Well, I'm at it again...trying to figure out how to make my classroom and curriculum better for my students. I like a lot of things about a lot of my units, but I found myself wondering if it would be more engaging and connected for students if I reordered some of the units. SO...this is what I'm thinking:
Unit 1: Numbers and Units
I am hoping to collaborate some on this with the science teacher. We will teach unit conversions together. It will be interesting as I have never done something like this before.
Unit 2: Functions
This is the big change. Instead of doing all the standards that are "close" to 8th grade standards first, and then starting functions second semester, I'm going to start with functions right away. I want have a more "function" focus throughout the year. I also really, really want my students to develop a lot of flexibility with their functional thinking, so hopefully having more time will help. (Some of the flexibility I want to see: evaluating from equation, graph, table; understanding function notation and y= are similar; find average rate of change and tie it into slope; thinking about "characteristics" of a graph: x/y-int; increasing/decreasing; extrema)
Unit 3: Linear Functions
So after a broad introduction to functions, we will focus on various types of function on and off. Linear is first!
Unit 4: Exponents and Radicals
As a preface to Exponential Functions unit next, we will manipulate exponential and radical expressions (hopefully with and without variables).
Unit 5: Exponential Functions
Back to another big function group. Going to discuss the characteristics of an exponential function algebraically, graphically, and numerically.
Unit 6: Sequences
Here we tie arithmetic sequences to linear functions and geometric sequences to exponential functions. Hopefully my students can see the domain of each of these functions will be restricted to the natural numbers. Also want to make sequences more challenging by including variables in the terms.
Unit 7: Polynomial Operations
Adding, subtracting, multiplying, and factoring polynomials. I LOVE polynomials. I need to make sure my students see more than just quadratics here, but it's OK if it's my focus.
Unit 8: Quadratic Functions
I have a lot of good things here, but it is not quite a cohesive unit yet. Needs a little bit more work to develop into that. Hopefully by not being THE LAST unit I will be able to be more cohesive.
Unit 9: Statistics
Saving statistics for this point will allow application of the three types of functions we study. We can do some fun regression for various functions.
Unit 10: Solving Equations
This will include solving linear equations (which we will constantly review throughout the year, since it is 8th grade, too), quadratic equations, and systems. I think I'm going to like that systems can involve quadratics :). We might have to discuss why we don't solve exponential functions yet in Algebra 1.
Five units a semester seems doable, right? Better than 12? I think we did 8 this year. I'm hoping some intentional unit-specific planning this summer will allow me to progress better throughout the year.
Let me know what you think! Am I missing something big that won't work with this? Have you tried it this way before? How did it go? I'll post learning targets and unit outlines later in the summer (hopefully)! But probably not chronologically.
-Kathryn