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In math education some people define rigor as working systematically through sequential skills with plenty of repetition. Some people define it as strong focus on logical creativity, building the ability to adapt and apply mathematical concepts to new problems and increasing levels of complexity. There aren't really many programs that cover both of these, because they're philosophically different. The first believes that accurate computation is the most basic foundation, the second that deep understanding is the foundation on which further math learning is built.
I'm more in the latter camp. Singapore Math has worked well as our basic goto math curriculum during the primary years. The only problem we've had is that it has been so good at helping my kids master K7th math that they've finished it before age 10 and haven't been ready for the very highschoolish style of presentation of the Singapore Secondary programs.
Miranda
Mountain mama to two great kids and two great grownups
Define rigor.
In math education some people define rigor as working systematically through sequential skills with plenty of repetition. Some people define it as strong focus on logical creativity, building the ability to adapt and apply mathematical concepts to new problems and increasing levels of complexity. 
With Singapore, what do I need? I assume that I would need the Home Instructor's Guide, Student Textbook, Student workbook. What about the extras: Intensive Practice, Challenging Word Problems, Extra Practice, Math Express, Brain Maths, etc.? It's so confusing to me! We're probably looking at level 1B or 2A to start. What manipulatives do I need? I can't find a list of recommended materials on the Singapore site, but maybe I've missed it.
Thanks for all your help!!
With Singapore, what do I need? I assume that I would need the Home Instructor's Guide, Student Textbook, Student workbook. What about the extras: Intensive Practice, Challenging Word Problems, Extra Practice, Math Express, Brain Maths, etc.? It's so confusing to me! We're probably looking at level 1B or 2A to start. What manipulatives do I need? I can't find a list of recommended materials on the Singapore site, but maybe I've missed it.
Thanks for all your help!! 
Once, I wanted more practice on a subject, so I went to math mammoth and got some supplementary material. Sometimes, we don't do the book sequentially. For example, if dd is really frustrated with a section, we might find something unrelated to focus on for a while. And then come back to where we left off.
Overall, I am very happy with this.
As far as manipulatives, I haven't bought any yet. We have used the little square legos for "ones" and stacked towers of ten of them for "ten". I may break down and buy some rods and unit pieces. But, I would take the manipulatives search one day at a time. You may be surprised with what you can do with household stuff. We do have some tools (I don't think of these as manipulatives) ruler, compass, protractor, etc.
Amy
Mom to three very active girls Anna (15), Kayla (12), Maya (9).
For manipulatives we've used coins mostly (pennies, dimes and the Canadian $1 coin for 1's, 10's and 100's). We do own cuisenaire rods from our preSingapore time using Miquon math, since we don't start Singapore until the 2A/2B level in this family. We do own a metre stick, metric measuring cups and a nice Ohaus twopan balance in grams, but that's just because we're geeky Canucks, not because we felt we couldn't do Singapore Math without those things.
Miranda
Mountain mama to two great kids and two great grownups
With Singapore, what do I need? I assume that I would need the Home Instructor's Guide, Student Textbook, Student workbook. What about the extras: Intensive Practice, Challenging Word Problems, Extra Practice, Math Express, Brain Maths, etc.? It's so confusing to me! We're probably looking at level 1B or 2A to start. What manipulatives do I need? I can't find a list of recommended materials on the Singapore site, but maybe I've missed it.
Thanks for all your help!! 
DD 9 DS 7 yrs
I think the Extra Practice OR the Intensive Practice books can be helpful if you want some additional practice because there isn't much drill in the workbooks. Getting both would be overkill, IMO. I've picked up both books to compare and there are 2 Intensive Practice books per grade versus 1 of the Extra Practice and the problems seem similar. If you think you might want some extra drill, but aren't sure, I'd go with the Extra Practice book only.
And if you can get your hands on the Challenging Word Problems books  get them! They are now out of print, but are great! You could use these regardless of whatever math program you go with.
JMHO.
Laura  Mom to ds (10) and dd (7) "Time stands still best in moments that look suspiciously like ordinary life." Brian Andreas.
There's also a yahoo group where you can ask questions about it.
I've only been using it with my daughter for a month or so, but I'm impressed. The curriculum is challenging and really encourages kids to think about math. There are folks in the Yahoo group and on the WellTrained Mind forums who've been using it much longer, and/or are using it with older kids.
It's also free.
I am interested in this progam for my students tell me more.
we have been using Singapore for years and are just reaching the end of it. We used the textbooks and the workbooks, because starting around 4a, I have the kids go over the the textbook by themselves to learn the concepts and the additional problems and reviews in the text book made sure we covered every topic thoroughly when they were a bit tricksy. I can't speak highly enough of challenging word problems, but i am not sure the new editions are out yet. we also do a bit in intensive practice. we are mathy and like the HARD problems! an important note, it really helps to understand the pictorial method of problem solving that Singapore uses. this allows children to solve much harder math problems w/o using algebra. I didn't know this at first and ended up teaching my boys basic algebra just to be able to solve some of the word problems in CWP4. I found joining the Yahoo singapore math group to be quite helpful.
NM, I found answers on the web site after searching a bit more.
Lovin' my fourpack: M, S, a different M, and me.
I seem to be one of the few here who loves Saxon math. I know it can be repetitive, but the repetition really does aid in mastery. For what it's worth, I am a math person myself (finished top of my math class in Naval Nuclear Power "A" School) and I consider Saxon top notch. I will say I don't care much for Saxon K. By kindergarten my kids have been ready for the 1st grade workbook, so we just skip Saxon K. I hope you enjoy using whatever you choose!
Homeschooling Mama of 6 wonderful kids (14, 12, 10, 9, 7, and 5)
Homeschool Tracker  keeps me sane
My favorites: Teach Your Child to Read in 100 Easy Lessons, Saxon Math, Easy Grammar, Sonlight, Writing with Skill
Just to provide an alternative perspective, you might take a look at the Mathematics Enhancement Programme out of the UK.
There's also a yahoo group where you can ask questions about it.
I've only been using it with my daughter for a month or so, but I'm impressed. The curriculum is challenging and really encourages kids to think about math. There are folks in the Yahoo group and on the WellTrained Mind forums who've been using it much longer, and/or are using it with older kids.
It's also free.
We use MEP too. If you are looking for advanced math concepts taught early on then I would recommend looking at it.
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