I did not make mine show his work. Especially at that age. When he got to where he needed to later, it took a few weeks to get him to show his work. Why torture him for years with something he can learn in a few weeks when the need is obvious? I think we are hung up on making kids do things they don't need to do now just so they can do it later when they need it. When they need it, they can learn how to do it just fine. I think have him redo any he gets wrong by showing his work. That should be sufficient to get some practice. Or give him some harder problems where he does not know the answer right away. Definitely don't make him show his work with mental math.

What you say is true also of books purporting to be "Singapore math." There is variation in quality of the various options now available, including material said to be based on "Singapore math" or products labeled as such.

When you want to buy something that costs 7 cents with a dime and 5 pennies, what do you do? Give the dime and get 3 cents back. You have to have to have to show this with base-10 types of manipulatives. Preferably ones that you can't take apart, or don't allow to take apart, the tens. Or, the other way is to take away 5 and then 2 more. That should not be so hard if you have really spent all the time you should have on number bonds, different ways to make each number, different ways to make 10 especially. The other way is just counting backwards until you have it memorized, or maybe using a math tape, like they do in schools here, just counting backwards without paying attention to place-value at all, but that is not really math. Well, the counting backwards is, I guess, but simply memorizing is not. Though that has to be done eventually for speed. The whole program is about building on earlier knowledge, and this is an example. They build on place-value and number bonds. They will do this throughout. And doing it this way is laying a foundation for more mental math later. Like subtracting from 100. Or, subtract 8 inches from a foot and 4 inches. Or 40 minutes from an hour and 10 minutes. Easy to just subtract 40 minutes from the hour (60 minutes), get 20 minutes, so there are 30 minutes left.

From what I have seen of Math in Focus, which is not too much, they are trying to turn mental math into a procedure, and give all the steps, and just one set of steps, which is not how it is taught in the Primary Mathematics. Math in Focus is an adaptation for US teachers who want procedures I think. Number bonds (in Primary Mathematics) is just to discuss some initial thinking about the numbers, but you don't use them after the initial discussion about different ways to solve the problem mentally. Then you let the child use a way he can do easily. So you accommodation different ways of thinking. From the few pages I have seen of MiF, they don't do that. Maybe they do, but it does not sound like it from your description. There are different US math programs, some work better for some kids than others, they are all different, they also all have some things in common about how math is taught in the US. Like how proportions are taught. There are different Singapore math programs. Some will work better for some kids. They have things in common in certain approaches to learning math. but within those approaches things are going to be taught differently, based on what the author thinks. The MiF is based on a program that is meant for more general student population. I would guess teachers adapt it for more capable students even in Singapore. It may have been further adapted for US classrooms. So, let him the mental math the way he wants. There is no reason for him to follow their steps if he can do it mentally his way. That is the point of mental math. Maybe other parts of the program are useful, unless they also are trying to make it into procedural approach with other topics as well.

I am not that fond of the readers, but they are meant to be discussed, not just read the stories. The point is not really the reading, and it is not really story based learning. There is a lot of math on each page - Like with the Boy Who Cried Wolf the groups of sheeps change on each page, you have groups of 3, then 4, then 5. The color of the collars is important. The arrangement of the boy's lunch on the mat - the mat is first in a square and then in a rectangular shape and then a different shape, different ways to arrange the four tile, so you could talk about area and perimeter. There are shapes on each page, like the shape of the sandwich and on the lunch box. Also sometimes odd and sometimes even number of sheep when they are paired. And the days of the week. Obviously lots of ways to groups the kids - color of shirts, hats, boy, girl, glasses, carrying a tool and sub-classifications, like red shirt but different color pants/skirts. Lots of different things to discuss in Baa Baa Black Sheep other than grouping of bags. Number of balls of yarn on each page and spools of thread and bees. I don't know if that all is worth $3 a book, though, and you can reproduce all the ideas with objects like different ways to sort - I can think of number of dots on different shapes with different colors maybe. I read somewhere that discussion was an important part of the Singapore curriculum - lots of discussion. At all the levels. But it starts this way at K level, which is why there are those pages for discussion at the beginning of each unit in the textbook. Supposed to draw the kids into the math, I think. But it is easier to do in a classroom, when you have different kids noticing different things (or having different methods of solution, which is best if any?).

