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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions
A Story of FunctionsA Close Look at Grade 9 Module 1
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Session ObjectivesExperience 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.
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
AgendaModule 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 CClosure and Reflection
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Grade 9 Module 1 OverviewInsert Table of Contents
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
What’s in G9-M1Topic 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
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Todays Focus: Topics A and B
Which standards for mathematical practices will be the focus of these lessons?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Focus Standards for Topics A and BA.SSE.2
Lesson 6: Numerical Expressions—The 4-Number GameExit TicketConsider the expression: • Draw a picture to represent the expression.
• Write an equivalent expression by applying the
Distributive Property.
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
N-Q.1
A.CED.2
Focus Standards for Topics A and B
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Grade 9 M1 L3 Problem Set
Focus Standards for Topics A and B
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Types of Lessons1. Problem Set
Students and teachers work through examples and complete exercises to develop or reinforce a concept or procedure.
2. SocraticTeacher leads students in a conversation to develop a specific concept or proof.
3. ExplorationIndependent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge
4. ModelingStudents practice all or part of the modeling cycle with problems that are ill-defined and have a real world context.
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lesson OrganizationTeacher• 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)
Student
• Classwork
• Problem Set
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Exploration Lesson: Graphs of Quadratic Functions
G9-M1-L2 Student Materials Example 2
G9-M1-L2 Student Materials Example 3
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Reflecting on Lesson 2What 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?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Exploration Lesson: Two Graphing StoriesLesson 5Example 1Problem Set #1 and #2
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Reflecting on Lesson 5What 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?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Socratic Lesson: Algebraic ExpressionsLESSON 7 Exercises 5-8Exit Ticket
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Reflecting on Lesson 7What 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?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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.
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
What’s Left in Topics A and BLessons 1, 3 and 4—Graphing Stories
Lesson 6—Algebraic Expressions
Lessons 8 and 9—Generating Polynomials
Teacher pp. xx to xx
Teacher pp. xx to xx
Teacher pp. xx to xx
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lessons 1, 3, and 4: Graphing StoriesLesson 1—Graphs of Piece-wise Defined Linear FunctionsLesson 3—Graphs of Exponential FunctionsLesson 4—Typical Water Usage at a School
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lesson 6: Algebraic Expressions
Exercise 1: The Four Number GameExercise 3: The Four Number Game with VariablesExercise 4: Combining Like Terms IS the Distributive PropertyExercise 5-7: Geometric Models
Leela is convinced that Do you think she is right?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lesson 8-9: Generating PolynomialsGenerating 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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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Preview Topic C
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lesson 10 and 11: Solutions
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lessons 12 and 13: Solving Equations
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Lessons 12 and 13: Solving Equations
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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.
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions
A Story of FunctionsG9-M1 Mid-Module Assessment
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Find Your Partners
A—your assessment buddyB—someone from your school or school districtC—someone with a different job than you haveD—someone with the same job as you have
• not from your same school or district
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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.
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Agenda
Take the mid-module assessmentScore the mid-module assessmentMap skills and concepts on the assessment back to the
standards and the lessons
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Mid-Module Assessment
Work with a partner on this assessmentpp. xx-xx
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Scoring the Assessment
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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?
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Functions
Biggest Takeaway
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N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M 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.