A Story of Functions

A Story of Functions Overview of Grade Nine

Session Objectives Understand and explain the coherence across the grade 9 curriculum by describing the focus of each module and relating the modules to each other.

Agenda Table of Contents Review Revisit the Common Core Shifts Break-Out Sessions by Module Module 5 Closure and Reflection

A Story of Functions Curriculum Overview • WHAT’S NEW • Adjusted module names and number of days per module • Shifted some standards to improve flow and coherence of the course • Module 1 has extra days to allow for scaffolding and flexibility • Module 5 is a culminating unit for the year

Table of Contents Module 2 DRAFT

Table of Contents Module 3 DRAFT

Table of Contents Overview DRAFT

Common Core Instructional Shifts How will I support students and my colleagues to adapt to this new scope and sequence for teaching Algebra 1?

Examine a Module Overview in Depth What is the ‘story’ of this module? Focus standards Foundational standards Math practice standards The modeling cycle

Module 2: Descriptive Statistics • G9-M2: Descriptive Statistics • Distributions and their shapes • Measures of center and spread • Modeling relationships of numerical data • on two variables

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

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

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

VERY DRAFT Module 5—A Synthesis…

PARCC Prototype Item The next portions ask students to create a recursive and an explicit formula for the number of cells at the end of the previous week.

PARCC Prototype Item

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.

Algebra 1 Overview Work with your module overviews to paraphrase the significant mathematics developed in each module within each domain.

Common Core Instructional Shifts How will I support students and my colleagues to adapt to this new scope and sequence for teaching Algebra 1?

Biggest Takeaway

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.

A Story of Functions