GV Middle School Mathematics Mrs. Susan Iocco December 10, 2014

Characteristics of the “New” Standards The Standards are: ● fewer and more rigorous than in the past. ● have increased clarity. ● aligned with college and career expectations. ● internationally benchmarked. ● designed to include rigorous content and application of higher-order skills. ● researched based.

Some Key Terms ●Clarity and Specificity ○ Skills and concepts are clearly defined. ○ An ability to apply concepts and skills to new situations is expected.

Some Key Terms ● Coherence ○ Instruction, assessment and curriculum are aligned. ○ Conceptual understanding and procedural skills are equally stressed. ○ Progressions of topics and performances are developmentally sound.

Some Key Terms ● Focus ○Key ideas, understandings, and skills are identified. ○Deep learning of concepts is emphasized. ○Adequate time is devoted to a topic to counter the “mile wide, inch deep” criticism leveled at most current U.S. standards

Practice and Content Standards Standards for Mathematical Practice o 8 Practices o Describe ways in which students ought to engage in mathematics Mathematical Content Standards o Content Standards per grade o Describe what students should understand and be able to do Together they provide the “how” and “what” of mathematics

The Changes in the PA Standards PDE has changed the focus of math from “mile wide, inch deep” philosophy to a more focused, in-depth set of skills and concepts at each grade level. There is: ○ A shift in skills- greatest impact at grades 4, 5, and 6. ○ An expectation of mastery of skills (depth vs. breadth). ○ A drive for students to “explore and express” math thoughts

Examples of Shifts in Mathematical Teaching for All Grade s More emphasis at each grade on reasoning, problem solving, modeling, decision making, and engagement. More emphasis on connecting practice standards with content standards at each grade

Examples of Shifts in Content- Intermediate Grades More emphasis on: ● applying strategies and using properties ● relationships between and among shapes ● developing an understanding of geometric figures based on their properties ● identifying patterns ● measuring with precision and purpose ● analyzing and solving problems based on data.

Examples of Shifts in Content- Intermediate Grades Less emphasis on: ❏ Measuring in isolation ❏ Making measurement conversions outside of the context of a problem solving situation ❏ Locating random points on the coordinate system ❏ Computing in isolation

Shifts in Emphasis Shifts in Emphasis in Grade 6 Shifts in Emphasis for Grade 7 Shifts in Emphasis for Grade 8

Standards for Mathematical Practice: A Key Component These eight Practice Standards are designed to help students internalize concepts for a greater understanding of mathematics. They are the “habits of mind” of a productive mathematical thinker. 1.Make sense out 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 sense of structure. 8.Look for and express regularity in repeated reasoning.

Big Ideas and The Standards for Mathematical Practice Make sense of problems and persevere in solving them. ❖ Multiple representations are presented to help the students move from concrete to representative and into abstract thinking. ❖ Essential Questions help students focus and analyze. ❖ In Your Own Words provide opportunities for students to look meaning and entry points to a problem. Reason abstractly and quantitatively. ❖ Visual problem solving models help students create a coherent representation of the problem. ❖ Opportunities for students to decontextualize and contextualize problems are present in every lesson.

Big Ideas and The Standards for Mathematical Practice Construct viable arguments and critique the reasoning of others. ❖ Error Analysis; Different Words, Same Question; and Which One Doesn’t Belong features provide students the opportunity to construct arguments and critique the reasoning of others. ❖ Inductive Reasoning activities help students make conjectures and build a logical progression of statements to explore their conjecture. Model with mathematics. ❖ Real-life situations are translated into diagrams, tables, equations, and graphs to help students analyze relations and to draw conclusions. ❖ Real-life problems are provided to help students learn to apply the mathematics they are learning to everyday life.

Big Ideas and The Standards for Mathematical Practice Use appropriate tools strategically. ❖ Graphic Organizers support the thought process of what, when, and how to solve problems. ❖ A variety of tools, such as graph paper, number lines, and manipulatives are available as students consider how to approach a problem. ❖ Opportunities to use the web, graphing calculators, and spreadsheets support student learning. Attend to precision. ❖ On Your Own questions encourage students to formulate consistent and appropriate reasoning. ❖ Cooperative learning opportunities support precise communication.

Big Ideas and The Standards for Mathematical Practice Look for and make use of structure. ❖ Inductive Reasoning activities provide students the opportunity to see patterns and structure in mathematics. ❖ Real-world problems help students use the structure of mathematics to break down and solve more difficult problems. Look for and express regularity in repeated reasoning. ❖ Opportunities are provided to help students make generalizations. ❖ Students are continually encouraged to check for reasonableness in their solutions.

Our New Texts Big Ideas Math

The Authors: Math Educators Ron Larson ●Professor of Mathematics at Penn State Erie ●Ph.D in mathematics ●Lead author of a comprehensive program for mathematics that spans middle school, high school, and college courses ●Is in constant touch with the needs of students and teachers through numerous professional activities

The Authors: Math Educators Laurie Boswell ●Lead teacher of mathematics in Lyndonville, Vermont ●Teacher of mathematics from elementary through college levels ●Ed.D in Mathematics ●Recipient of the Presidential Award for Excellence in Mathematics Teaching ●Co-author of numerous math programs

About the Program ●Big Ideas is activity-based. ●There are less topics presented at a deeper level. ●There are opportunities for students to process concepts in their own words. ●There are real world connections in every lesson. ●Essential Questions are presented to help students focus and make connections. ●There are online resources for students, parents and teachers

Parent/Student Components Easy access to all components through the Big Ideas Math website ●24/7 online access to student text ●Parent online resources include: o Parent letters for each chapter which include “At Home Activities” o Basic Skills and Skills Review Handbooks o History of the Standards initiatives o A Game Closet