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Need Math advise for my friend's PS kids


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My friend wants to teach math at home to her kids. They are going into 6th and 7th grade. We won’t know what materials PS uses for another two weeks. Her goal is to deepen the knowledge of math beyond what PS usually provides. Since her kids are older, I am less familiar with materials. My first instinct is to point her to AoPS (this is the program we are planning on using after SM primary) or direct her to Discovering Mathematics (Singapore). Her kids are bright, but I haven’t worked with them on math, so it’s hard to tell how well they can handle challenges. I know AoPS has pre-tests, so we can place them into the right program. Are there any other challenging and interesting programs? Can you help me steer her in the right direction? I don’t want to recommend a program that will look just like what PS teaches. That will serve no purpose. Thanks!

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Another that is on my radar-screen for a pre-AoPS type math program is "Mathematics 6" which is sometimes (wrongly) called Russian Math 6.

 

Don't get bent, the author was actually Latvian ;) :D

 

Bill

 

Good one Bill!:)

 

Since the friend under the discussion is Russian, I wonder if she will object to a Latvian author. :lol:

On a serious note I have mixed feelings about old USSR textbooks (if that’s what they are). On one hand I can solve any math problem, but I solve them blindly. Unlike my husband who can work out proves for any formula, I was just told to memorize the formulas. I need to go back and look at those textbooks before I place blame. It is possible that my teacher was at fault. On the other hand, Kisilov Geometry textbook we used was fantastic.

Is this the right link for a book?

http://www.perpendicularpress.com/math6.html

 

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Good one Bill!:)

 

Since the friend under the discussion is Russian, I wonder if she will object to a Latvian author. :lol:

 

We are all Soviets now comrade :D

 

On a serious note I have mixed feelings about old USSR textbooks (if that’s what they are). On one hand I can solve any math problem, but I solve them blindly. Unlike my husband who can work out proves for any formula, I was just told to memorize the formulas. I need to go back and look at those textbooks before I place blame. It is possible that my teacher was at fault. On the other hand, Kisilov Geometry textbook we used was fantastic.

Is this the right link for a book?

http://www.perpendicularpress.com/math6.html

 

 

That is the right book. It has won a lot of awards and high praise for not being a memorize the formula type book. I have not used it (with the exception of some brief lessons based on an idea in the preview) so I don't have first-hand experience. But everything I have heard about Mathematics 6 has been highly positive.

 

Bill

 

ETA: Yes, it was a Soviet era textbook. BTW I have Kiselov's Geometry in Russian loaded on my iPad. Not understanding Russian it does me no good, but there you have it.

Edited by Spy Car
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this is the English version for Kiselov :)

http://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202

I am hoping on day a bright mind on this board will compare and contrast this book with AoPS geometry. I am not that bright :)

 

USSR also had special math schools where "math geniuses" studied. Those kids may have used different textbooks than regular schools. I will definitely get the copy and take a look at it. Thanks!

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this is the English version for Kiselov :)

http://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202

I am hoping on day a bright mind on this board will compare and contrast this book with AoPS geometry. I am not that bright :)

 

USSR also had special math schools where "math geniuses" studied. Those kids may have used different textbooks than regular schools. I will definitely get the copy and take a look at it. Thanks!

 

You can get a better deal ordering from the publisher:

 

http://www.sumizdat.org/

 

I have read both high praise and criticism of Kiselev. But I would have nothing more to offer than hear-say.

 

Bill

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Another that is on my radar-screen for a pre-AoPS type math program is "Mathematics 6" which is sometimes (wrongly) called Russian Math 6.

 

Don't get bent, the author was actually Latvian ;) :D

 

Bill

 

Don't want to split hairs but the authors were Estonian actually.:001_smile:

However the textbooks (there is also Math 5 and Math 4) are still in use in numerous schools in Russia (and several other ex-USSR countries) so in a way it is Russian math I guess.

 

 

 

USSR also had special math schools where "math geniuses" studied. Those kids may have used different textbooks than regular schools.

 

Roadrunner, do you by any chance mean the Math Highs Schools or do you have in mind something else entirely?

