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© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions A Story of Functions Overview of Grade Nine
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Functions
A Story of FunctionsOverview of Grade Nine
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Agenda
Table of Contents ReviewRevisit the Common Core ShiftsBreak-Out Sessions by ModuleModule 5Closure and Reflection
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Table of Contents Module 2DRAFT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Table of Contents Module 3DRAFT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Table of Contents OverviewDRAFT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Common Core Instructional Shifts
How will I support students and my colleagues to adapt to this new scope and sequence for teaching Algebra 1?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Examine a Module Overview in Depth
What is the ‘story’ of this module?Focus standardsFoundational standardsMath practice standardsThe modeling cycle
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Module 2: Descriptive Statistics
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G9-M2: Descriptive Statistics• Distributions and their shapes• Measures of center and spread• Modeling relationships of numerical data
on two variables
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Module 3: Linear and Exponential Functions
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• 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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Module 4: Polynomial and Quadratic Expressions, Equation and Functions
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• 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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Module 5: A Synthesis of Modeling with Equations and Function
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• Key features of quadratic and non-quadratic graphs• Linear vs. exponential vs. quadratic growth• Modeling with a variety of functions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Module 5—A Synthesis…VERY DRAFT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
PARCC Prototype Item
The next portions ask students to create a recursiveand an explicit formula for the number of cellsat the end of the previous week.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
PARCC Prototype Item
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Key Shifts of G9 Curriculum:
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• 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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Algebra 1 Overview
Work with your module overviews to paraphrase the significant mathematics developed in each module within each domain.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Common Core Instructional Shifts
How will I support students and my colleagues to adapt to this new scope and sequence for teaching Algebra 1?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
Biggest Takeaway
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Functions
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 3 provides 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.