In the Primary Mathematics, they do the "column" method only briefly with 2-digit numbers at the beginning of 2A before quickly moving into doing it with 3 digit numbers in order to show how it works. This is a strategy used throughout the curriculum - to show a new method with easy problems first that they can do already with the old method (mental math, making tens, etc. for adding and subtracting 2-digit numbers). Is your almost 6 year old doing 2A now? Can he easily add and subtract 3-digit numbers mentally? If so, maybe for the addition have him add more than 2 numbers, like a 3 or 4 3-digit numbers, using mental math compared to the algorithm, assuming he is OK with the thousands and ten-thousands place since the answer will be more digits likely, or numbers that have all the digits greater than 5 where there is renaming over more than one place. For subtraction, give him problems where there is renaming over more than one place, like 812 - 478. If he can do those kinds easily mentally, then I guess you just have to add more digits to show the usefulness of the algorithm or get him to practice it, or not worry about it until you get to larger numbers, or a problem he gets wrong mentally.

I think if you report errors (there is a link at the top of the errata page) they get added to the errata.

Maybe I am in the minority, but I don't think kids have to show their work at that age. Later, yes, when other skills and maturity in expressing themselves catch up. And they can easily learn later. Just because they don't learn how to show their work at 7 or 8 does not meant they won't learn when they are 14 or 15 and taking classes at the Community College or somewhere where they have to, or just before that to prepare them. Talk about it some, but don't push it. If they are having trouble expressing themselves, explaining how they got an answer, that will come when they are older.

It is in US edition. Not in standards edition. The point is what should your child do if they can't answer a problem? They actually do have the skills to find the answer. So you discuss it. How could we solve this? You can list equivalent fractions for both. You can use fraction bars. Either way would work. Or you can throw your hands up in the air and say you were never taught the steps for this so can't solve it. Actually, it might be a misprint.

You don't need to go to training. Just work on lots of problems. Different kinds. If you just follow examples, fill in numbers for already drawn bars, and so on, then you don't really learn them. If you work on a problem where you don't have it pre-drawn pre-exampled and stick with it, then you really learn them.

My understanding is that in the Primary Math the textbook is not supposed to "connect all the dots" for the child. The textbook is something you use to guide them to think about the problem. Not see the answer before they have to think. The teacher is supposed to guide and discuss and introduce the topic concretely. In my opinion, US math and newer math textbooks do too much of the thinking for the child. So they don't develop the ability to be intuitive. And that the US math books expects the teacher not to know much and not be able to guide the student in thinking and discussing the problems. A math book addressed to the child can only deal with the level of the child's understanding, whereas a teacher knows more and can, if good, discuss different approaches, look at a problem from different angles, really understand it. I think that is the purpose of the HIGs, to give me more background than the student. I think that it is the concrete introduction, the discussion, the getting students to think before being told, that is why the Primary Math gets such good results.

All you have to do is use the corner of an index card. Fit it in the angle and see if it is smaller or larger. That is why they have them make a right angle by folding the paper. Partly to see that it is a fourth of a circle. But folding a paper can be a little off if not lined up. So use the corner of an index card. No need for a protractor. This is in the HIG.

I thought it was fun to discuss the math and think about it. I guess I like teaching the math and that was important enough to me not to leave them on their own. I tried it once, let my son learn the math on his own, and he just did not get the depth as well. But then, mine learns better by hearing. My other son learns better by reading, I think, but I was more on top of things teaching him. I guess it is a good thing that there are many programs to choose from.

That is a good idea. I also teach using the textbook, not just give it to my student. I write most of the problems on the whiteboard. For the reviews and practices, I copy those pages and tape them to one side of a composition book, leaving the other side for ds to work them out on. We don't use the workbooks on those days, so it isn't going back and forth. I use the textbook, he uses either the composition book or the workbook. It works really well that way. I think the program is meant to be taught by a teacher, not a book. And adjusted to the student. I can throw in ideas from the guide if I think I need to. And there are more than enough ideas from the guide. I looked math Math Mammoth, but I guess I like teaching math, think my kids learn more that reading examples in a book, and the Primary Math is flexible enough for that.