When my kid was using SM (Standard Ed), I tortured him all year round (52 weeks) with all four books. We did (and still do) math five days a week. At that time he was spending maybe 30 minutes a day on WB/IP/CWP (solo), and maybe another 30 min on the Textbook with me. He picks up concepts pretty quickly so we didn’t linger too long on any single topic. He was able to complete the full cycle in a school year (a bit faster in the lower grades). He never skipped any IP nor CWP problems. IP went pretty quickly (on pace with TB + a week each for the exams), but CWP started to lag around L3. By L5/L6 we were a half level behind since I only forced 30 minutes of math solo on him a day (lectures with Dad don’t count as torture – it is enlightenment :laugh:). Most of the time, we skipped over 70% of the WB problems, focusing on the equivalent material in IP instead (at higher levels they don’t match so well so I had to pull out MM problem sets in lieu of WB). I felt CWP was an important enough part of the program to make an emphasis on it (especially at the lower levels; you can only stare at 9+2 so many times). And at the higher levels, the CWP really made him think (sometimes spending his whole half hour on a problem). I think those really prepared him for later work.

Imagine that at your job (8 hours or more a day, 260 days a year), all you do is read dissertations. Now further imagine that each dissertation consists of densely packed chicken scratch that you can barely read. Finally, imagine that you are somehow to glean meaningful insight into whatever is being written out, and then add your own insights in the context of said chicken scratch. Oh, and maybe also correct the grammar mistakes along the way, for good measure. I think very quickly you will come to appreciate that your job is infinitely easier to perform properly if the dissertations were typed neatly and in a consistent format.

As a current practitioner, I'm not really convinced a lot of math is really need to be good at programming. Certainly there are some topics that are needed (Boolean algebra for instance), but on the whole it's really about the thought process. Maybe I'm just jaded - they forced a lot of math on me :D

Yes, just so. The logic of programming is entirely distinct from the practice of writing code. The former is abstract and theoretical. On the other hand, the practice of writing code is concrete. It is lexically and syntactically bound to whatever language is used; the computer will not understand you otherwise. My kid took a Java 'programming' course (not with AOPS). I am pretty sure he learned no Java at all, just what to type and where (especially since it did not compile and I had to help him fix it...). Looking at this syllabus, I'm tempted to ask him if he wants to try this next. The post test looks a lot like a midterm exam... :thumbup1:

This looks a lot like the books I used in college for discrete math (CS side; I also took similar classes from the math dept, but that's more theory than I'd care to remember :laugh:). I'm not sure he's quite ready to dive into this yet but I will tease him with it a bit (he's a big fan of secret codes and stuff atm). Thanks!

Thank you for all these wonderful suggestions! I'm hoping at least one will pique his interest.

My DS9 is currently in the Number Theory chapter of AOPS PreAlgebra. While he appears to understand the material, his error rate in the problem sets was higher than his average. When I asked him about it, he claimed this was because NT is "boring". Please recommend some material (texts, problem sets) that might him help see why NT is cool and interesting. Otherwise this will be a long chapter :p

Along the same vein: http://www.wolframalpha.com It's much more than a simple calculator program, thoughIt's a very powerful program that can be used for a variety of topics to include: math of all levels (from 1+1 to axiom of choice), science (e.g., schroedinger's cat), and general nonsense (e.g. how much wood would a woodchuck chuck if a woodchuck could chuck wood). The free version doesn't shown step by step, though. Also available for iOS and Android devices at a pretty cheap rate (for what you're getting). Sometimes the apps go on sale for a buck or two. BTW that last is apparently about 361.92 cc per day. Wolfram even cites a research paper. :D

I have a question: Why is 0 not a multiple of 12 or 9? From http://mathforum.org/library/drmath/view/60913.html: Let x and y be integers. Then x is a multiple of y if there exists another integer z such that x = y*z. That is the definition. Now let x = zero and let y be an arbitrary integer. Can we find an integer z such that 0 = y*z? I think you'll see that choosing z = zero will do the trick every time. So zero is a multiple of every integer. Did I misinterpret this explanation?

