A 3rd grade Western math question

[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.

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!

As have we all, good for you taking the time to bring that forth, I'm glad to see it was an informative thread after all..

[JesseFrank]

Sara ran 8 km less than Jan and also 8 km less than Myra, so she ran 16 Km less than both of them.

64 Km - 16 km = 48 Km.

So 48 Km is the distance all three ran together ,

48/3 = 16Km that each of them ran.

Jan and Myra ran an additional 8 km on top of that .

16 + 8 = 24 km

16 +24 + 24 - 64Km

Edited April 27, 2014 by JesseFrank

[thepool]

Seems the "teachers" cannot agree solution !

[sustento]

On the contrary what's been demonstrated in this thread is that many problems have more than one solution - and I'm not a teacher!

[wprime]

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.

Forget about the memory, just add up the numbers first then multiply the result by the long number.

[muchogra]

3rd grade way - trial and error.

.....

In higher math, they have a fancier name, called Iteration Method, With the computing power nowadays, such a method is used for most problems as most life cases have no analytical solutions!

I grooved initially for I read as 2 races. First being the 3 of them ran 64, Then, in the second, the 2 ran 64, and the other ran 8 behind. and I set up the equations accordingly.... Yeah, that's what the 4 big Hein did to me.

Correctly speaking it's 3 equations and 3 unknowns and that's what should be taught to the kids!

[thepool]

I am amazed that "teachers" are still debating this very simple "problem" !

[nidieunimaitre]

I am amazed that "teachers" are still debating this very simple "problem" !

You don't get it, do you?

I am not amazed by your post!

"The teachers" are not debating the mathematical "problem", they are debating teaching methods, didactics.

[nidieunimaitre]

3rd grade way - trial and error.

.....

In higher math, they have a fancier name, called Iteration Method, With the computing power nowadays, such a method is used for most problems as most life cases have no analytical solutions!

I grooved initially for I read as 2 races. First being the 3 of them ran 64, Then, in the second, the 2 ran 64, and the other ran 8 behind. and I set up the equations accordingly.... Yeah, that's what the 4 big Hein did to me.

Correctly speaking it's 3 equations and 3 unknowns and that's what should be taught to the kids!

You mention "4 big Hein".

Let us assume that you mean Heineken.

If that assumption is correct, I can deduce that:

1/ Yes you were drunk when you made your comments.

2/ You get drunk easily.

3/ You like to drink imitation beer - is that to show off, as "Hein" is fashionable? / or is it because you know nothing about beer? / or because you are dutch? / or because you were forced through torture?

[muchogra]

I am amazed that "teachers" are still debating this very simple "problem" !

Please don't take away what good teachers contribute to our knowledge! Be grateful what you have learned. The rest is on yourself and most importantly your attitude!

[wooloomooloo]

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!

As have we all, good for you taking the time to bring that forth, I'm glad to see it was an informative thread after all..

Informative to me, too. Not from an algebraic perspective but to learning in general.

A colleague said to me recently that I'm the best teacher. I can understand that that statement is personal and not necessarily the thoughts of all my colleagues.

This particular colleague is someone whom I like to spend time explaining the process and calculations because they're avid in stealing my experience and are therefore more productive and knowledgeable in their post.

There are others that are content for me to constantly think for and babysit their working life, which wastes both our time and my tutorial skills may come across as more abrupt. Ultimately, they want me to earn their salary for them without putting in the effort.

But, ask me the question, and if I know the answer, I will endeavour to succinctly respond.

[Jasun]

The answer is zero. This is a trick question as everyone knows Thais don't walk (let alone ru) anywhere.

[zeichen]

Actually algebra should be started in the 3rd or 4th grade. This isn't a very complicated math problem. You do realize that the western countries are so far behind on math education it is almost pathetic. In China kids are doing calculus by grade 10 so doing simple alegebra by 3rd grade.

Also with trial and error you could figure it out even if you don't know basic algebra.

Math is only as complicated as you make it. I know of quite a few kids under the age of 8 that could do that problem. I personally think that grade 4 or 5 though would probably be more appropriate for most Thai kids until they improve the education system.

