(just at elementary)
So is the language album - and history - and geography....
It is true that the traditional Montessori elementary level mathematics album (and the others listed) does not contain some information that is required by every state in the US and probably by most standard school requirements around the world's first-world countries.
But let's think about cosmic education.
Mathematics is not a stand-alone subject by itself.
Mathematical principles are embedded in the very life around us; the very things that support that life.
Mathematics as a human language has come down to us through history as a gift from our ancestors. We have built upon it, used it, expanded it, created a supranature with it -- we live it every day and we pass it on to those who come after us.
We humans by nature have a mathematical mind (bear with me on this one - future Montessori Nugget!).
So let's think about this.
What is "missing" from the mathematics elementary album?
--graphing: look in geography (economic geography with production and consumption); also see botany and zoology studies; it is also included in math, but not as a stand-alone album page; be sure you have an album with ALL the exercises.
--estimation: used in practical situations all over the place, most notably in geography (economics), fractions, long division
--statistics and probability: really get into it with economic geography; also covered in history studies
--comparisons (greater, equal): exercises within math presentations
--measurement: may be introduced in math, but heavily utilized in every other area of the room in practical life situations --- check Geometry ;)
--money: practical life (Goings Out, literal practical life); extension of various decimal fraction album pages and experience is assumed when children are working on divisibility (early math)
What is "missing" in language?
--Research skills: no formal album page exists, but exercises, presentations and almost all follow-up work requires it. The entire elementary sequence focuses on research - show the children how to use tools as they come across them; formally these things are introduced in economic geography (upper elementary), but the children are very likely to know it all by then, if they've truly been exploring their own interests already.
--telling time: see the history album
--5 paragraph essays: they're not necessary.
"Missing" in history:
--local history - timelines and charts: the children build these themselves according to the local educational requirements and their own interests (no album can cover every single "local history" requirement - so guidelines are given to create your own)
--the album just seems too short: because the history album provides the framework and the highlights - the children's interests and the local educational requirements dictate the details; encouraging the use of many different sources for information, rather than depending on just one source that may or may not be accurate or non-bias, or even cover everything.
"Missing" in geography:
--everything that should have been done in primary, can be taught quickly in elementary with similar materials - so elementary geography "officially" speaking does not include functional geography. This is a research area for the children - as they study cultures, climatic zones, peoples of various places and times, they will be learning political geography at the same time.
--basic map skills: Goings Out - maps of museums, bus routes, maps of the city, etc.
The main thing to remember is that, since elementary Montessori is based on cosmic education, just picking and choosing one or two subjects won't cover all the concepts needed in that subject (ie mathematics - you'll need biology, geography, history and language to "complete" the math cycle).
Please reply back with anything that seems to still be missing. I'd like to make this post as comprehensive as possible, so we can honestly say which public school requirements are truly missing.