Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Thursday, February 6, 2014

Adolescent Algebra - and More

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.

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 - wouldn't that be nice if the owner of KotU was so thoughtful? Yeah, I'm working on it. ;) ). 

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're going 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

  • 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).

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.

Links for it (non-affiliate):
NAMTA's page for Montessori Algebra for the Adolescent By Michael J. Waski
Table of Contents

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.


  1. Ohh, thank you for a glimpse of what is to come! This sounds fascinating. I am looking forward to hearing more as you all start off on this journey.

  2. Thank you! Thank you! I'm excited that there is SOMETHING for Montessori middle school years! I keep thinking I'm going to run out of Montessori stuff at some point and then just have to pick up a regular curriculum because no one has created the Montessori version yet! Yipppeeeeee!

    1. On the KotU Discussion community, I had started an adolescent discussion group, that partially went off-group to private e-mail. I will pick it up again soon. The point to saying that is that we do have a rough sketch for the middle school and high school years - and together as homeschoolers we can start fleshing out how to work out those years.

      I think most of us won't move to a formal curriculum (at least for middle school), focusing on specific "real" resources for a variety of studies. I think those who go through elementary Montessori homeschooling will have an easier task of adolescence than it first seems. Think in "big picture" (cosmic ed, great lessons) and fill in the details based on individual interests and aptitudes.

      I am both happy and sad that it is all coming soon. Too soon. 2 more years here..... :(

  3. Jessica, do you know where to get the algebra tiles which are mentioned in this book? Or do you know how I can make them?
    I have purchased this too and I love it. Thanks

    1. The algebra tiles are (get this!?) foam sheets - from the craft store. I will be making ours soon and will have a post up about them. Another lady who attended had an idea for the x-variable that I also want to try out: elastic (to show it is any length - we don't know what x is) ;)