I have a lot of experience with Singapore and love it, but I'm not sure it would be an obvious choice for this particular situation. They spend a couple of pages here and there setting up the idea that 5 x 6 means "five of the sixes" or "five groups of six" but other than that there's not much conceptual teaching at that level. After that it's just a question of working through a few pages designed to help with memory work of the timestables ... and that's spread over two grade levels with the upper timestables coming in 3rd grade IIRC. Further conceptual work on the associative and commutative properties of multiplication and how they pertain to multi-digit multiplication and mental math ... that comes later in the 3rd and 4th grade books.
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If your ds has a good conceptual understanding of multiplication, then it's mostly a question of memorization at this point, and Singapore doesn't have a lot of repetition. If he doesn't have a good conceptual understanding I'm not sure that Singapore is really set up to teach that properly without working through bits and pieces at the various levels.Â
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So although I've never used it, I wonder if Mammoth Math might have something a little more suitable. Then again I don't think of multiplication as being very complicated. My kids were introduced to it as kindergarteners through various discovery-oriented manipulative based games in Miquon Math, and they seemed to just develop a natural facility with it. You might not need a workbook or program at all if you just keep following his lead.
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Miranda