Overview of Algebra Curriculum

1. Overview of Algebra Curriculum Erie 1 BOCES

2. Opening Exercise: • The ratio of songs on Jessa’s phone to songs on Tessie’s phone is 2 to 3. Tessie deletes half of her songs and now has 60 fewer songs than Jessa. How many songs does Jessa have?

3. The ratio of songs on Jessa’s phone to songs on Tessie’s phone is 2 to 3. Tessie deletes half of her songs and now has 60 fewer songs than Jessa. How many songs does Jessa have?

4. Modeling real-world situations using graphs • The first 5 lessons in module 1 for Algebra introduce the major functions that will be taught during the school year through videos • linear model • quadratic model • exponential model

5. Key Shifts of G9 Curriculum: • A focus on the solution set. • How does the solution set stay the same or change as we modify the equation. • Graphs of equations are pictorial representations of solution sets. • The graph of the function, f, is a pictorial representation of the solution set of y = f(x). • How does the graph of the function stay the same or change as we modify the function. • Students experience learning and modeling:  Start with an intuitive notion --> play with examples and look for structure --> find rogue examples and figure out what to do with them ---> arrive at a nice definition.

6. Key Points • Module 1 plants the seeds of the work of the year, connecting the work to real world contexts, and also provides a deep study of algebraic equivalence, the structure of expressions, and reasoning of solving equations. • Module 2 continues to connect the work of the year to real world contexts from a data perspective, motivating the intense study of exponential and quadratic functions to come. • Module 3provides a deep study of exponential functions, introduces function notation. • Module 4 provides a deep study of quadratic functions. • Module 5 serves to synthesize the year by providing situations of linear, exponential, and quadratic forms, where the student is required to recognize the model to be used.

7. Module 3: Linear and Exponential Functions • Formal function notation – a study of arithmetic and geometric sequences and exponential functions • Rates of change – contrasting linear and exponential • Interpreting graphs of functions – domain, range, increasing, decreasing • Relating equation notation to function notation • Absolute value function – studying transformations – how graphs change when equations change

8. Module 4: Polynomial and Quadratic Expressions, Equation and Functions • Explaining properties of quantities represented by an expression based on contextual situation • Identify ways to rewrite quadratics and the usefulness of each • Operations with polynomials • Symmetry in quadratic graphs • Solving quadratic equations, deriving the quadratic formula

9. Module 5: A Synthesis of Modeling with Equations and Function • Key features of quadratic and non-quadratic graphs • Linear vs. exponential vs. quadratic growth • Modeling with a variety of functions

10. Today’s task: We will take a closer look at each of the lessons in module 1 and module 2 Each group will write up a lesson analysis form for each of their assigned lessons Groups will be combined to discuss the lessons they analyzed Then each new group will dissect the module assessments modify questions if needed and create multiple choice questions to complement the mid-module or end-of-module assessment assigned Whole group share out