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Don't want to split hairs but the authors were Estonian actually.:001_smile:

 

Right you are. My mistake.

 

 

However the textbooks (there is also Math 5 and Math 4) are still in use in numerous schools in Russia (and several other ex-USSR countries) so in a way it is Russian math I guess.

 

 

Was Nurk the author (or co-author) of these? I always wondered if Mathematics 6 was produced in isolation, or if it was part of a series?

 

Bill

Edited by Spy Car
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Roadrunner, do you by any chance mean the Math Highs Schools or do you have in mind something else entirely?

 

 

Yes. I think they started from grade 5 or 6. I could be wrong. those schools focus (they still exist) around math, so their course of study is accelerated. I don't know anybody who studies in a "math school", but I suspect they have different textbooks and approach.

USSR also did this with music. You had music schools where in addition to regular course of study they incorporated music history, theory and private lessons into the curriculum. I can tell you that the knowledge you acquire in the US while earnng a Bachalor's degree in music is equivalent to high school education of those music schools.

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Was Nurk the author (or co-author) of these? I always wondered if Mathematics 6 was produced in isolation, or if it was part of a series?

 

Bill

 

Math 4 - E. Noor, E. Nurk, A. Telgmaa

 

Math 5 - E. Nurk, A. Telgmaa --> same authors, listed in same order as Math 6, not sure if Telgmaa was only a co-author though.

 

Also:

Math 7 - E. Nurk, A. Telgmaa, A. Undusk, However A. Undusk is mentioned as principal author in some sources.

 

Math 8 - M. Lepik, E. Nurk, A. Telgmaa, A. Undusk,

 

Each of those comes with 1 or 2 workbooks.

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Yes. I think they started from grade 5 or 6. I could be wrong. those schools focus (they still exist) around math, so their course of study is accelerated. I don't know anybody who studies in a "math school", but I suspect they have different textbooks and approach.

USSR also did this with music. You had music schools where in addition to regular course of study they incorporated music history, theory and private lessons into the curriculum. I can tell you that the knowledge you acquire in the US while earnng a Bachalor's degree in music is equivalent to high school education of those music schools.

 

This model was followed/copied in some Eastern European countries too so I'm a "product" of one of those Math schools.:-) Not for geniuses but there was a lot of math and it was very rigorous, however the focus was not on acceleration. In my time we started in grade 8 so they were called Math High Schools, nowadays they start in grade 5. There were (still are!) Foreign Language Schools, and Art Schools in addition to the Music schools you mention.

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This model was followed/copied in some Eastern European countries too so I'm a "product" of one of those Math schools.:-) Not for geniuses but there was a lot of math and it was very rigorous, however the focus was not on acceleration. In my time we started in grade 8 so they were called Math High Schools, nowadays they start in grade 5. There were (still are!) Foreign Language Schools, and Art Schools in addition to the Music schools you mention.

 

Would higher math such as algebra, geometry, etc. have been integrated, or separate like in the US?

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Would higher math such as algebra, geometry, etc. have been integrated, or separate like in the US?

 

 

In my days, we had geometry twice a week for four years and algebra three or four times a week (we studies on Saturdays. That changed later). In higher grades it was trig and "higher mathematics," which I believe corresponds to calculus. The scheduling was similar. So it wasn't integrated, but ran parallel.

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In my days, we had geometry twice a week for four years and algebra three or four times a week (we studies on Saturdays. That changed later). In higher grades it was trig and "higher mathematics," which I believe corresponds to calculus. The scheduling was similar. So it wasn't integrated, but ran parallel.

 

Interesting - thanks! Did you have separate textbooks for algebra and geometry then? Can you comment on the scope and sequence, such as, what grade level typically included prealgebra? I'm wondering what "math 7" and "math 8" would be.

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Interesting - thanks! Did you have separate textbooks for algebra and geometry then? Can you comment on the scope and sequence, such as, what grade level typically included prealgebra? I'm wondering what "math 7" and "math 8" would be.

