a story of functions

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions

A Story of FunctionsA Close Look at Grade 9 Module 1


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.



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



Grade 9 Module 1 OverviewInsert Table of Contents



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



Todays Focus: Topics A and B

Which standards for mathematical practices will be the focus of these lessons?



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.



N-Q.1

A.CED.2

Focus Standards for Topics A and B



Grade 9 M1 L3 Problem Set

Focus Standards for Topics A and B



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.



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



Exploration Lesson: Graphs of Quadratic Functions

G9-M1-L2 Student Materials Example 2

G9-M1-L2 Student Materials Example 3



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?



Exploration Lesson: Two Graphing StoriesLesson 5Example 1Problem Set #1 and #2



Socratic Lesson: Algebraic ExpressionsLESSON 7 Exercises 5-8Exit Ticket



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.



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





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



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?



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:



Preview Topic C



Lesson 10 and 11: Solutions



Lessons 12 and 13: Solving Equations



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?



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.


NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions

A Story of FunctionsG9-M1 Mid-Module Assessment



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



Session Objective

Identify critical aspects of instruction that prepare students to reason and/or conduct modeling included on the mid-module assessment.



Agenda

Take the mid-module assessmentScore the mid-module assessmentMap skills and concepts on the assessment back to the

standards and the lessons



Mid-Module Assessment

Work with a partner on this assessmentpp. xx-xx



Scoring the Assessment



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?



Biggest Takeaway



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.

a story of functions

Documents

content module

content of grade

minutes materials

story of ratios

sampling of lessons

story of functionsa

total minutes

mornings session