When written out, the method I described looks exactly like the standard algorithm. I just placed an emphasis on place values while working. My son does fine with division. His problem now is that some numbers look like letters :p

I teach a sort of oddball method that seems to work for my kid. It's easier for me to show than actually put into words, but here is how I would have approached the example you provided. In the example I write like this: XX (yy) where XX is the number and yy is the value of the number. 0. Start with the highest place value in the divdend (in this case ten thousand). 1. How many 37 ten thousands fit into 8 ten thousands? None so skip this place since it's at the beginning of the number. 2. How many 37 thousands fit into 85 thousands? 2 so put 2 on the 5 (thousand) and subtract 74 (thousand), leaving 11 (thousand). Bring down the 4 (hundred) 3. How many 37 hundreds fit into 114 hundred? 3 so put 3 on the 4 (hundred) and subtract 111 (hundred), leaving 3 (hundred). Bring down the 3 (tens). 4. How many 37 tens fit into 33 tens? None. But we can't skip this place because it's in the middle of the number, so put 0 on the 3 (tens). Bring down the 4 (ones). 5. How many 37 ones fit into 334 ones? 9, so put 9 on the 4 (ones), and subtract 333 (ones), leaving 1 (one). 6. Oops we ran out of places in the whole number, so what's left is the remainder. At higher levels the method continues: how many 37 tenths fit into 10 tenths, and so on. Note also that the written form is closer to the traditional method (write 74 not 74000). By this reasoning in Step 4 the student sees why there should be a 0 in the tens place.

The actual building of a consumer-level desktop computer really boils down to connecting various large-scale parts together, and will likely not take more than a few hours to a day, even for the most novice builder (I'm assuming a passing familiarity with the various terms, enough so that they are understood when encountered in the instructions). As such I think it would be tough to create a half credit course just for that. Since he's more into hardware, check out the Raspberry Pi. It's a nifty little piece of computer hardware (emphasis on little!) that runs about $35: http://www.raspberrypi.org Also, have you considered making the project into a semester-long research paper? That way, the building of the computer can be the culmination of all the research, while the half credit can easily be justified by the research and the resultant paper. Some ideas for what might go into the paper: * History of computing (here computing meaning electrical or mechanical) a. Famous people: Charles Babbage, Ada Lovelace, Alan Turing, Gordon Moore, Bill Gates, Steve Jobs, etc. (no shortage here) b. Timeline of computing (major events in evolutionary history of computing hardware and software, perhaps also of computer science and/or of theory of computing) * Computer hardware a. Decrease in size over time (vacuum tubes vs. transistors; Moore's Law; desktops -> laptops -> tablets -> phones -> watches -> ???) b. Personal computer architecture (IBM PC vs. Apple; Intel vs. PowerPC) c. Various components that go into a modern personal computer. Plenty of potential topics for discussion in this area. Can be as detailed or terse as you like, depending on the interest. i. Motherboard, CPU, RAM, hard drive, video card ii. Why heat dissipation is important ("heat sink"). Can even tie physics into here by discussing why the CPU gets hot in the first place. iii. How do all the parts talk to each other? d. Difference between consumer-level computer ("desktops", "laptops") vs. industrial or military-grade computers ("embedded systems", "single board computers") * Computer software: Operating systems (e.g., Windows, MacOS, UNIX), programming languages (e.g., assembly, BASIC, C/C++, Ada, Java, HTML, Perl, Python)

A hexahexaflexagon is a 6-faced hexagon that flexes... agon and agon :lol: Apparently there are many different flavors of these puzzlers. DS is currently working his magic on this one: http://loki3.com/flex/rhombus.html

Thank you all for the reassurance. I hope that with continued guidance and some more time we can get these under control (perfection is not expected, but quality work is).

My DS, who is almost 9, has a good grasp on the concepts ("the whys"), but he often gets answers wrong because he lacks attention to detail when performing the manual calculations ("the hows"). These do not occur all the time, but they happen often enough that I am concerned. From what I can tell, he exhibits this behavior in two key areas: 1. Arithmetic error In this case, it's as if sometimes he doesn't even see the numbers on the page; the calculation will plain just be wrong. I ask him to go over it again, and he will quickly see where he made the mistake. I'm fairly sure it's not his command of the facts (in his daily work there are a few drill problems and he has no issues with those). 2. Transcription error While working on a multi-step problem, he will correctly find the partial answers, but then jot them down incorrectly while using those partial answers in another part of the problem. So for example: "Find the area of a circle whose radius is 4.5 inches". He will correctly calculate that r*r = 20.25, but then when calculating pi*(r*r), he will write 21.25*3.14 (or whatever happens to be flavor of the week). Are these errors expected at this age? Will attention to detail simply improve with age and practice, or should I try to actively guide him?