[vietdoc]

If Jan and Mya ran the same amount of miles and Sara ran 8 less than Mya that means she also ran 8 less than Jan.

64/2=32+32

J 32-8=24

M 32-8=24

S 8+8=16

Edited May 4, 2014 by vietdoc

[Scott]

An off-topic post has been removed.

[lomatopo]

Without understanding the associated lesson, lecture, curriculum, text I'd say this is an introductory Algebraic reasoning word problem with a single unknown and a single equation, which might be targeted at western 6th/7th graders, or maybe M1 or M2 here.

I can't see this being a 3rd grade like problem, unless there is a Tiger Mom involved somehow?

Here in Thailand I'd be looking for students to understand the language, words (ran, miles, same, less, total, etc.) and be able to represent or derive the single unknown, represent it in an equation, solve for the unknown, then check their result by substitution back into the equation, and finally understanding that the result agrees with the original wording of the problem.

Edited May 4, 2014 by lomatopo

[MartinL]

Can't be bothered to read all this thread, so maybe a satisfactory answer has already been given.

J = M

S = (M-8)

=> J + M + S = 64

=> J + M + (M -8) = 64

=> 3M = 64 + 8 = 72

=> M = 72/3 = 24

=> Jan = 24, Mya = 24, Sara = 16.

[Scott]

I was absolutely terrible at arithmetic and any mathematics until I took algebra in University. I barely passed it in high school, partially because I had a not particularly good teacher. In University, we had a very large class twice a week and then a small class with a Teaching Assistant. The TA had this almost magical way of explaining the concepts. All the pieces and all the math began to fall into place and I went on to take quite a few math courses and a number of statistics classes.

I wish that I would have had someone teach me the very basic concepts about equations and algebra when I was in 3rd grade.

[culicine]

Actually algebra should be started in the 3rd or 4th grade. This isn't a very complicated math problem. You do realize that the western countries are so far behind on math education it is almost pathetic. In China kids are doing calculus by grade 10 so doing simple alegebra by 3rd grade.

Also with trial and error you could figure it out even if you don't know basic algebra.

Math is only as complicated as you make it. I know of quite a few kids under the age of 8 that could do that problem. I personally think that grade 4 or 5 though would probably be more appropriate for most Thai kids until they improve the education system.

You could teach the mechanics of differentiation to lower high school. I asked a 9th grade student in my school about the calculus they were doing at Kumon. The formulae are of course quite simple, but he couldn't tell me what a tangent or a limit was. Thus they had little understanding of the topic. I see that here everyday here. Lot's of one-upmanship among parents to show off how 'smart' their kids are. But at the end of the day they really don't know much.

[vietdoc]

If Sara ran 8 miles less than Mya that means she also ran 8 miles less than Jan

64-16=48

Jan and Mya ran the same amount of miles

48/2=24

[SlyAnimal]

Jan's miles run = J

Mya's miles run = M

Sara's miles run = S

J = M

S = M - 8

J + M + S = 64

Using what we know to covert into a single variable

J + J + (J - 8) = 64

2J + (J - 8) = 64

3J = 64 + 8

3J = 72

J = 72/3

J = 24

Jan = 24 miles

Mya = 24 miles

Sara = 16 miles

That's the equation I'd likely write on the board for my students if I was showing them the answer in class.

I teach maths to M1 - 3 students, and would back the M3 students to do it, as that's part of the M3 cirriculium (Although I taught it in term 2, so given to them now they'd fail lol). Although it'd mainly just be the smart students, the others often just look at word problems and get confused by too many words they don't understand (They'll see a word and get worried about the meaning, when they'll often just be replacing it with x or y anyway).

And if this was a question for a Grade 3 as in Prattom 3, so for a 8 or 9 year old, I'd be very impressed if any of the students can get that correct. And am surprised that they're teaching them that type of question in primary school, as even in NZ we didn't get those types of questions until high school (Well we had a few questions like that at some maths competitions I went to, but those questions were deliberately difficult). Your son must be in some kind of advanced class if the teacher is teaching this kind of question.

