When I last left this topic, I had a rather different arrangement of the Essential Understandings based on a theme of graphing, algebraic arithmetic and solving. We took this to our department head, and had a discussion with her about these. Her very valid concern with that arrangement was that the learners may not see the connections between quadratics and graphing, factoring, completing the square, etc. and polynomials and graphing, etc.

So, we have re-arranged our essential understandings by “theme” of type of function.

Below you will find our new arrangement for the Alg 2 first semester. The “Keys to Success” is a series of brochures and self check mastery, and the parenthetical numbers are the book section numbers. The book is not the driving force on this though, the district’s blueprint is. We won’t get the final version of that until July sometime.

The goal is to have the learners connect the graph, the algebra, and everything else we do inside the them together. We will be doing essentially the same mathematics 4 times, and then I need to make the connections clear and consistent through the classwork and assignments.

Now that we have an list of essential understandings, we need to go through and decide what demonstration and transfer of skills will be considered as evidence for the learner understanding the understanding. That is the next step.

**Keys to Success (chap 1 & 2: reviews of alg 1)**

- Integers
- Expressions
- Evaluate
- Solve
- Slope
- Graph Lines
- Equations – Lines
- Exponents
- Factoring
- Parent Functions

**theme: Linear functions**

- Can you graph more than one equation on the same graph? (3.1)
- Can you explain where the multiple equations intersect or not intersect, and what that means? (3.1)
- Can you solve a system of equations with substitution? (3.2)
- Can you solve a system of equations with elimination? (3.2)
- Can you graph two or more inequalities on the same graph? (3.30
- Can you shade correctly the two or more regions indicated by the inequality? (3.3)
- Can you add and subtract matrices? (3.5)
- Can you do scalar multiplication with matrices? (3.5)
- Can you find the determinant of a 2×2 matrix or larger matrix with and without technology? (3.6, 3.7)
- Can you multiply two matrices together with and without technology? (3.6, 3.7)
- Can you use inverse matrices to solve linear systems with more than 2 equations? (3.4 & 3.8)

**theme: Quadratic Functions**

- Can you graph a quadratic function, labeling the values of the vertex, axis of symmetry, and the minimum or maximum & solutions or zeros? (4.1 & 4.2)
- Can you solve quadratic equations by factoring where a = 0? (4.3 & 4.4)
- Can you solve quadratic equations by factoring where a 0? (4.3 & 4.4)
- Can you solve quadratic equations using square roots? (4.5)
- Can you compare and contrast the different methods of solving quadratics? (4.5)
- Can you complete the square for a = 1? (4.7)
- Can you complete the square for a 1? (4.7)
- Can you add and subtract complex numbers? (4.6)
- Can you multiply and divide complex numbers? (4.6)
- Can you graph complex numbers? (4.6)
- Can you use the quadratic formula to solve quadratic equations? (4.8)
- Can you use the discriminant to determine if the roots are real or complex? (4.8)
- (rethink in July)
- Can you use quadratics in real world situations? (4.10)

**theme: Polynomial Functions**

- Can you describe the end state, rise and fall, max and min, and zeros of a polynomial function? (5.2)
- Can you evaluate a polynomial function given a value? (5.2)
- Can you add and subtract polynomial functions? (5.3)
- Can you multiply polynomial functions? (5.3)
- Can you factor perfect cube trinomials? (5.4)
- Can you factor non perfect cubes by grouping? (5.4)
- Can you divide polynomials through standard long division? (5.5)
- Can you divide polynomials through synthetic division? (5.5)

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[…] whole endeavor was that in the end the whole thing just turned out to be a list of skills much like this one. We expected C students to be able to do the straight skill work. We expected B students to be able […]