I apologize in advance. My comment is totally off topic, but this: is precisely why no one actually exists in the Universe, and anyone you might actually meet is but a figment of your imagination :laugh:

Process Skills In Problem Solving: http://www.singaporemath.com/Heuristic_and_Model_Approach_s/151.htm. Price isn't too bad (~10). I'd go back to L3 and work through those if possible. I think it would be quite a stretch to start with L5 without any prior exposure. PS is more instructive than CWP and goes into detail how to apply the various bar model to various concepts. CWP would be a good resource for practice. Irony aside, the practice level CWP questions often don't need to be modeled but the challenging ones are great practice.

Thank you. I understand this now. Despite the section being titled 'Fractions of a Set' it didn't occur to me that the size of each square ('unit') could be a fraction of each person's total. For a while there I was afraid the concept of 'Fraction' became unglued :D After reading your bar model, I went back and re-did the algebra with T/8 = R/15. Growing up I was always taught to eliminate the fractions to make manipulations easier (No exceptions under penalty of death!). Of course it still worked, but (7/15)R = 350 is more intuitive once I got over breaking that rule.

Thanks everyone who offered their solutions. It helped me to expand my understanding of bar model. My intent with this question is to try and understand the concept and rationale behind the usage of the bar model in general, and for these types of questions in particular. I'm not trying to teach DS any algebra with these questions, although we may circle back sometime and work this problem that way. In particular, I want to highlight the Process Skills method for this concept (which they call Comparison Unit Model Concept). Here is the question from Process Skills Level 5 (Section 2.3 example 2): '3/4 of Tony's savings was equal to 2/5 of Rizal's savings. If Tony saved $350 less than Rizal, how much did they save altogether?' The solution offered by the book: 'Before drawing the model, convert 3/4 and 2/5 to fractions with same numerator, such that 6 units of Tony's savings was equal to 6 units of Rizal's savings. 3/4 = 6/8; 2/5 = 6/15. 15 - 8 = 7 units. 7 units -> $350. 1 unit = $350 / 7 = $50. (15+8) units -> 23 x $50 = $1150 Total'. In their solution, they highlight that yes 6 of Tony's is equal to 6 of Rizal's, and on Tony's bar there are 8 total sections (2 unshaded), and on Rizal's bar there are 15 total sections (9 unshaded). Also in the picture is that $350 represents the last 7 of Rizal's sections, which extend past Tony's 8 sections. Please explain how they arrived at this methodology. I cannot follow it, even though I was able to solve this problem with the a bar model (but I solved for Rizal's money first then circled back to Tony's money then added them up). I can't follow what the numerator and denominator represent anymore in their solution. In fact no part of the solution makes sense to me. TIA again :laugh:

The part I don't follow is how you know that each square is 6cm? As Q is 5 squares and P is Q plus 6cm all I know for sure is that each of Q's squares is the same value, but cannot claim that those squares are 6cm.

Please explain how to solve this problem using the bar model method. I looked at the answer and it seems so simple but I just can't understand where it comes from. I even read the Process Skills (Book 5!) topic on this, but the explanation is so terse. The question comes from Challenging Word Problems Level 4, Section 5 (Fractions of a Set), Challenging Problem #7 (page 59 in my book): "Rod P is 6 cm longer than rod Q. 3/5 of the length of rod Q is equal to half the length of rod P. What is the length of rod Q?" Using algebra I can find the answer, but I need to see how the bar model is used to solve this. Thanks!

Your method is equivalent; there's nothing wrong with what you're doing. In fact you should take this opportunity to explain and explore the commutative property of addition (and perhaps also explore the fact that subtraction is the inverse of addition). Whether you use the proper terms or not certainly depends on the child but I think the concepts should be explored even at Level 1. After all, an understanding of The Why of It has to start somewhere.

Never had the Teacher's Manual, so can't comment on that. The Home Instructor's Guide for the Standard Edition is very good. However you may not actually need it, depending on your comfort level with math in general and the Singapore style in particular. IMO, Level 2 is a seminal level of SM (along with parts of L3), and having the HIG for that is very much worthwhile.

The Lexile website has a section just for this purpose: http://www.lexile.com/fab/ From what I understand, that number is supposed to be the child's instructional level. Having searched for books against it, I have to say I don't find that necessarily accurate for my kid. Based on his Lexile score, the books we find for him are often too easy. However, this could be because the score is artificially low for him (he tends to rush through tests). I suggest you use the site to find some books within range, then have them read a few random pages to you. Then ou will be able to tell how accurate the number is for them, and can plan accordingly in the future.

Hmm, I've never been referred to as a 'she' before. I wonder if this means I can get the mom discount at Legoland?? :laugh: Seriously though, this is why I like this forum - a simple question yields such an informative discussion :) Thanks!