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My DS10 has been ahead of his 5th Grade Math classmates in speed of learning in typical Math taught. When students, like this switch to Singapore Math, do they typically still remain ahead of their peers? Is there a way to pretest with Singapore Math? Or adjust the pace for quicker learners? He tested 50% in 6th grade Singapore Math that he will do for next year. School thinks they should not move him up another grade.

Any suggestion to know more about Singapore Math?

Last year, the teacher did see his ability but, could not meet his needs for speed of learning.

I would tend to think that a fast math learner would continue to learn quickly on any math curriculum, as long as it wasn't defective and chock-full of repetition. Singapore Math has a separate workbook for each half-year that you can skip, in part or in full, to keep interest higher and allow for a faster pace, and you can in addition skip some of the drill in the textbook itself.

There are no pretests built into Singapore Math, as far as I know (ETA: I'd forgotten about the level assessments that are linked to by LittleCherub below). What I do with DS6 is assess how well he knows material we encounter, and throttle the number of skipped questions up or down accordingly (or alternately let him do them in his head instead of on paper to save time).

The amount of time taken for a section or page depends on the number and type of problems. At the end of sections and subsections are reviews, where there are a lot of problems on a page. I would estimate that DS6 averages 3-5 minutes per page in the textbook, not counting enrichment from the teacher's guide.

I guess that I'd agree that 50% knowledge is not mastery, but the material in the Singapore books is condensed enough so that he could probably clear at least sixth grade over the summer with no sweat. Then maybe you could re-make your case based on beginning-of-year increased MAP scores or similar.

Yeah, but I think the OP is thinking about curriculum compacting, which would ideally involve pre-tests for each little section (as I understand it). I could be wrong.

ETA: The linked-to tests seem to be for placement at the appropriate half-year level, so the main problem is that they're not granular enough for use as curriculum compacting pretests.

A few more thoughts:

I've come to realize that at least for home schooling or other one-on-one instruction, pretests may be largely unnecessary. When you're familiar with a child's abilities and can see that working a particular type of problem is very quick and easy, the child complains of boredom or expresses a wish to get on to the next section, etc. you can skip some repetitive material on an ad-hoc basis. The material itself fulfills the function of a pretest then, and the structure of Singapore Math lends itself well to this. Pretests are obviously more useful for compacting in a classroom setting, since a teacher may need a number of questions right and wrong to be able to check off on a progress checklist.

With Singapore math, I think it would be possible to quickly construct one's own pretests. This sort of pretest would also be palatable to a (reasonable) teacher, if the Singapore Math is planned to be administered at school as part of differentiation. And if the teacher preferred to do it, it wouldn't take long at all, and could be reused for future children also taking Singapore Math.

For constructing a pretest for a Singapore Math section, one could skip to the review pages for that section, and pick one or two representative questions of each type, either from the review pages or the workbook. I guess retyping or otherwise copying the questions (and answers) would be in order, to make it easy to reuse the pretest. Or one could simply give all of the review questions as a pretest, which might involve some repetition but would still compact quite a bit. If a child failed the review questions by getting a lot of them wrong, it might actually help reinforce and strengthen for them to do the same questions again later after learning the concepts.

Another way would be just to skip to the review section and have the child do the word problems there. This way would let the child skip almost all the material in the section if they displayed mastery, while still giving them extra problem-solving practice, and hopefully avoid any boredom. The only problem would be if there were no word problems in the review section for a concept taught in the section, so one would have to be alert to that possibility.

One general concern with compacting math this way might also be that a child might need a little more practice on certain operations to improve speed and/or accuracy. Good judgement in how many problems to include in a pretest would address that concern. The Singapore Math review problems do include more quickie operation-practice types of questions than word problems, so that might be a good reason to just use the entire review part as a pretest.

I think that with a teacher receptive to the idea of curriculum compacting, volunteering to create pretests could help.