, I know Tywais, a nice guy, I reckon. He also teaches at CMU.

Edited April 26, 2014 by muchogra

[wolf5370]

Susento you may like his answer but you didn't post any better solution prior..

I liked his answer because I never thought of it. I'd automatically use algebra to solve a problem like that because that's how I was taught. Using iteration didn't occur to me but there again I'm not 9. Sorry if you found my posts unhelpful.

I think that is what the problem was for several of us myself included. Algebra, advanced algebra in high school, college level algebra and all the advanced math courses starts clouding the 'simplistic' approaches to a problem and instinct goes for the most common approach we have trained in for years. I vaguely remember these types of questions but that has been many decades ago.

edited because something wrong with the quotes

Yes indeed!

This now brings back memories....

I was 11 years old, and had to do a test for a scholarship for secondary school.

2 trains heading towards one another, at different speeds, where will they meet and when?

I easily solved the problem using algebra, only to be told by the priest "yes with algebra it is of course very easy"

I did get my scholarship for a state school though....

(Moved the quote for you above )

Oh God - I hated those train questions - I think they were invented to torture 8 year old boys! A train leaving Newcastle travelling at 70mph to London passes a train going in the opposite direction at 3:12pm. If the London train left at 2:53pm and the distance between London and Newcastle is 150 miles (no idea if that's true btw - Geography not a strong point ). Then what colour is the bear?

...or something like that.

[wolf5370]

Partington and susteno are both correct. There is no missing or extra mile that you mention or fractions. Just reverse the procedure and plug the numbers in and they work correctly.

J = M = 24 (They ran the same distance)

J + M = 48

(J + M) + S = 64

48 + S = 64

S = 64 - 48 = 16

So M+J+S = 24 + 24 + 16 = 64

As for 3rd grade, depends on if it is Prathom 1-6 (the lower grades) or Maythom 1-6 (the upper grades). But sounds like the OP is referring to Prathom 3.

Now have to figure it out in the perspective of a 9 year old.

Your way is a way a non-scientific person would do

You obviously don't know very much about Tywais

Yeah, I know Tywais, a nice guy, I reckon. He also teaches at CMU.

Let's take his solutions:

M=48 and S=16

Now, how did S run 8 miles less than M? (It seems 32 to me!)

Unscientific people assume, and make belief . People fall for it, just like politics we have now in Thailand!!

He didn't say M=48, he said J + M = 48.Although he did seems to start with the answer and work to the question, which would surprise an examiner I think .

In algebra I would have said:

J + M + S = 64 (as given)

s + 8 = J = M

LET: A = S + 8

AS: (S + 8) + J + M = J + M + S + 8 = J + M + A = 64 + 8 = 72

AS: A = J = M ; A + M + J = 72

A = J = M = 72/3 = 24

THEREFORE: M = 24, J=24 and A=24 ; AS: A = S + 8, S = A - 8 = 24 - 8 = 16 ; GIVING: S = 16

That would be a full answer for examination purposes and thus all the AS/THEREFORS/etc. However, one could not expect a 9 year old to do that!

[WarpSpeed]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

Excellent!You also accounted for the 8 missing miles I insisted correctly was there, well done!!

No worries Years of home schooling (and maths tutoring back home in the UK) - most kids need to be shown why as well as how - algebra is great, but it can cause maths blindness when kids do not understand why and are just told how. This can be really hard to correct later - so I think it is good that you are doing just that so you can walk your kid through. Puzzle questions like these can be fun for the kids if they understand how to attempt them without the pressure - and it opens the mind up for other logic problems. There are some good maths puzzle books out that are aimed at 10 years (and made more fun - like a normal puzzle book) - well worth the tiny investment I feel - can be fun for dads too

Incidentally - I found an old maths booklet from the 1940s. It is filled with O Level (16 year old) past maths papers from the pre war era. No calculators (some allow slide rules !) - but I really struggled on some of those questions myself (and I have a Masters!) - maths has definitely got easier over the years (especially as its all decimals and none of this guinies, pounds, shillings and halfpennies) - either that or my brain has gone more than I thought.

Regards, yes and previous to this I was homeschooling as well and my sons are both honor roll students, my oldest is "A" honor roll, but had to make a living and they need the socialization skills I feel are also necessary. I also teach them to use practical application I was even complimented by the store manager the other day for how I teach my boys how to work out the best deals by weight etc. when shopping. I always try to demonstrate practical daily, real life applications as that was always a pet peeve I had while I was going to school.

I was really at odds with my missus initially about how to teach them by applying logic and reason and not always the approved or "accepted" method, she's Chinese so rote was the norm without reason and now she's see the result first hand and is completely on board and converted as to the important differences.

[muchogra]

Oop, I read the problem incorrectly. My bad. I apologize.

Here, should be the solution:

j+m+s=64

j=m

s=m-8

3 equations, 3 unknowns.

