Adolescent Algebra - and More

UPDATE 2019: This review is for the original Algebra for the Adolescent. Mike Waski has now published a second version, in two volumes (one for lower and one for older adolescents) and has separated out the Geometry to its own album entirely. Please visit The Math Institute to learn about all the resources for adolescent math studies!

The algebra album has new lessons and even more photos than before, from all that I hear. And the first two chapters of the Geometry album? Yep. Spectacular!


Original Post:

At long last, there is an "album" for the adolescent age - at least for mathematics - and OH does it COVER mathematics!
Signed Numbers, Graphing, Lines, Inverse Operations, Inequalities, Exponents, Combining Like Terms, Factoring, Absolute Value, Binomial Theorem, Quadratics, Transformations, Sequences, Functions, Exponential and Logarithmic Functions, Polynomials, Trigonometry, Complex Numbers, Further Work (Matrices, Vectors, Conic Sections), Calculus - ALL get their own chapters!

Then Geometry (a whole section on Euclid) and Arithmetic (one page description of what to do) each get an appendix. 

It is perfect! I love it! I can't wait to delve into it with my son (well, yes, I can, because I don't want him to grow up TOO fast; but I am also SO satisfied we have the perfect resource for the middle school and possibly early high school years).

It arrived via UPS yesterday. Yes, I paid $16 and change for shipping. I didn't feel like contacting them to have them send it media mail. I probably could have driven and picked it up for less, but it saved time. (Edit: 8/20/2019 - Shipping prices are different now with the new website, see links below)

It comes printed on front/back, 3-hole punched, ready for a binder....

Or 2 binders. I didn't want that many pages in one thick binder. So I split it, noting the chapter headings contained in each. It comes with two printed cover pages (presumably a "cover" and a "title" page, so I split those to the binders).

Fully Illustrated!!!

If you are familiar with Montessori math (NAMTA presumes you have training when you purchase this album), you will be able to follow along very quickly; the introduction chapter provides a good outline for how to work through the material with the children - not in linear fashion. There is also a flow chart in the appendix which shows initial presentation (everyone gets one way or another), suggested follow-up presentations (not everyone "needs" - some things the child needs to demonstrate understanding one way or another; some things are entirely optional) and the ultimate key experiences (all children should get to those ones).

If you are new to Montessori math, the wordy introduction might be overwhelming but will be VERY helpful.

The materials list is decent, although it lists chapter number rather than presentation needed for (but, ahem, that is more information than the Keys of the Universe albums provide - only listing the material and not even the chapter or specific album page it is used for. Yes that organization is in progress! ). 

GUESS WHAT!? Those expensive wooden squares and cubes we elementary Montessori homeschoolers keep balking at the price for a few small elementary presentations!? And think we might just going to skip? Yeah. They're in here! I am so happy - it means more work with them, more use of a somewhat expensive material - and more fuel for my adamant stance that we don't need "more" materials - we just need to go DEEPER with what we have.
(for the record, I did try to think of cheaper alternatives; in the end, I went with the wooden set from IFIT - I am 100% pleased and I know I can re-sell them if/when the time comes)

Indeed, there are very few new materials, comparatively speaking; most of which can be hand-made, with instructions included; or find relatively easy alternates. 

Other elementary materials include (I'm not promising I am covering it all here - there could be more as I'm just browsing quickly down the list): 

• Geometry sticks
• fraction circles
• bead bars, squares, cubes
• wooden cubing material (noted above)
• Powers of 2 and 3 (AMI only includes the power of 2 at elementary; but the power of 3 is available)
• Second and Third Pythagorean Insets
• Binomial Cube (my friend! the link here is about the trinomial, but the concepts apply)
• Checkerboard
• Pegboard
• Fourth and Fifth Power Material (not included in AMI KotU albums - other albums may use these???)
• Special Triangle Box (the box of 12 blue right-angle triangles)
• Yellow Material (area and volume)
• Large and Small Solids

Drawbacks:

• no page numbers noted in the table of contents. ANNOYING. 
• needs tabs to find the chapters (because of no page numbers) - easy enough fix. 

This album covers a LOT of ground at just over 800 pages. I could imagine using this material for the equivalent of 7th, 8th AND 9th grades, with possibly some of it being a foundation for additional high school studies - it gets into trigonometry, etc. We may very likely do this album for middle school, then see about placement testing or other testing into/out of high school math courses (or seeing how Life of Fred fits into the whole thing when the time comes - I cannot yet say if there are enough credit-hours here for which courses on a high school transcript - I need more time with it, comparing directly with actual trig coursebooks, for example).
EDIT: after attending his workshop, there are portions here that are solidly high school. This album set goes all the way through. 

I highly recommend picking up this resource when your elementary child is around age 10 - so you can have time to get organized with it ---- the author suggests that some of the work could begin in elementary with a ready-child; and the AMI albums (including KotU) have work that COULD bridge into adolescence. So you'll want some time to get a feel for it and find what path your child will need.


