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NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
A Story of Functions
A Close Look at Grade 9 Module 1
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Session Objectives
Experience and model the instructional approaches to teaching the content of
the lessons of the first module.
Articulate how the topics and lessons promote mastery of the focus standards
and how the module addresses the major work of the grade.
Make connections from the content of previous grade levels to the content of
this module.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Participant Poll
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Classroom teacher
School leader
Principal
District leader
BOCES representative
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Agenda
Module Overview
• Focus Standards for Topics A and B
In-Depth Examination of Module 1 Topics A and B: Lessons 1-9
• Demonstration Lessons
• Exploring Topics A and B
Preview Topic C
Closure and Reflection
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Grade 9 Module 1 Overview
Insert Table of Contents
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
What’s in G9-M1
Topic A: Explore the main functions of the year (linear, exponential and
quadratic) through graphing stories (making graphs of situations)
Topic B: Study the structure of expressions, define what it means for
expressions to be equivalent, re-write various polynomial expressions in
equivalent forms using the properties of equality and the distributive
property.
Topic C: Precisely explain each step in the process of solving an equation,
inequality or system of two linear equations or inequalities
Topic D: The modeling cycle – solving problems using equations and
inequalities in one variable, systems of equations in two variables
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Todays Focus: Topics A and B
Which standards for mathematical practices will be the
focus of these lessons?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Focus Standards for Topics A and B
A.SSE.2
Lesson 6: Numerical Expressions—The 4-Number Game
Exit Ticket
Consider the expression: 𝑥 + 𝑦 + 3 × 𝑦 + 1
• Draw a picture to represent the expression.
• Write an equivalent expression by applying the
Distributive Property.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Focus Standards for Topics A and B
N-Q.1
A.CED.2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Focus Standards for Topics A and B
Grade 9 M1 L3 Problem Set
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Types of Lessons
1. Problem Set
Students and teachers work through examples and complete
exercises to develop or reinforce a concept or procedure.
2. Socratic
Teacher leads students in a conversation to develop a specific
concept or proof.
3. Exploration
Independent or small group work on a challenging problem
followed by debrief to clarify, expand or develop math knowledge
4. Modeling
Students practice all or part of the modeling cycle with problems
that are ill-defined and have a real world context.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson Organization
Teacher
• Student Outcomes
• Lesson Notes (in select lessons)
• Classwork
• General directions and guidance, including timing guidance
• Discussion points with expected student responses
• Student classwork with solutions
• Scaffolding Boxes
• Exit Ticket
• Problem Set (with solutions)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Student
• Classwork
• Problem Set
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Exploration Lesson: Graphs of Quadratic Functions
G9-M1-L2 Student Materials Example 2
G9-M1-L2 Student Materials Example 3
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Reflecting on Lesson 2
What were the focus standards in this lesson?
What teaching and learning strategies helped to make this content accessible
to all learners?
How does the teacher version support student engagement and learning?
Which SMPs do students engage in during this lesson?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Exploration Lesson: Two Graphing Stories
Lesson 5
Example 1
Problem Set #1 and #2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Reflecting on Lesson 5
What were the focus standards in this lesson?
How does the teacher version support student engagement and learning?
What teaching and learning strategies helped to make this content accessible
to all learners?
Which SMPs do students engage in during this lesson?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Socratic Lesson: Algebraic Expressions
LESSON 7 Exercises 5-8
Exit Ticket
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Reflecting on Lesson 7
What were the focus standards in this lesson?
How does the teacher version support student engagement and learning?
What teaching and learning strategies helped to make this content accessible
to all learners?
Which SMPs do students engage in during this lesson?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Standards for Mathematical Practice
Three Components of Rigor
• Fluency
• Conceptual Understanding
• Application
FOCUS QUESTION: How do the SMPs support these
three components. Find specific instances within the
lessons.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
What’s Left in Topics A and B
Lessons 1, 3 and 4—Graphing Stories
Lesson 6—Algebraic Expressions
Teacher pp. xx to xx
Teacher pp. xx to xx
Lessons 8 and 9—Generating Polynomials
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Teacher pp. xx to xx
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Lessons 1, 3, and 4: Graphing Stories
Lesson 1—Graphs of Piece-wise Defined Linear Functions
Lesson 3—Graphs of Exponential Functions
Lesson 4—Typical Water Usage at a School
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Lesson 6: Algebraic Expressions
Exercise 1: The Four Number Game
Exercise 3: The Four Number Game with Variables
Exercise 4: Combining Like Terms IS the Distributive Property
Exercise 5-7: Geometric Models
Leela is convinced that
(𝑎 + 𝑏)2 = 𝑎2 + 𝑏2 . Do you
think she is right?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Lesson 8-9: Generating Polynomials
Generating polynomials based on base-10 or base-n arithmetic provides a
strong connection to work in elementary grades and makes meaning out of
operations on polynomials
The properties of real numbers provide a justification for the equivalency of
statement like the one shown below:
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NYS COMMON CORE MATHEMATICS CURRICULUM
Preview Topic C
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A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 10 and 11: Solutions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Lessons 12 and 13: Solving Equations
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Lessons 12 and 13: Solving Equations
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Biggest Takeaway
What are your biggest takeaways from this session?
How can you support successful implementation of
these materials at your schools given your role as a
teacher, school leader, administrator or BOCES
representative?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Key Points
• Lessons 1-5 are meant to introduce, not “cover”, the various functions to
be covered in the year.
• Students walk away from these lessons firmly connected to the idea that
graphs (and equations) are used for modeling real life situations.
• The lessons serve to require students to be ever aware that variables are
merely placeholders for numbers.
• Timing of lessons cannot possibly meet the needs of all student
populations. Teachers should preview the lesson and make conscious
choices about how much time to devote to each portion.
• While many exercises support the mathematical practices in and of
themselves, the discussions and dialog points are often critical for both
their content and for enacting the mathematical practices.
• Study carefully the Lesson Notes on physics and quadratic functions.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
A Story of Functions
G9-M1 Mid-Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Find Your Partners
A—your assessment buddy
B—someone from your school or school district
C—someone with a different job than you have
D—someone with the same job as you have
• not from your same school or district
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Session Objective
Identify critical aspects of instruction that prepare
students to reason and/or conduct modeling included
on the mid-module assessment.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Agenda
Take the mid-module assessment
Score the mid-module assessment
Map skills and concepts on the assessment back to the
standards and the lessons
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment
Work with a partner on this assessment
pp. xx-xx
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
Scoring the Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Connecting Standards, Assessment and Lessons
Select 1-2 questions and answer the following questions.
What focus standards does this question address?
What foundational standards must be in place for success?
What mathematical practice standards
does this question address?
Which lessons will help prepare my students
for success on this assessment?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Biggest Takeaway
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Key Points
• The assessments in Module 1 are designed to take 2 days per
assessment.
• As much as possible, assessment items are designed to asses
the standards while emulating PARCC Type 2 and Type 3 tasks.
© 2012 Common Core, Inc. All rights reserved. commoncore.org