Solving the simultaneous equations yields:

j=24

m=24

s=16

My bad! But, it's the scientific way of solving a problem!

[wolf5370]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

Excellent!You also accounted for the 8 missing miles I insisted correctly was there, well done!!

No worries Years of home schooling (and maths tutoring back home in the UK) - most kids need to be shown why as well as how - algebra is great, but it can cause maths blindness when kids do not understand why and are just told how. This can be really hard to correct later - so I think it is good that you are doing just that so you can walk your kid through. Puzzle questions like these can be fun for the kids if they understand how to attempt them without the pressure - and it opens the mind up for other logic problems. There are some good maths puzzle books out that are aimed at 10 years (and made more fun - like a normal puzzle book) - well worth the tiny investment I feel - can be fun for dads too

Incidentally - I found an old maths booklet from the 1940s. It is filled with O Level (16 year old) past maths papers from the pre war era. No calculators (some allow slide rules !) - but I really struggled on some of those questions myself (and I have a Masters!) - maths has definitely got easier over the years (especially as its all decimals and none of this guinies, pounds, shillings and halfpennies) - either that or my brain has gone more than I thought.

Regards, yes and previous to this I was homeschooling as well and my sons are both honor roll students, my oldest is "A" honor roll, but had to make a living and they need the socialization skills I feel are also necessary. I also teach them to use practical application I was even complimented by the store manager the other day for how I teach my boys how to work out the best deals by weight etc. when shopping. I always try to demonstrate practical daily, real life applications as that was always a pet peeve I had while I was going to school.

I was really at odds with my missus initially about how to teach them by applying logic and reason and not always the approved or "accepted" method, she's Chinese so rote was the norm without reason and now she's see the result first hand and is completely on board and converted as to the important differences.

Yes socialising is always the con to home-schooling - especially here where it is somewhat quaint (most Thais seem to think that only delinquents and mentally challenged are home schooled IME). Likewise my girls are way ahead of the curriculum (they are both doing IGCSE courses EDEXEL), which is of course the pro (we can spend more time with them and provided 1 on 1 teaching and access to materials etc).

My wife is also Chinese descent (2nd generation on her father's side), but was privately educated, she has always seen the merit in educating the girls to the best we could afford (in the UK that was private - here we started that way, but moved to home schooling after 2 years). Likewise in shops too - get my kids to keep a running tally of the shopping basket - compared prices on weight/volume etc - and calculate the change. We have a reputation In the local 7-11 of giving the money over at the same time we hand a full basket (couple of times a day - we live opposite one) - smiles when its baht on (which is most of the time other than pricing/shelving errors - or when we simply don't have the shrapnel).

Too much reliance is put on calculators at secondary/high-school these days - I only allow calculators for trig and logs and rarely otherwise - better if they know how to work things out and it also teaches them to remember recurring numbers that are outside the usual 12 times table set (25s for example come up often).

[wolf5370]

Oop, I read the problem incorrectly. My bad. I apologize.

Here, should be the solution:

j+m+s=64

j=m

s=m-8

3 equations, 3 unknowns.

Solving the simultaneous equations yields:

j=24

m=24

s=16

My bad! But, it's the scientific way of solving a problem!

Yes - in this case though we are told J and M are equal (your second equation) - so we can say there are only 2 unknowns X (that being both J and M) and S.

So we have

LET: X = J = M

1. 2X + S = 64

2. S = X - 8

Substituting for S: 2X + X - 8 = 64 SIMPLIFY: 3X = 72 THEREFORE: X = 72/3 = 24

Substituting for X: S = 24 - 8 SIMPLIFY: S = 16.

boom boom

[nidieunimaitre]

Using calculators..... don't get me started!

Very useful for adding, multiplying multi digit numbers, yes, but provided students also make a rough estimate.

And do students know HOW to use calculators??? I remember when teaching at teachers training college -in Europe- my students had to multiply different numbers with the same -long- number (say 12345,678 X different numbers). Not a single student thought of putting 12345,678 into the calculator's memory!

Next they had to add up the results. And you guessed it, they wrote down the results, and fed them back into the calculator to add them up.

I read somewhere that Einstein predicted that there would come a time when people would not be able to cope with technology.

That time has come! But not sure if it realy was Einstein who said that.

[nidieunimaitre]

Oop, I read the problem incorrectly. My bad. I apologize.

Here, should be the solution:

j+m+s=64

j=m

s=m-8

3 equations, 3 unknowns.

Solving the simultaneous equations yields:

j=24

m=24

s=16

My bad! But, it's the scientific way of solving a problem!

Yes - in this case though we are told J and M are equal (your second equation) - so we can say there are only 2 unknowns X (that being both J and M) and S.

