NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
A Story of Functions
A Close Look at Grade 9 Module 5
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Opening Exercise
Critique the following problem from G9-M5 Lesson 6:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
A Story of Functions
A Close Look at Grade 9 Module 5
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Participant Poll
•
•
•
•
•
Classroom teacher
Math trainer
Principal or school leader
District representative / leader
Other
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Session Objectives
• Experience the instructional approaches to teaching
the content of Grade 9 Module 5 lessons.
• Articulate how the 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
modules and grade levels to the content of this
module.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Orientation to Materials (if needed)
Examination and exploration of:
• Topic A
• Topic B
• End of Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Session Objectives
•
Examination of the development of mathematical
understanding across the module using a focus on Concept
Development within the lessons.
•
Introduction to mathematical models and instructional
strategies to support implementation of A Story of Ratios.
•
Consideration of scaffolding to provide multiple entry points
for students at all levels.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Session Objectives
•
Examination of the development of mathematical
understanding across the module using a focus on Concept
Development within the lessons.
•
Introduction to mathematical models and instructional
strategies to support implementation of A Story of Ratios.
•
Consideration of scaffolding to provide multiple entry points
for students at all levels.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
A Story of Ratios
Scaffolding Mathematics Instruction
Key Points
• Amplify Language
• Move from Concrete to Representation to Abstract
• Give Specific Guidelines for Speaking, Reading,
Writing, or Listening
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Amplify Language
• Give clear mathematical definitions
• Explain multiple meanings
• Maintain consistency and point out
interchangeable terminology
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Move from
Concrete to Representation to Abstract
• Use familiar contexts
• Visually organize thinking
• Provide multiple representations
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Give Guidelines for
Speaking, Reading, Writing, or Listening
• Provide structured opportunities to speak and
write in English
• Give explicit instructions in student-friendly
language
• Use visuals or examples in giving instructions.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Key Points
• Amplify Language
• Move from Concrete to Representation to Abstract
• Give Guidelines for Speaking, Reading, Writing, or
Listening
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
What’s In a Module?
Teacher Materials
• Module Overview
• Topic Overviews
• Daily Lessons
• Assessments
Student Materials
• Daily Lessons with Problem Sets
Copy Ready Materials
• Exit Tickets
• Fluency Worksheets / Sprints
• Assessments
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
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.
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 real-world
or mathematical problems that are ill-defined.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
What’s In a Lesson?
Teacher Materials Lessons
• Student Outcomes and Lesson Notes (in select lessons)
• Classwork
• General directions and guidance, including timing guidance
• Bulleted discussion points with expected student responses
• Student classwork with solutions (boxed)
• Exit Ticket with Solutions
• Problem Set with Solutions
Student Materials
• Classwork
• Problem Set
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Orientation to Materials (if needed)
Examination and exploration of:
• Topic A
• Topic B
• End of Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Flow of Module 5
A Synthesis of Modeling with Equations and Functions
• Topic A: Elements of Modeling
• Analyzing a Graph
• Analyzing a Data Set
• Analyzing a Verbal Description
• Topic B: Completing the Modeling Cycle
• Modeling a Context from a Graph
• Modeling from a Sequence
• Modeling a Context from Data
• Modeling a Context from a Verbal Description
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
What are students coming in with?
• G9-M1 Relationships Between Quantities and
Reasoning with Equations and Their Graphs
• G9-M2 Descriptive Statistics
• G9-M3 Linear and Exponential Functions
• G9-M4 Polynomial and Quadratic Expressions,
Equations and Functions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic A – Lesson 1: Analyzing a Graph
• Example 1
• Exercises 1-6
• Problem Set
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic A – Lesson 2: Analyzing a Data Set
•
•
•
•
Opening
Exercise 1
Exercise 2
Problem Set – Problem 4
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic A – Lesson 3: Analyzing a Verbal
Description
•
•
•
•
Exercise 1
Exercise 2
Exercise 3
Exercise 4
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Key Points – Topic A
• The lessons in Topic A serve to consolidate student
knowledge about linear, exponential and quadratic
functions.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Orientation to Materials (if needed)
Examination and exploration of:
• Topic A
• Topic B
• End of Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic B – Lesson 4: Modeling a Context
from a Graph
• Example 1
• Exercise 2
• Exit Ticket:
• Why might we want to represent a graph of a function in
analytical form?
• Why might we want to represent a graph as a table of
values?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic B – Lesson 5: Modeling a Context
from a Sequence
• Opening
• Are there functions that could model this data well?
• If a student has up to 30 min of actual gym time during
practice, how many exercises in the circuit would she
be able to complete?
• Do we believe in patterns?
• Problem Set – Problems 2-4
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Opening Exercise
Critique the following problem from G9-M5 Lesson 6:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic B – Lessons 6-7: Modeling a Context
from Data
• Lesson 6 Example 1 and Exercises 1-3
• Lesson 6 Exit Ticket
• Lesson 7 is designed to use the regression analysis of a Ti84 to find equations that model data
• Lesson 7 Exercise 2
• Lesson 7 Exit Ticket
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Topic B – Lessons 8-9: Modeling a Context
from a Verbal Description
•
•
•
•
•
Lesson 8:
Lesson 8:
Lesson 8:
Lesson 9:
Lesson 9:
Example 1-2
Problem Set: #1
Problem Set: #2
Exit Ticket
Problem Set #2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Key Points – Module 5 Lessons
• Reinforce the notion that we are modeling with
functions –
• Push students to recognize when they are or are not given
enough information to be sure that the function will be an
accurate representation of the data or information described.
• Use precision when speaking and encourage students to do the
same by questioning them for accuracy and precision.
• Remain aware of the discrete vs. continuous domain in the
context of the situation.
• Approach Lesson Summaries as opportunities for students
to consolidate their knowledge – ask & scaffold, don’t tell.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Orientation to Materials (if needed)
Examination and exploration of:
• Topic A
• Topic B
• End of Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Functions
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment
Work with a partner on this assessment
© 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
Key Points – End-of-Module Assessment
• Shorter modules, like G9-M5 do not have Mid-Module
Assessments, only an End-of-Module Assessment designed to
assess all standards of the module.
• Recall, as much as possible, assessment items are designed to
asses the standards while emulating PARCC Type 2 and Type 3
tasks.
• Recall, rubrics are designed to inform each district / school /
teacher as they make decisions about the use of assessments
in the assignment of grades.
© 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 the study of
Module 5?
How can you support successful implementation of
these materials at your schools given your role as a
teacher, trainer, school or district leader,
administrator or other representative?
© 2012 Common Core, Inc. All rights reserved. commoncore.org