© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Overview

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Shape of Math in A+ Countries 2 Mathem atics topics intende d at each grade by at least two- thirds of A+ countrie s Mathema tics topics intended at each grade by at least two- thirds of 21 U.S. states

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Instructional Shifts 3

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Map 4

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Story of Units Aligned to the Learning Progressions 5 Coherence Across the Grades Grade 2: 3 tens or 3 units of 10 (Grade 2 OA Standards) Grade 3: 3 fours or 3 units of/groups of four (Grade 3 OA Standards) Grade 4: 3 fourths or 3 units of one-fourth (Grade 3 NF Standards)

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Story of Units Aligned to the Learning Progressions 6 Coherence Across the Grades Learning 12 tens = tenths = 1.2 Learning 4 thirds 4/3 = 1 1/3 or even 4 threes = 12

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Story of Units Aligned to the Learning Progressions 7 Grade 3Grade 4Grade 5 Number and Operations in Base Ten Standards (NBT) Counting up and down by ones, tens and hundreds, both with the number line and place value chart are essential from Grade 3 forward to rounding and mental math. Meaningful understanding of all operations with base-ten whole numbers Understanding place value’s extension into decimal fractions and operations

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points: 8 A Story of Units is being written in alignment with the Instructional Shifts required by the CCLS. All standards for each grade have been carefully included in the module sequence. The P-5 modules are designed with deliberate coherence to capitalize on the learning progressions that are embedded in the CCLS. The activities promote a careful balance of fluency practice, conceptual understanding, and application, which aligns with the instructional shift, rigor.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 9

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Standards for Mathematical Practice 10 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Focus Standards for Mathematical Practice 11

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Mathematical Practice in Lessons 12

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Point 13 A Story of Units brings the Standards for Mathematical Practice to life. Although all practices are integrated throughout the curriculum, individual lessons may highlight one or two practices specifically to facilitate educators in developing these habits of mind in their students.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 14

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Publishers’ Criteria 15 I.Focus, Coherence, and Rigor in the CCSSM II.Criteria for Materials and Tools Aligned to the Standards III.Appendix: “The Structure is the Standards”

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Focus, Coherence, and Rigor 16 At any given grade level 75% of the year should be spent on major areas of work. The first half of the year should predominantly cover major areas of work.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Indicators of Quality in Instructional Materials and Tools for Mathematics 17 There are separate teacher materials that support and reward teacher study. The use of manipulatives follows best- practices. The visual design isn’t distracting or chaotic. Support for English language learners and members of other special populations is provided.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Analysis Grade 2—Module 3

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 19

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 20 Table of Contents Overview Topics including daily Lesson Plans Module Assessments Fluency Progression

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 21 Module Overview What is this module about? What is the purpose of the Overview?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 22 The Overview of Module Topics and Focus Lessons chart lists the teaching sequence towards attaining mastery of the standards highlighted in each lesson. Teaching sequences are the appropriate sequential order for developing mathematics skills. Teachers “build a ladder” to help students: develop conceptual understanding synthesize and apply knowledge from earlier concepts Walk Through and Analyze Module Components

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 23 Fluency – New and Familiar Fluency activities promote automaticity of skills, allowing students to reserve cognitive resources for higher level thinking.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 24 Structure provided by Universal Design for Learning (UDL) Asks teachers to consider: multiple means of representation multiple means of action and expression multiple means of engagement

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 25 Charts provide suggested scaffolds for: English Language Learners Students with Disabilities Students Performing Above Grade Level Students Performing Below Grade Level

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 26 Marginal Notes to Teachers in Lessons

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 27 Topic Opening: Focus standard(s), instructional days, and coherence links Introductory paragraph Concept chart (one lesson per concept) Mathematical Practices Brought to Life

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 28 Topic A - Suggested Lesson Structure

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 29

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 30

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 31 Rigor in Daily Lessons: Conceptual Development

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 32

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 33 Each lesson contains daily assessments: Activity Sheets Exit tickets Homework Walk Through and Analyze Module Components

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 34 Each module has an accompanying section for Supplementary Materials: Assessment Tasks Exit Tickets for each lesson Mid-Module Assessment Task End-of-Module Assessment Task Cross Modular Assessment Task Fluency Progressions Bank of activities to assist with planning Intentionally organized to revisit previously learned skills to develop automaticity, to build for the day’s concept or to anticipate future concepts Walk Through and Analyze Module Components

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 35 A Story of Units includes 5-7 modules for each grade level. A curriculum map and grade level overviews are provided in A Story of Units: A Curriculum Overview for Grades P-5. Topics break into concepts and concepts become lessons. The concepts may be displayed in the classroom as the learning objectives for the lessons.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 36

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Lesson Components of the Module 37

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Lesson Components of the Module 38

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 39 The Distribution of Instructional Minutes diagram displays the 3 components of rigor. The Suggested Lesson Structure pie chart shows the breakdown of a lesson based upon a 60 minute class. The Publishers’ Criteria emphasize that materials must reflect the Standards’ balanced approach to mathematics, stressing both conceptual understanding as well as procedural skill and fluency. There is a balance of activities and tasks and a balance of how time is spent.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 40 Daily Assessments Worksheets Exit Tickets Homework Assignments Daily assessments provide valuable data to inform teachers and direct instruction. Students have daily opportunities to apply conceptual understanding learned during lessons and are held accountable for independent work.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 41 Assessment Tasks Mid-Module Assessments End-of-Module Assessments Cross-Modular Assessments

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 42 Homework Sheets Build upon what students learn in the lesson for the day Provide opportunities for students to check their understanding and confirm they can solve problems independently

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 43 Rigorous problems that produce a variety of student responses are embedded throughout the module. For these problems, answers alone are insufficient. Students must be able to thoroughly explain their thought processes. Possible student work may include bar diagrams, number sentences, area models, paragraphs, etc.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Engageny.org 1 module for 2 nd and 5 th grade Videos of teachers actually using strategies with students Presentations Rigor Breakdown- with videos