 

Yes, we had separate textbooks. Unfortunately I don't remember the scope and sequence. It's been 20+ years. :) I do remember math moved slowly and steadily, providing enough time to really absorb the material. Basically what we learned in four years of geometry is what poor high school kids in the US are cramming in one year. It was a very good approach, I think.

Grades 10 and 11 (the school used to be K + 11 grades in the USSR at that time) were devoted to calculus. I believe we started algebra in 6th grade, but again, it was very slow and steady.

I won't be using Russian math with my kids. My husband (our family mathematician :) ) reviewed AoPS and this is the road we will take. One think I will probably do is run algebra and geometry parallel instead of sequentially.

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Math 4 - E. Noor, E. Nurk, A. Telgmaa

 

Math 5 - E. Nurk, A. Telgmaa --> same authors, listed in same order as Math 6, not sure if Telgmaa was only a co-author though.

 

Also:

Math 7 - E. Nurk, A. Telgmaa, A. Undusk, However A. Undusk is mentioned as principal author in some sources.

 

Math 8 - M. Lepik, E. Nurk, A. Telgmaa, A. Undusk,

 

Each of those comes with 1 or 2 workbooks.

 

Thank you very much for this information!

 

I am presuming they have not been translated? Do you know if they are easily available in Russian?

 

Bill

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whoa, Bill, looks like you need to have a chat with Mr. Harte. Promise him a market amongst homeschoolers :tongue_smilie:

 

You think I don't plan on calling him (or emailing) when he returns from his summer program studying in Moscow? :D

 

I would love to order a Mathematics 4 if it anywhere near (my perception of) the quality of Mathematics 6.

 

Bill

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Yes, we had separate textbooks. Unfortunately I don't remember the scope and sequence. It's been 20+ years. :) I do remember math moved slowly and steadily, providing enough time to really absorb the material. Basically what we learned in four years of geometry is what poor high school kids in the US are cramming in one year. It was a very good approach, I think.

Grades 10 and 11 (the school used to be K + 11 grades in the USSR at that time) were devoted to calculus. I believe we started algebra in 6th grade, but again, it was very slow and steady.

I won't be using Russian math with my kids. My husband (our family mathematician :) ) reviewed AoPS and this is the road we will take. One think I will probably do is run algebra and geometry parallel instead of sequentially.

 

This is very interesting - I appreciate your comments - thank you!!! :)

 

(For hs-ing dd, I'm thinking of doing Nurk's Mathematics 6 and then AoPS Prealgebra, or Math 6 and then some other prealgebra. Not to mention, I think I could easily have dd use Mathematics 6 instead of MM 6, which would mean starting in a few weeks, though she loves MM and might kill me because it would be a big change - Math 6 is more formal-sounding. If I were to stick in a smitch more on negative numbers right now, Dd would be a few lessons away from being able to try the AoPS Prealgebra pretest, though I don't want her to do prealgebra just yet - she's not that student - I think she could use one more year of solidifying concepts, arithmetic and problem solving, and we have plenty of time. And then what about the two Dolciani prealgebra texts that I have.... far too many choices :D)

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You think I don't plan on calling him (or emailing) when he returns from his summer program studying in Moscow? :D

 

I would love to order a Mathematics 4 if it anywhere near (my perception of) the quality of Mathematics 6.

 

Bill

 

Yep, I figured as much :lol:

 

He'd need to do a Math 5 also ;)

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Math 4 - E. Noor, E. Nurk, A. Telgmaa

 

Math 5 - E. Nurk, A. Telgmaa --> same authors, listed in same order as Math 6, not sure if Telgmaa was only a co-author though.

 

Also:

Math 7 - E. Nurk, A. Telgmaa, A. Undusk, However A. Undusk is mentioned as principal author in some sources.

 

Math 8 - M. Lepik, E. Nurk, A. Telgmaa, A. Undusk,

 

Each of those comes with 1 or 2 workbooks.

 

Can you point me to the website where I can order those? I think I solved my friend's problems. I found Math 6, but that's about it.

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Can you point me to the website where I can order those? I think I solved my friend's problems. I found Math 6, but that's about it.

 

If you find them will your friend be teaching in Russian, or are you all going to translate them (and forward me a copy :D)?

 

Bill

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Would higher math such as algebra, geometry, etc. have been integrated, or separate like in the US?

 

It was mostly integrated, but also parallel the way Roadrunner describes it. However I don't remember us having separate textbooks (it's been 20+ years for me too:-(). Although I think we had separate classes informally called Geometry (included plane and solid geometry, trigonometry etc) and Algebra (everything else) which totaled about 13-16 hours per week depending on the grade.

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If you find them will your friend be teaching in Russian, or are you all going to translate them (and forward me a copy :D)?

 

Bill

 

Her kids can read Russian, so my guess is she is going to hand them the book and have them do it and my husband will be testing them in English :)

Why is it that only level 6 is translated?

Oh, by the way, have you seen this? http://ucsmp.uchicago.edu/Transl.html

They have grade 1, 2 and 3 Russian math translated. Again, no samples, so it's hard to tell if it's worth it. They also Japanese math. Thank you University of Chicago :)

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Her kids can read Russian, so my guess is she is going to hand them the book and have them do it and my husband will be testing them in English :)

Why is it that only level 6 is translated?

Oh, by the way, have you seen this? http://ucsmp.uchicago.edu/Transl.html

They have grade 1, 2 and 3 Russian math translated. Again, no samples, so it's hard to tell if it's worth it. They also Japanese math. Thank you University of Chicago :)

 

I am aware of the UCSMP translations, but are they the same series? I don't know.

 

I always intended to order them, but our plates were full.

 

Now I need some Level 4, 5, 6 options to line up.

 

Bill

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I'm really not sure how easily available they are. i found the list here: http://www.koolibri.ee/?mcid=62&type=subjects&scid=63?&lang=ee but the site is in Estonian so can't really figure out how to order.

 

Math 4 Interactive textbook - Pages 1-20 - http://failid.koolibri.ee/koduleht/lehitseja/vene_matem_4_1/index.html

Table of contents for Math 5 Part 1 in Russian - http://www.koolibri.ee/download/?action=binary&id=4579 and

Part 2 - http://www.koolibri.ee/download/?action=binary&id=4580

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Her kids can read Russian, so my guess is she is going to hand them the book and have them do it and my husband will be testing them in English :)

Why is it that only level 6 is translated?

Oh, by the way, have you seen this? http://ucsmp.uchicago.edu/Transl.html

They have grade 1, 2 and 3 Russian math translated. Again, no samples, so it's hard to tell if it's worth it. They also Japanese math. Thank you University of Chicago :)

 

I am aware of the UCSMP translations, but are they the same series? I don't know.

 

I have them :tongue_smilie: and they appear to not be the same series. The authors are Moro, Bantova and Beltyukova. If anything, Harte's translation of the Nurk book is far superior, because he took care to make it a usable textbook for a US classroom, whereas I think the UCSMP grade 1,2,3 books might have been "examples." Looking at the UCSMP 1,2,3 books now, they do include a few pages describing the Soviet math system in the front. I don't have time to read the preface now - will try later - off to the pool with the gang...

 

But thank you for reminding me - I keep forgetting that I have these. For first grade math, it's too bad the book is not meant to be written in.

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I have seen the UCSMP translations. There is nothing in them to adapt them to anything, besides translating, but I don't honestly think there was much to coordinate. They don't have instructions to the teacher, for example. (This is not a "criticism," merely an observation.) They are basically a series of math problems with some text in explanation. The money and "culture" of the book are in the original (kopeks and rubles, lots of junior troupes or whatever they are called fixing things up).

 

I'd love to know what options there are for 4 and 5 year levels.

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I have seen the UCSMP translations. There is nothing in them to adapt them to anything, besides translating, but I don't honestly think there was much to coordinate. They don't have instructions to the teacher, for example. (This is not a "criticism," merely an observation.) They are basically a series of math problems with some text in explanation. The money and "culture" of the book are in the original (kopeks and rubles, lots of junior troupes or whatever they are called fixing things up).

