About 6 months of minecraft creative mode :). He was 3rd grade.

On balance I feel both are great programs. I own (and have used) both. My kid preferred SM for the pretty pictures. I preferred SM for the IP, CWP, and Process Skills. Plus I thought the TB was not so cluttered compared to each MM sheet.

Some background: It took my son 18 months to finish AOPS Pre-Algebra. During that time, he completed every section exercise and every review and challenging problem. He worked very hard throughout the book, and I would say he has come away with a very thorough understanding of the material. We started Intro to Algebra 2 months ago. In that time he has completed 4 chapters (45 minutes a day, 5x a week; lecture replacing exercises as needed). He has completed all section and review exercises, and also completed a sampling of challenging questions. My concerns are: pace, understanding, and retention. 1. Pace - Is he going too fast? When he was younger, he went through a couple of years of SM in 9 months, so there is precedent. But still - a chapter every two weeks just seems...really fast for Algebra, especially considering the 5 weeks per chapter average from the Pre-A book. Right now, I only give him 3 or 4 challenging problems. I think even if I were to assign all the challenge questions, that may only extend each chapter by a week. Looking at some of those questions, I am hesitant to assign them all just for the sake of taking more time (plus I want to save them for review later). 2. Understanding - Is it possible to go so fast and still truly understand the material at a 'conceptual' level? Again, there is precedent from prior use of SM. In addition, looking through these 4 chapters, I'm finding very little in the way of 'concept' that hasn't already been explained by the Pre-A book. The one salient area I see is that when working a problem he often does not use his latest tools. I think that this will come with exposure and practice. How might I assess conceptual understanding beyond the review questions? Through the four completed chapters he has maintained about 85% accuracy on review exercises (of those 15% I would say 90% are silly errors (signs) and 10% conceptual errors). Based on this I would say that has at least shown procedural proficiency of the topics. 3. Retention - Will he remember all this stuff in a year? I think we are OK here. The AOPS questions seem great at mixing concepts together to keep them fresh (but someday he will run out of book...). But...there is Alcumus and the left over challenge questions. I think I will also torture him with the Algebra A/B online classes at some point. What else could I potentially include to help retention?

I think Wendy nailed the concrete aspects. For a more abstract treatment consider the following. On graph paper, draw any size rectangle. Work with it until there is no more doubt that A=bh. Then split the rectangle diagonally into two identical triangles. Draw many sizes of rectangle until again no doubt that there are always two triangles inside, and the triangles are the same size. Thus area of triangle is A=(bh)/2. (One half base times height is due to commutative property). Then introduce the 'related rectangle' for a triangle: For any triangle, you can put a rectangle around it such that one side of the triangle forms one side of the rectangle. The other side of the rectangle is given by the height of the triangle. Work this until convinced that the Area of the triangle really is still A=(bh)/2 (break up the rectangle into two or three pieces). The parallogram is just two triangle stuck together, so A=2*(bh/2).

Yes get the answers. I'm sure you have better things to do than spend 30 minutes on a problem only to have your kid say 'Are you sure??'

Actually, in the case of an actual matrix, order does in fact matter. That is, a 4 by 7 matrix is not the same as a 7 by 4 matrix (in fact the first is the transpose of the second, and vice versa). More to the point of the OP's question, when dealing with multiplication at this level, whether it's written 4x7 or 7x4 doesn't so much matter from a pragmatic perspective - the product is the same. However, at a deeper conceptual level, it's nice when the student actually understands that "4 groups of 7" (4x7) is distinctly different from "7 groups of 4" (7x4). Indeed, one can hear the difference in the naming of the thing: "4 times 7" = "7 + 7 + 7 + 7" vs "7 times 4" = "4 + 4 + 4 + 4 + 4 + 4 + 4" (As an aside, this point becomes even more salient in computer science when dealing with array indexing. Since all data memory is essentially flat, a 'matrix' has no real meaning, and is defined in terms of rows and offsets).

I would recommend the PreA book. The first chapter alone is worth the price if you really go through it and internalize all the proofs.

