In April I went to Jonathan’s NCTM session titled “Curriculum with a Message”. I had been fascinated by his ideas on Algebra 2 for a while but wasn’t fully understanding what the year looked like. I left the session really itching to do this with my next Algebra 1 or Algebra 2 course. I still don’t know what I’m teaching for the upcoming school year, but today I started to look into what this might look like for a Virginia Algebra 1 course (NOTE: we are not a CCSS state).
Before getting started, two of our standards include translating verbal expressions algebraically and representing linear and quadratic functions using multiple representations (verbal, tables, equations, graphs). I plan on doing both of those regularly throughout the course, and including concrete and other pictoral/symbolic representations as needed.
Big Idea #1: Equivalence
Our students are expected to do the following:
- evaluate expressions given replacement sets using absolute value, square roots, and cube roots
- use the laws of exponents
- add, subtract, multiply, and divide polynomials
- factor 1st/2nd degree bi/trinomials in 1 variable
- simplify square roots of whole numbers and monomial expressions
- simplify cube roots of integers
- add, subtract, and multiply 2 monomial radical expressions with numerical radicands
I would add into this part of the year solving multistep equations and inequalities (and literal equations) since we have to teach them to use properties to justify their steps. I don’t know what this big idea would look like but I’m imagining lots of open middle problems. I’m imagining this big idea taking from the beginning of school (day after Labor Day) to around Thanksgiving.
Big Idea #2: Graphically Representing and Understanding Linear and Quadratic Relationships
That’s a long big idea title but it gets the point across. I’m choosing to start with graphs first because I believe that when students have the ability to visually represent things it’s much easier to connect to the algebraic, more abstract versions.
Standards that would belong in this part are:
- graphing two-variable linear equations and inequalities
- graphing two-variable quadratic equations
- systems of two linear equations or inequalities
- characteristics of relations
- direct variation
- parallel and perpendicular lines
I think mostly with this big idea my goal would be to do a lot of word problems and get those words into a variety of visual representations; drawing, making tables (that then turn into graphs), etc. Those characteristics would be used to help us determine the reasonableness of our problem set-ups and solutions, as well as visually provide answers for word problems (like when the water will run out, when the ball is the highest, etc.). Depending on snow days, this would take until Presidents’ Day-ish.
Big Idea #3: Algebraic Representations of Linear and Quadratic Relationships
The idea here is that we would move from “nice, easy” numbers to realistic numbers, which is why graphs and other representations wouldn’t be our best option anymore.
Topics include all of the exact same things as Big Idea #2, but now we would focus on equations. Two things that would need to be included are:
- parent function transformations of y = x with m and b
- linear and quadratic regression
This would take until a week or so before the standardized test so there would be some time for test prep. The only standard that isn’t included is inverse variation. Such an annoying one to include when you don’t do rational functions. So I’d be sure to touch on that during test prep and then maybe do a mini-unit on inverse, joint, and combined variation after the test?
So basically this course would be three trimesters and each trimester would have a different theme… I’m not going to flesh it out any more until I know I’m teaching Algebra 1 next year, but if anyone has comments/questions/suggestions, I’m all ears!