So we have

LET: X = J = M

1. 2X + S = 64

2. S = X - 8

Substituting for S: 2X + X - 8 = 64 SIMPLIFY: 3X = 72 THEREFORE: X = 72/3 = 24

Substituting for X: S = 24 - 8 SIMPLIFY: S = 16.

boom boom

Please do not confuse a member who is in the proces of sobering up.

[sustento]

Thanks for all the answers. You've broadened my mathematical mind

[culicine]

I teach high school maths, but don't see a non-algebraic way to do it. At this level then seem to use block models, at least in my son's Singaporean books. J and M are the same, so we can call them 2X. S is 8 less, so we can call that X-8. They add to give 64, so X -s 24. Sara is 8 less, giving an answer of 16. It's a little advanced for third graders. I think 5 graders could have a good go at it though.

[WarpSpeed]

Using calculators..... don't get me started!

Very useful for adding, multiplying multi digit numbers, yes, but provided students also make a rough estimate.

And do students know HOW to use calculators??? I remember when teaching at teachers training college -in Europe- my students had to multiply different numbers with the same -long- number (say 12345,678 X different numbers). Not a single student thought of putting 12345,678 into the calculator's memory!

Next they had to add up the results. And you guessed it, they wrote down the results, and fed them back into the calculator to add them up.

I read somewhere that Einstein predicted that there would come a time when people would not be able to cope with technology.

That time has come! But not sure if it realy was Einstein who said that.

Smart phones??

Anyway, good to see the discussion continuing. I taught my son the methods proposed today and thanks to all who took it seriously, and with special recognition to nidieunimaitre and Wolf5370, it started off a bit dodgy but eventually got to the point of the thread, again many thanks and stop off at the motoring forum any time if one needs any motoring advice I can provide in return.. Carry on...

Edited April 27, 2014 by WarpSpeed

[Gsxrnz]

OK, here we go, straight from a Greek island, and non-algebraic, so that even 3rd grade educated westerners that hate modern teaching can understand it.

64 has to be divided into 3 parts, of wich 2 are equal, 1 is 8 down.

Let us say the answer is 27 / 27 / 10

This is not correct, since the difference is not 8

Let us say the answer is 26 / 26 / 12

This is not correct, since the difference is not 8

So we try 25 / 25 / 14

.

Next try 24 / 24 / 16

Halelujah! We found the answer!

And without algebra!

That's how I used to do it at school as algebra never made sense to me in the beginning. But the poxy teachers always wacked the ruler across my knuckles for not showing the workings. I learned early in life that the ends can indeed justify the means.

To warpspeed - show your kids this way of "trial and error substitution", and this will help them comprehend the more structured algebraic equations when they come across them. It did for me and that was nearly 45 years ago.

[WarpSpeed]

^ Have, just today.. Regards..

[partington]

Got bored reading other replies - but this is the way I did, thinking as a young teen (3rd grader???? - not all Americans here) so avoiding algebra.

Jan, Mya and Sara ran a total of 64 miles last week.

Jan and Mya ran the same number of miles.

Sara ran 8 miles less than Mya.

How many miles did Sara run?

So J and M ran the same and S run 8 less. So if S had ran the same then the total would have been 8 more ( 64 + 8 = 72 ).

And they would have run the same each, thus 72/3, which is 24. So J and M ran 24 and S ran 8 less than 24 which is 16. To check ( 24 + 24 + 16 = 64 )

This is a logic question really - what we term as verbal reasoning (non-verbal reasoning being symbols etc usually). In the good old day of grammar schools back in the UK (some still survive), the entrance exams (11 plus for national tests - or some counties held their own) included NVR and VR and questions like this were common. So, back in the 70s kids of 10 and 11 would be expected to answer such questions (of course they were trained to in lessons!) - I doubt many would be able to now-a-days though.

I too have to say this is indeed a simpler way of solving the problem, and much better from a child's perspective.

I was wrong in my post. I've learnt something here!

[naboo]

3rd grade way - trial and error.

If the two ran 30 miles each, the other ran 22 miles. Total 30+30+22=82 miles. Too much.

If the two ran 25 miles each, the other ran 17 miles. Total 25+25+17=67 miles. Too much.

If the two ran 20 miles each, the other ran 12 miles. Total 20+20+12=52 miles. Too little. etc etc.

The algebra way would be:

2x + (x-8) = 64

3x = 64+8 = 72

x = 72/3 = 24

24 miles each for the two and 24-8 = 16 miles each for the other.

A tricky question at grade 3, and not one I'd give for homework - unless it was an extension for a brighter kid. maybe the OP's child is brighter than the parents?

[Scott]

A number of off-topic, nonsensical posts have been removed.

[wprime]

x+y+z=64
x=y
y-z=8

Therefore
2x+z=64
x=8+z

2(8+z)+z=64
16+3z=64
3z=48
z=16

Unless they expected the kid to work it out with trial and error, this is not 3rd grade maths, at least not in Australia, simultaneous equations aren't taught until grade 7 for most (or 5-6 in specialised schools).