Alternatively of course, if you said Grade 3, but meant Mattayom 3, then this question is quite normal for that level.

[BlackArtemis]

In the Thai cirriclum solving for unknowns is a 3rd grade standard. Multiple step equations are in Thai textbooks, but often more in the vein of "tom, tim, and bob run 34km. If tom ran 13km 300m and tim ran 15km and 400m. How far fid bob run? This has only one unknown and the student can solve it without the use of variables and inverse ooerations. Though these difficult problems pop up, especially on the NT. People here have the idea that forcing kids into stuff early means a good program. Developmental readiness is a little known concept. ...

Sent from my GT-I9500 using Thaivisa Connect Thailand mobile app

[Metanoia]

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.

You're right that younger learners in Singapore use block methods before moving to algebra.

The approach is similar, its mostly replacing our "x" with "blocks" to make it more visual.

Hard to type it out, but here's my take.

Let distance ran by S be [ ]

Therefore,

S : [ ]

J : [ ]+ 8

M: [ ] +8

Total : 3 [ ] + 16 = 64

3 [ ] = 48

[ ] = 16

[harrry]

Wille brought an extra tray of 42 cookies home from his job as a caterer. 18 of them are chocolate chip. Of the rest of the cookies, half are peanut butter, and the other half are oatmeal.

How many peanut butter cookies are there?

is a question from grade 4 US curriculem on Khan academy similar level of reasoning.

[culicine]

Wille brought an extra tray of 42 cookies home from his job as a caterer. 18 of them are chocolate chip. Of the rest of the cookies, half are peanut butter, and the other half are oatmeal.

How many peanut butter cookies are there?

is a question from grade 4 US curriculem on Khan academy similar level of reasoning.

I think that is a little simpler and does not need any algebraic reasoning. I won't do a solution as I think that one is easy enough to solve by most people on this board:)

[stubuzz]

<script type='text/javascript'>window.mod_pagespeed_start = Number(new Date());</script>

In the Thai cirriclum solving for unknowns is a 3rd grade standard. Multiple step equations are in Thai textbooks, but often more in the vein of "tom, tim, and bob run 34km. If tom ran 13km 300m and tim ran 15km and 400m. How far fid bob run? This has only one unknown and the student can solve it without the use of variables and inverse ooerations. Though these difficult problems pop up, especially on the NT. People here have the idea that forcing kids into stuff early means a good program. Developmental readiness is a little known concept. ...

Sent from my GT-I9500 using Thaivisa Connect Thailand mobile app

I agree, my daughter is in a math/science program and she does not understand the math. I regularly have to spend an hour or two a night to reteach the day's lessons. Moreover, some of the homework questions involve the use of skills they haven't yet learned. Her teacher has claimed the questions are a mistake, i would say incompetence.

After speaking to the manager, she told me this is the 'new style' of teaching math and they will soon get the hang of it. I told her that most of the children in the class still have not mastered the core skills of addition, subtraction, multiplication, and division, but it fell on deaf ears.

[SlyAnimal]

After speaking to the manager, she told me this is the 'new style' of teaching math and they will soon get the hang of it. I told her that most of the children in the class still have not mastered the core skills of addition, subtraction, multiplication, and division, but it fell on deaf ears.

Yeah the new style, is that they don't actually teach students anything. Instead they just check their names, let them chat to their friends for a while, stand in straight lines and sing the national anthem, after which they can go home.

The learning is done with their private tutors, as the classes are too big and it's too hot during the day to teach anyway. Particularly as the students are so tired from all the time they spend studying, therefore it's better to just let them play during school time, and then they can study after school.

Oh yeah, I'm joking, but sometimes it does seem this way.

[simon43]

For heaven's sake! I worked out the answer in my head in under 1 minute and I am not anywhere decent at Maths. I was teaching simple algebra like this to my class of 7 year olds in Myanmar last year......

[AnotherOneAmerican]

I'm impressed a 9 year old can run 24 miles.

[mesquite]

I haven't read the entire thread, but you have three equations and three unknowns. It is very easy to solve, for someone taking high school algebra. This is way too advanced for third grade, which I assume is age 8 or 9.