Definitely try AOPS PreA. The pre-test is kind of pointless though. It is not reflective at all how hard the book is. My advice if you decide to use it: spend a lot of time on chapter 1. Really understand all the concepts and properties and get used to the idea of proving why the arithmetic works the way it does. It will save you much headache in later chapters when she makes silly errors in signs.

After SM 6B we did AOPS PreA, because torturing the boy is fun. Now in AOPS Algebra he finds everything so far 'not that hard'.

The college board has a PDF showing correspondence between ACT and SAT (CR+M). Based on this I would say a "respectable" score is 1200 SAT which it says is 26.

5 has some meaty stuff in it; would not recommend to skip that. 6 is the weakest, and IIRC doesn't have much in way of 'new' material that isn't repeated later. Drop 6 if you must, but consider compacting if possible.

Try an Alcumus account? You can set the level and there's lots of problems. If your son understands the math, there's is no point in doing it again.

I have no actual recommendation but I thought I'd mention something. There's theory and practice to CS. Theoretical CS is all math and is pretty boring unless you know you are going to do CS for a living. Practical CS is mostly programming and that can be interesting. But you need the boring background and math first. In HS I would recommend to focus on the practical side to avoid burn out (did I mention CS is boring?).

My kid did not like writing things out. But I felt that book was the right time to teach organisation, so I made him write out everything for every single problem. Only for chapter 1 though. Good times :) Now he has no problem organising his work.

The language used by Arduino is C with some extras and some libraries for interfacing with the board. I think there are alternatives to C for Arduino but you cannot interface with the board directly. Although you can buy a Netduino, which uses the .NET framework, and then use C# (which is pretty close to Java). Python is not supported for direct interfacing to Arduino board (though you can 'cheat' and talk to the board using the serial port). The syntax of Python is not like C, so there will be some learning curve. Java is like C++ but not exactly, so again learning curve but smaller. The power for all languages lies in the functionality provided by various libraries, so there will always be some learning curve involved (for example on Arduino there is the avr-libc).

Might I recommend C instead? Easier to learn by far and it's widely used in industry. The details of <insert current fad language here> is hard to grasp, but the logic of languages in general is not. 11 is probably too soon (although I learned at 11...) for all the minutiae of any language I think. My old standby has always been 'Teach Yourself C in 21 days'. It teaches all the basics of the language and programming in general. Sadly it is not that kid friendly (no cartoon characters) but the text is not difficult to understand.

I tortured my kid for 45 minutes a day 5 days a week for 15 months: ~225 hours. But he did every single problem in that book.

Your son is 5 so probably no SM book is going to entertain. All the SM books look basically the same. The WB is the most boring looking of the lot. The TB at least has color in the newer versions.

IMO, this (and all similar problems of this sort at the2-3 level) is a logic puzzle. When my son was younger, we would reason these out, using whatever was available at hand to describe the various scenarios. Although algebra was never formally discussed, whatever he eventually wrote down was effectively a linear equation. We did sometimes used bar model for the tougher ones (CWP4+). In this case, I would consider it a success if my student realized that a Dog is 2 pounds more than a Moneky: If D+C+M = 12 AND C+2M = 10, then D = M+2 (because after the dog left and another monkey joined we are still 2 pounds lighter). The rest follows directly, and is more pattern matching than math at that point.

FWIW, my kid is advanced in math and can't do mental math to save his life. I learned to let that go early. If the concepts are being understood and mastery is demonstrated on paper, move on.

Well...sort of? :) There's a number on the front on each book, but grade level is such a relative term. They correlate strongly with the Singapore math texts, FWIW.

I second this. Having used both zacarro and process skills, I prefer process skills. More focused, more detailed teaching and harder problems.

Don't know about MOEMS (I'm curious too), but I know the AOPS folks have AMC problems and solutions. Would those work for what you're trying for?

How do you plan to proceed? Pressing forward only, or is some backtracking OK? I admit to knowing nothing about ACE. It very well could be a principles based approach. In any case, Singapore and MEP are highly regarded. Singapore middle levels may be hard without prior exposure. AOPS is good also but is generally seen as a more challenging program (both format and content).

Maybe they just don't like geometry? I don't remember us spending too much time on it, couple of months (TB+WB+IP+CWP). But we did skip around in the problem sets.