 

I'd love to know what options there are for 4 and 5 year levels.

 

 

Sounds like textbooks from my childhood. Are they talking about young pioneers? (first step on the road to the communist party) :lol::lol: and the rubles... no mention of food ration cards? :lol:

 

Frankly SM and AoPS look so good, I don't know why even bother with anything else.

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Sounds like textbooks from my childhood. Are they talking about young pioneers? (first step on the road to the communist party) :lol::lol: and the rubles... no mention of food ration cards? :lol:

 

Bourgeois humor get you sent to gulag Comrade :D

 

Frankly SM and AoPS look so good, I don't know why even bother with anything else.

 

Mother Russia doesn't let go that easily :tongue_smilie:

 

Vladimir

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Sounds like textbooks from my childhood. Are they talking about young pioneers? (first step on the road to the communist party) :lol::lol: and the rubles... no mention of food ration cards? :lol:

Sadly, no! (But the problems are pretty clever. The thinking behind them is neat.) Something about Singapore irritates me but I can't put my finger on what.

 

Frankly SM and AoPS look so good, I don't know why even bother with anything else.

At what age can one use AoPS?

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At what age can one use AoPS?

 

The suggested Grade Level of the Algebra book is 6 and up. There is a long-anticipated Pre-algebra book that is expected to be released any day now.

 

I do not know if the recommended Grade Level will be 5th or what.

 

Bill

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Supposedly, the AoPS Prealgebra book would follow the completion of K-5 math. The readiness test is now up on the AoPS website's Prealgebra Course page.

 

 

Ok, I finally got around to looking at the UCSMP books. The "Textbook Series Preface" states:

 

The textbooks were originally translated to give U.S. educators and researchers a first-hand look at the content of mathematics instruction in educationally advanced countries....

 

The resource component's translations includethe entire Soviet curriculum (grades 1-10), standard Japanese texts for grades 7-11, and innovative elementary textbooks from Hungary and Bulgaria.

 

So, they weren't formatted for classroom use. The preface goes on to discuss the Soviet math system:

 

In grades 1-3 it was taught in combination with intuitie geometry, while grades 4-5 combined arithmetic, intuitive geometry, and an introduction to algebra. Soviet students were taught geometry continuously over ten years. By mandate, intuitive geometry constituted at least 20% of the curriculum in grades 1-5.

 

From grade 6 on algebra and geometry were taught as separate subjects in parallel sequences. Semi-deductive plane geometry based on geometric transformations was tuaght in grades 6 through 8 and three-dimensional geometry in grades 9 and 10. To our knowledge, no nation outside the former Soviet bloc has attempted to teach calculus to such a large percentage of students of secondary school age.... some critics considered the upper-level curriculum in particular to be ... too theoretical, abstract, and rigorous for the general population.

....

The Soviet primary school texts and workbooks are characterized by the early introduction of multidigit numbers, the use of variables, equations and inequalities, and an abundance of word problems from grade 1 on. The intuitive geometry component was created in accordance with the van Heile-Freudenthal theory of developmental levels in learning geometry.

 

It also references the study A World of Differences: An International Assessment of Mathematics and Science (ETS, 1989) (see this link to the ERIC database where the PDF can be downloaded for this doc - I have not looked at it).

 

You (any of you LOL) may also be interested in this little paragraph:

 

Russian Grade 6 Algebra begins with the basic concepts of expressions, statements with variables, and relations, and proceeds to linear and quadradic functions and their graphs, exponents, polynomials, andsystems of linear equations. This book has been used with great success for clsoe to twenty years by all twelve-year-olds in the Soviet Union. An examination of the text indicates that several of the important topics it covers are unfamiliar even to a substantial portion of American high school graduates.

 

 

I wonder if that one has ever been translated...

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Sadly, no! (But the problems are pretty clever. The thinking behind them is neat.) Something about Singapore irritates me but I can't put my finger on what.

 

 

At what age can one use AoPS?

 

 

Would you mind posting one problem? I remember those word problems being difficult. When I first got SM I thought they were similar in the level of difficulty.

