# Singapore and mental maths

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We have been using Horizons 3, and I have just realised that my dd9 really can't do mental maths at all. My fault, as it seems natural to me, and I just assumed it was for everyone.

I have heard a lot about how good Singapore is at teaching mental maths. I am adding 3 of the supplemental Singapore books, all of which show solutions. I am hoping this will be enough to set us on the right path, but in the event that it's not:

1) Am I correct that Singapore explicitly teaches mental maths?

2) In which level / book is this taught?

We'd prefer to buy new syllabus books directly from Singapore, so info on those books would be appreciated, although any responses welcome!

Nikki

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:lurk5:

I spent an evening recently trying to find a list of the mental math techniques Singapore teaches, or at least a description or example of how the curriculum goes about doing it. I came up dry, wrt to a Singapore-specific approach.

However, I did find a general description of mental math techniques - kind of the overarching idea behind it all - that helped me truly, finally comprehend the whole concept - enough so that I think I can teach mental math without needing a special curriculum.

What was it? At the core, most mental math techniques are just using the commutative, associative and distributive laws to turn unfriendly numbers into friendly ones. E.g. 597 + 456 isn't immediately obvious, but (600 - 3) + (460 - 4) = 600 + 460 - 7 = 1053 is trivial. 976 x 25 looks daunting, but (976/4) * 25*4 = (1000-24)/4 * 100 = (250-6)*100 = 24,400 is simple.

My understanding is that all Singapore does, wrt mental math, is nothing more than that basic principle, explicitly illustrated in several frequently used ways, combined with lots of practice to develop a good number sense.

There are also some common speed math tricks, which - while based on the same fundamental laws - are less obvious ways of decomposing certain types of numbers into friendlier ones. I've no idea if Singapore teaches them (does anyone know?), but any number of speed math books contain them. (I have Speed Mathematics Simplified, which integrates abacus techniques with the tricks.)

(There are some complete speed/mental math systems that allow you to do nearly any problem mentally without requiring you to be able to find friendly numbers - the Trachtenberg system, for one - but I'm near positive that Singapore isn't teaching anything like that.)

HTH

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Thank you both for the information.

I was in fact looking to supplement Horizons 3 with a Singapore word sum book anyway, then did the placement tests for Singapore, and realised that the gaps between Horizons and Singapore were bigger than I expected, particularly in the area of word problems and mental maths. I thought I'd finish up the year in Horizons, with Singapore to supplement, then perhaps make a switch back to Singapore (dd found Gr1 Singapore too repetitive). I was wondering whether I would have to backtrack to find where mental maths was taught, so it is helpful to know it is covered in each level.

It didn't occur to me to look for mental maths techniques separately from a curriculum, so thanks for the idea. Since I realised the gap in dd's understanding, I've been showing her how I think through problems, but would like to do it more sytematically.

Nikki

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Instead of picking your way through Singapore, you could pick up the first two or three Maths Express Speed Maths Strategies books. You needn't teach all the techniques, just the handful you feel would be most useful.

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Thank you both for the information.

I was in fact looking to supplement Horizons 3 with a Singapore word sum book anyway, then did the placement tests for Singapore, and realised that the gaps between Horizons and Singapore were bigger than I expected, particularly in the area of word problems and mental maths. I thought I'd finish up the year in Horizons, with Singapore to supplement, then perhaps make a switch back to Singapore (dd found Gr1 Singapore too repetitive). I was wondering whether I would have to backtrack to find where mental maths was taught, so it is helpful to know it is covered in each level.

It didn't occur to me to look for mental maths techniques separately from a curriculum, so thanks for the idea. Since I realised the gap in dd's understanding, I've been showing her how I think through problems, but would like to do it more sytematically.

Nikki

Nikki,

If you do decide you want a whole new curriculum I think Right Start is just as strong as Singapore on mental math, but doesn't make the other logical leaps that Singapore does. Singapore is my first love of programs, and Right Start is...well they don't love it but they don't hate it either. :D

Heather

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The Home Instructor Guides for Singapore teach mental math techniques and contain mental math exercises.

Mary

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Singapore has a Supplement series called MathExpress that is specifically geared towards speed/mental math strategies. For my then 3rd and 4th graders, I started them out on MathExpress Level 2 (addition/subtractions double, triple digits) and having them go through all the levels. It explains strategies then have several pages of practice problems that are supposed to be timed.

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I've used some of the supplements, but use Singapore as our primary math as well. IME, it is the texts that do the teaching of techniques.

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• 1 month later...

:lurk5:

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I think Math Mammoth does a very good job of mental math techniques from the very start. You might e-mail Maria Miller, the author, and see what she suggests. http://www.mathmammoth.com/add_subtract_3.php

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Yes, Singapore explicitly teaches mental math. It is taught at all or nearly all levels.

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No, Singapore does not only teach math mentally (I think that is what you are asking). It is touched upon in all levels. There is usually a chapter in each level that covers it specifically. Basically they are just strategies for solving problems mentally. I think you could teach that without Singapore if the only reason you are considering it is for the mental math.

Mental math is explicitly taught in one or so chapters in each book. However, it is *used* throughout the books.

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