I’ve been working on a comprehensive set of notes for Pre-Algebra for over a year now. While I wouldn’t call them perfect, I’ve finally got the notes into a state that I’m happy to share with the rest of the world.
I had an initial draft version of these notes last August, but they had many problem that I’ve had to work on. The biggest issue was that I hadn’t actually taught through a Pre-Algebra course before. Covid, changing so many things like it has, meant that I couldn’t use printed notes as I’d hoped at the start of the school year, but as the year progressed and our understanding of teaching in a pandemic developed, I was able to start incorporating printed notes at times. Following the end of the school year, I went through the entire course in detail, using my students’ experiences over the year to refine the notes and even expanded certain topics that need more time to develop. The result of that review is what I’m sharing here.
I plan to keep improving these notes, as well as produce other material to support them. I have a first draft of practice exercises for the first three units, though those still need much more work before I’m ready share. Eventually, I’d like to create a catalog of resources and activities, aligned to each section of the notes, that would give any Pre-Algebra teachers (including myself) a huge leg-up in developing their own curricula, but that dream is still a long way off.
A note of caution that I’ve written these notes with the Oklahoma Academic Standards in mind. (Standards alignment document coming soon, hopefully.) While I’d love for as many teachers as possible to use these notes, be aware that I haven’t referred to Common Core or whatever other standards you might be using at all, so there may be some topics you expect that are missing or incomplete. I’d love to fill in those gaps for other states and countries one day, but no promises.
Here’s the next version of my notes. If you’ve missed this so far, I’m writing a complete set of fill-in-the-blank notes for Algebra 2, specifically with the Oklahoma Academic Standards in mind. See my post sharing the first draft of the notes for my reasons for doing this.
There’s a lot of small fixes here, with things that could be written clearer, some additional examples, and, sadly, a lot of typos and other mistakes. The most substantial edits were to section 8.4, on natural exponents and logarithms. I’ve always been dissatisfied with the way the value of the constant e is justified in classes which precede calculus. I’m hoping that this explanation will satisfy students by alluding to the calculus, without teaching it explicitly.
In my last post, I made available notes for the entire year of Algebra 2, following the Oklahoma standards. I mentioned that the notes are a work in progress. Hopefully in time for the new school year for most, here is an updated version.
Changes focus on the first six chapters, which should get anyone following the notes in order through the fall semester. I aim to have version 0.3, which will focus on fixes to the remaining chapters, done by Christmas.
Fixes to lots of errors and typos, both in the text and in the worked examples.
A number of paragraphs rewritten to be clearer.
A handful of additional examples.
Additional space for select examples.
Additional diagrams to explain concepts, including the picture below.
As before, there is a set of blank notes for students, and a set of the notes with all the blanks and examples completed. These notes remain free to use for teachers to distribute to their students in their own classes.
I’ve been working on a big project over summer: a set of student notes with fully worked examples for an entire year of Algebra 2.
You might be wondering why I did this. I’m not even teaching High School currently, as I’m taking a couple of years to attend grad school. While I’m doing some teaching, it’s been as a TA for Calculus 1, certainly not for Algebra 2. Even so, I’ve still spent a lot of time thinking about Algebra 2 curriculum over the past year, and had a lot of conversations about it with Sarah, as she is has been teaching Algebra 2 since last August. It turns out, even after taking some time away, my passion is still for high school math.
These are the ideas I’ve had for the function of these notes:
They’re aiming to meet the Oklahoma Academic Standards, though in places they step back to strengthen the conceptual foundation, and in others they go beyond the standards. Eventually I’ll produce an alignment document to explain all the links.
This is not a complete curriculum, but I see it functioning as a “skeleton” on which a complete curriculum could be built.
The notes focus almost purely on the mathematics, not on “real world” applications (with a few exceptions in statistics topics). This is not because these are unimportant; on the contrary, they are vital. But I believe these are better addressed using methods other that pre-prepared notes.
The intent is that the notes would be hole-punched and kept in a binder. This means if a teacher doesn’t like how I’ve done something, they can change it. Remove the parts you don’t like. If you don’t think there are enough examples, add more.
Teachers can incorporate the notes and examples as they wish into their lessons. While textbooks give they answers to examples away from the start, with fill-in-the-blanks, the teacher can choose at what point in the class discussion they make the correct answers known.
You might remember that I was working on a book of Algebra 2 practice questions. That’s still ongoing, but it’s been overtaken somewhat by these notes. But that’s okay, because I see these as two aspects of the same long-term project. Having the notes planned out should make planning questions a lot easier.
If all of this sounds good, here’s the great news: I’m going release the notes as I work on them. And while they’re still just a first draft at this point, that first draft is entirely done, and hopefully in a usable form for the upcoming school year.