 

I am hoping with can jump into AoPS after SM 6B. Please don't laugh at me that we have planned this so far out. My kid is just starting 2a and I have been trying to sequence the AoPS already. :lol:

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Would you mind posting one problem? I remember those word problems being difficult. When I first got SM I thought they were similar in the level of difficulty.

 

I am hoping with can jump into AoPS after SM 6B. Please don't laugh at me that we have planned this so far out. My kid is just starting 2a and I have been trying to sequence the AoPS already. :lol:

 

Look at the AoPS Prealgebra pre-test - calculating negative numbers is required, but I think that's included in SM Standards (or in any case, easy enough to supplement if it's not in there, such as in the US ed. - I don't have either so I don't know). Other than that, I'd think the pre-test should be a piece of cake for someone coming out of 6B.

 

As for a problem from UCSMP, I cracked open the Grade 2 book to the middle (page 167). Here is problem 656:

 

To buy a train ticket for the trip from Moscow to our station, two 15-kopeck coins and one 20-kopeck coin must be inserted in the ticket-vending machine. How much is the fare from Moscow to our station? How many tickets can be bought for 1 ruble?

 

on page 262, problem 1050:

 

There were 32 students in each of three third-grade classes. 8 students from each class were made Young Pioneers for May 1. How many other students in these classes remained to become Young Pioneers in the future?

 

The preface notes that of grade 1-3 textbooks, the Soviet texts provided more than double the number of "types" of problems, and that 95% of the American problems required only one operation, while 44% of the Soviet problems required two or more operations.

Edited by wapiti
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From Russian Grade 3, page 122, #471:

 

Two patrols of Young Pioneers walked towards each other from two villages. The Young Pioneers from one patrol walked at a speed of 4km per hour, while those from the other patrol walked at a speed of 3km per hour. THe patrols met after 2 hr. Find the distance between the two villages.

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Look at the AoPS Prealgebra pre-test - calculating negative numbers is required, but I think that's included in SM Standards (or in any case, easy enough to supplement if it's not in there, such as in the US ed. - I don't have either so I don't know). Other than that, I'd think the pre-test should be a piece of cake for someone coming out of 6B.

 

As for a problem from UCSMP, I cracked open the Grade 2 book to the middle (page 167). Here is problem 656:

 

 

 

on page 262, problem 1050:

 

 

 

The preface notes that of grade 1-3 textbooks, the Soviet texts provided more than double the number of "types" of problems, and that 95% of the American problems required only one operation, while 44% of the Soviet problems required two or more operations.

 

Yes, there were plenty of problems, but to my recollection, not that many word problems. Thanks for posting the world problems! Looking at them I can say we aren't missing anything with SM. What I am trying to say is SM is equally challenging. Now I have a peace of mind :)

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Are you pulling our legs, or is this for real?

 

Bill

 

Real. But not in a particulary scary way, like any refences to Beloved Leader and exterminating the decandent West or whatever. More stuff about factories than most US books I've seen, but it is pretty representative of real life, so it doesn't bother me.

 

Grade 2, #160

On the first day the Young Pioneers cleaned 45 m of the track at the school stadium, on the second day they cleaned 6 m less than on the first day, and on the third day they cleaned 8 m more than on the second day. How many meters of the track did they clean on the third day?

 

Grade 2, p 82, #25-4:

42 sacks of wheat were delivered to a mill from a collective farm. This was 6 less than the number of sacks of rye. How many sacks of rye were delivered to the mill.

 

This is my favorite problem in the Grade 2 book for Soviet references:

P 281 # 15

Our factory has its own grade school, technical school and training institute. Of 900 workers at the factory, only 1/3 of them are not in school. How many workers at the factory are continuing their studies?

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From Russian Grade 3, page 122, #471:

 

Two patrols of Young Pioneers walked towards each other from two villages. The Young Pioneers from one patrol walked at a speed of 4km per hour, while those from the other patrol walked at a speed of 3km per hour. THe patrols met after 2 hr. Find the distance between the two villages.

 

 

This day is just getting better and better!!! :lol:

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