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A Story of Units Overview

A Story of Units Overview. The Shape of Math in A+ Countries. Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states. Mathematics topics intended at each grade by at least two-thirds of A+ countries. Instructional Shifts. Curriculum Map.

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A Story of Units Overview

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  1. A Story of Units Overview

  2. The Shape of Math in A+ Countries Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states Mathematics topics intended at each grade by at least two-thirds of A+ countries

  3. Instructional Shifts

  4. Curriculum Map

  5. A Story of Units Aligned to theLearning Progressions • 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)

  6. A Story of Units Aligned to theLearning Progressions • Coherence Across the Grades • Learning 12 tens = 120 12 tenths = 1.2 • Learning 4 thirds 4/3 = 1 1/3 • or even • 4 threes = 12

  7. A Story of Units Aligned to theLearning Progressions

  8. Key Points: • 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.

  9. AGENDA • Examine Alignment with the Instructional Shifts • Examine Alignment with the Mathematical Practices • Examine Alignment with the Publishers’ Criteria • Examine PARCC Type I, II, and III Tasks • Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards • Watch a Video Clip of A Story of Units in the Classroom

  10. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  11. Focus Standards for Mathematical Practice

  12. Mathematical Practice in Lessons

  13. Key Point • 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.

  14. AGENDA • Examine Alignment with the Instructional Shifts • Examine Alignment with the Mathematical Practices • Examine Alignment with the Publishers’ Criteria • Examine PARCC Type I, II, and III Tasks • Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards • Watch a Video Clip of A Story of Units in the Classroom

  15. The Publishers’ Criteria • Focus, Coherence, and Rigor in the CCSSM • Criteria for Materials and Tools Aligned to the Standards • Appendix: “The Structure is the Standards”

  16. Focus, Coherence, and Rigor • 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.

  17. Indicators of Quality in Instructional Materials and Tools for Mathematics • 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.

  18. A Story of Units Module Analysis Grade 2—Module 3

  19. AGENDA • Walk Through and Analyze Module Components • Analyze Lesson Components of Module • Look at Rigorous Problems in the Module • Watch Video Clip

  20. Walk Through and Analyze Module Components • Table of Contents • Overview • Topics including daily Lesson Plans • Module Assessments • Fluency Progression

  21. Walk Through and Analyze Module Components • Module Overview • What is this module about? • What is the purpose of the Overview?

  22. Walk Through and Analyze Module Components • 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 sequentialorder for developing mathematics skills. Teachers “build a ladder” to help students: • develop conceptual understanding • synthesize and apply knowledge from earlier concepts

  23. Walk Through and Analyze Module Components • Fluency – New and Familiar • Fluency activities promote automaticity of skills, allowing students to reserve cognitive resources for higher level thinking.

  24. The Common Core Approach to Differentiating Instruction • 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

  25. The Common Core Approach to Differentiating Instruction • Charts provide suggested scaffolds for: • English Language Learners • Students with Disabilities • Students Performing Above Grade Level • Students Performing Below Grade Level

  26. The Common Core Approach to Differentiating Instruction • Marginal Notes to Teachers in Lessons

  27. Walk Through and Analyze Module Components • Topic Opening: • Focus standard(s), instructional days, and coherence links • Introductory paragraph • Concept chart (one lesson per concept) • Mathematical Practices Brought to Life

  28. Walk Through and Analyze Module Components • Topic A - Suggested Lesson Structure

  29. Walk Through and Analyze Module Components

  30. Walk Through and Analyze Module Components

  31. Walk Through and Analyze Module Components • Rigor in Daily Lessons: Conceptual Development

  32. Walk Through and Analyze Module Components

  33. Walk Through and Analyze Module Components • Each lesson contains daily assessments: • Activity Sheets • Exit tickets • Homework

  34. Walk Through and Analyze Module Components • 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

  35. Key Points • 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.

  36. AGENDA • Walk Through and Analyze Module Components • Analyze Lesson Components of Module • Look at Rigorous Problems in the Module • Watch Video Clip

  37. Analyze Lesson Components of the Module

  38. Analyze Lesson Components of the Module

  39. Key Points • 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.

  40. A Look At Rigorous Problems in the Module • 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.

  41. A Look At Rigorous Problems in the Module • Assessment Tasks • Mid-Module Assessments • End-of-Module Assessments • Cross-Modular Assessments

  42. A Look At Rigorous Problems in the Module • 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

  43. Key Points • 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.

  44. Engageny.org • 1 module for 2nd and 5th grade • Videos of teachers actually using strategies with students • Presentations • Rigor Breakdown- with videos

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