From a Facebook post in 2015:

A tidbit for anyone who owns the Montessori Algebra for the Adolescent album/book by Michael Waski ----
pg 221 has a typo he wants corrected: it should say "multiplication over addition" in the next to last line.

And get this - the algebra tiles that are used a LOT? They can be made out of foam-sheets (not foam board - that would be too thick - just the foam sheets that can easily be cut by hand! Awesome stuff. (the algebra tiles include the "green/gray counters" and "skittles" noted in the album)

Links for it (non-affiliate):
The Math Institute (also has some of the materials available for sale)
Table of Contents (will be updated soon)
Samples (will be updated)


I am writing this review on a snow/ice day with lots and lots and lots to do around our home - so I know I've not covered everything I'd've liked to cover. Please ask any and all questions and I'll respond with what is pertinent to what people want to know :)

Caveat: I cannot answer how this album aligns with following any elementary albums besides the AMI ones, because I have only seen tiny portions of non-AMI upper elementary albums.



6/15/2019: Updating to reflect a longer-term link for purchase and to note: GEOMETRY is now available as well!

Adolescent Algebra-Plus Album

I just bought this with part of my subbing income:

http://www.montessori-namta.org/Print-Publications/Adolescent-Readings/Montessori-Algebra-for-the-Adolescent

It will arrive in a couple of days.

I'll let you know my follow-up thoughts after this coming weekend.


My initial thoughts based on TOC and several samples:
I like it. It seems to follow quite well on the AMI elementary mathematics album; a 12-13 year old could finish up the end of the AMI elementary album as needed, then move into this album.

I'm not sure there are many illustrations though. I have been able to follow the samples based on my knowledge and experience with the AMI elementary mathematics album.
UPDATE: Plenty of illustrations! Woohoo!


More thoughts to come. Curl up with some warm peppermint tea and my favorite blanket in my cozy chair that I've not seen for a few months now (it's buried - time to resurrect it!).


(for the record, my final thoughts won't be for a few years yet - not until my son finishes it - and he's only just about to be 10 - so it will be a while ;) ).

Algebraic Trinomial Cube

This cube goes by several names - but the most important fact is that it is NOT the trinomial cube.

As Legoboy so recently and astutely discovered:

Poorly cropped - but
1) someone skipped getting dressed
2) I wanted to include an image
 of the squaring/cubing

"It's just like the trinomial cube!" He proclaimed when he first saw it. "But the colors are different," he side-commented to me to be sure I didn't ask him about the changing colors as I did with the tower of cubes versus pink tower.

But I still had him one-upped ;) "Hmm. Different colors, alright. I'll let you explore this while I go do something else and keep myself from interrupting you!" He just smiled and proceeded to work.

When he was done, he brought it to me, and said, "Oh Mama! The colors were VERY different! They didn't even match the lid on every layer like the trinomial! This is a CRAZY cube!" (keep in mind our trinomial cube is not in our home right now - it's over at the local school building).

I told him as soon as we get our trinomial cube back into our hands, I will show him the story of the Three Kings. Of course, just to be contrary, he says, "I already know about the Three Kings! I can skip that presentation!" (sound like some adults we know? I already know it (based solely on the title or perhaps the title and the main headings, then skip the actual content, which just MIGHT actually be nuanced different, if not entirely different... and then wonder why things aren't working right;) hehe - Yep, that describes me!)

"Oh no, my son, not THOSE three kings! These are the Cubed Kings!" That got his interest up! He's been asking for a week now. Perhaps next week we'll get to it. I like to keep up some anticipation (and I do want to review a couple of other concepts before working with the Kings.).

Yeah, we had fun with this one!

Stylized version - I know how tricky the illustrations can be!
Tricky - but NECESSARY
for each and every step!

Don't know the Kings?

Pick up a Keys of the Universe mathematics album ;)

HONEST review here - from a homeschooling mom - NOT from a Montessori trainee:
There is a free elementary math album available online, with which I usually agree as to the order and general set up of presentations, but I am thoroughly perplexed by its version of the Three Kings - (this part comes from me as a trainee: and I KNOW it! And I know what is trying to get across and what comes next.) Back to being JUST a homeschooling mom: But the instructions are confusing, the story is BLECK-boring until you realize that the *actual* story comes after the presentation in the album and is actually mildly interesting but leaves some strange questions, the whole set up begs to know what pieces to move when and as a mom I want it all together so I can SEE what is going on, and I really-really want those black pieces to be the same height as their king - it just makes sense when you see the other attendants the same height as their own king. But this album has them all laid flat.    It just does not look appealing - while mathematically correct, there is another way that makes the math more clear, leaves out the strange questions and keeps the appropriate parts of the presentation together in order. I'll stick with the Keys of the Universe version ;)
Sorry! I really do LIKE that album - I just don't "love" it and I'm very honest about things these days.