If this feels problematic…well, it is. How are students supposed to learn about something that has so many different moving parts to it? If even the experts can’t decide on what constitutes “Algebra” doesn’t that mean bad news for the beginning student?
With that said, I think it’s important that we start off our study of Algebra with a working definition that we can frame all of our discussions on, and here it is: Algebra is the study of patterns. Everything we discuss in Chapters A through I should be viewed through the lens of patterns. We will examine patterns, continue patterns, predict patterns, generalize patterns (write a formula that describes them) and more. I have found this is the best definition for students who are just learning about Algebra for the first time. It’s not that the others are wrong; it’s just that the perspective of patterns makes everything else make a little bit more sense if you’re just starting out.
Before we go any further: This page is talking about us studying “Algebra” — but isn’t this supposed to be a Pre-Algebra curriculum? The reason this curriculum exists is that I have been largely unsatisfied with Pre-Algebra curricula that I have used. The ones that I have seen are too much a rehash of what students do in elementary and lower middle school — a little bit on fractions, a little bit on decimals, a little bit on integers, and now we’ll throw a little Algebra at you here at the end of the course.
This curriculum flips that script on its head. We will learn Algebra right from the get-go. Chapter B is all about the Algebraic Properties. Then we can view all of those other topics (fractions, negative numbers, etc.) through the lens of Algebra. That way, students can get plenty of basic algebra practice before they actually take an Algebra 1 class. Additionally, it allows us to view those review topics through a completely different perspective; for example, students who have struggled with fractions in the past might have more success if they view those fractions through the lens of Algebra.
Good luck. Here we go…
Answer Key for Chapter A Practice Test (HW for Advanced P-A, In class work for P-A): ch A pract test key