NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
A Story of Ratios
Grade 6 – Module 6
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Session 2 Objectives
•
Understand the mathematical concepts within G6-M6.
•
Practice collecting evidence of effective instruction using
lesson transcripts.
•
Discuss feedback strategies for supporting scaffolding and
accommodation techniques for special populations.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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 Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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 Ratios
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 Ratios
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
A Story of Ratios
Curriculum Overview of A Story of Ratios
© 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 Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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
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
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
G6-M5 Topic Overview
Topic A: Understanding Distribution
Topic B: Summarizing Distribution that is Approximately
Symmetric using Mean and Mean Absolute Deviation
Topic C: Summarizing Distribution that is Skewed using Mean and
the Interquartile Range
Topic D: Summarizing and Describing Distribution
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Turn and Talk
• What difficulties would you anticipate with
student understanding of the mathematics in this
section?
• What scaffolds would be effective for addressing
those difficulties?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A re-wording
G6-M6
Example 1: What is a Statistical Question?
G6-M6
Example 1: What is a Statistical Question?
Jerome, a 6th grader at Roosevelt Middle School,
is a huge football fan. He loves to collect baseball
cards. He has cards of current players and
players from past seasons. With his teacher’s
permission, Jerome brought his baseball card
collection to school. Each card has a picture of a
current or past major league baseball player,
along with information about the player. When he
placed his cards out for the other students to see,
they ask Jerome all sorts of questions. Some
asked:
• How many cards does Jerome have
altogether?
• What is the typical cost of a card in Jerome’s
collection?
• Where did Jerome get the cards?
Jerome collects major league baseball cards.
Which of these questions is a statistical question?
Which of these questions is a statistical question?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
His collection contains cards of both current
players and past (retired) players.
Each card has a picture of a player as well as
information about that player.
His classmates asked Jerome the following
questions about his baseball cards:
•
•
•
How many cards does Jerome have
altogether?
What is the typical cost of a card in Jerome’s
collection?
Where did Jerome get the cards?
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
A game was played where ten tennis balls
were tossed into a basket from a certain
distance. The number of successful tosses
for six students where
4, 1, 3, 2, 1, 7
Find the mean number of successful tosses
for this data.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
4, 1, 3, 2, 1, 7
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Leads to this in
Lesson 13
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Turn and Talk
• What difficulties would you anticipate with
student understanding of the mathematics in this
section?
• What scaffolds would be effective for addressing
those difficulties?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Biggest Takeaway
Turn and Talk:
• What questions were answered for you?
• What new questions have surfaced?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios