Mathematics Standards and Model Curriculum Targeted Professional Development Meeting Presenter Name: Bonny Buffington Date: February 13, 2012

Targeted Professional Development Meetings Goal: To provide opportunities for Ohio educators to develop an understanding of the revised standards and model curricula in all four content areas: English language arts, mathematics, science and social studies

What do we already know? Put a dot on the chart paper that demonstrates your level of familiarity with the common core math standards and model curriculum.

Overview A Look Inside the CCSSM –K- 8 –High School Digging Deeper – MARS Tasks, Math Practices Model Curriculum Progressions Resources What Should Districts Be Doing Now? Sample assessment items

CCSS Principles Focus –Identifies key ideas, understandings and skills for each grade or course –Stresses deep learning, which means applying concepts and skills within the same grade or course Coherence –Articulates a progression of topics across grades and connects to other topics –Vertical growth that reflects the nature of the discipline

CCSS Mathematical Practices 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

Activity 1 MARS tasks Which of the practices are you using as you work on these tasks? A word about “Rich Problem Solving”

Reading Literacy, Writing Standards For science, math and technical subjects Part of the common core ELA standards Teachers of science, math and other technical subjects responsible for these standards, as well

A Look at the Literacy Standards Which of these do you already do in math? Explain. What would these standards look like in a math class? How do these standards fit with the new math common core?

What does literacy look like in the mathematics classroom? Learning to read mathematical text Communicating using correct mathematical terminology Reading, discussing and applying the mathematics found in literature Researching mathematics topics or related problems Reading appropriate text providing explanations for mathematical concepts, reasoning or procedures Applying readings as citing for mathematical reasoning Listening and critiquing peer explanations Justifying orally and in writing mathematical reasoning Representing and interpreting data

A Look at the Common Core Under the green “Educator” banner at the bottom of the page, click on “Academic Content Standards” Scroll down on the LEFT side and find “Mathematics” Click on “Mathematics Common Core State Standards and Model Curriculum “Mathematics Common Core State Standards and Model Curriculum

Format of K-8 Standards Grade Level DomainDomain StandardStandard ClusterCluster

Grade Level Introduction Critical Area of Focus Cross-cutting themes

Grade Level Overview Grade 4 Overview Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations—Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Mathematical Practices 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

Change of Emphasis K- Grade 5 K-2 Greater development of how numbers work Data analysis is just a tool for working with numbers and shapes Grades 3-5 Fractions then decimals Multiplication with inverse division Operation strategies and relationships developed BEFORE algorithm procedures

Change of Emphasis Grades 6-8 Beginning of Data Analysis and Probability Introduction of Integers, Coordinate Graphing Focus on Linear Algebra: numerically, graphically and symbolically Completion of Operations with fractions and decimals

CCSS for High School Mathematics Organized in “Conceptual Categories” –Number and Quantity –Algebra –Functions –Modeling –Geometry –Statistics and Probability Conceptual categories are not courses Additional mathematics for advanced courses indicated by (+) Standards with connections to modeling indicated by ( ★ )

Format of High School Standards Domain Cluster Standard Advanced

Conceptual Category Introduction

Conceptual Category Overview Domain Cluster

HS CCSS: Changing Content Emphases Number and Quantity –Number systems, attention to units Modeling –Threaded throughout the standards Geometry –Proof for all, based on transformations Algebra and Functions –Organized by mathematical practices Statistics and Probability –Inference for all, based on simulation

High School: Appendix A Activity 2: Differentiated Activity ES and MS: Comparison Document

Two Main Pathways

Explore the *Suggested* Pathways: How are the pathways structured? Describe unit resources. How do these courses differ from what you’re teaching now? Give one positive comment – what is good about going this direction with your teaching? Give one obstacle – what are some concerns about the new curriculum? What other information/resource do you need to change to the new common core? What are your next steps to use this information?

Comparison Document and Learning Progressions Explore your grade level. Look at the grades before and after What has changed? What is the same? Carefully examine the old indicators and new standards to describe needed instructional changes

Digging Deeper into the CCSS

Standards for Mathematical Practice Mathematical ‘Habits of Mind’

Concepts, Skills and Procedures Concepts Big ideas Understandings or meanings Strategies Relationships Understanding concepts underlies the development and usage of skills and procedures and leads to connections and transfer. Skills and Procedures Rules Routines Algorithms Skills and procedures evolve from the understanding and usage of concepts.

Concepts, Skills and Procedures Understand ratio concepts and use ratio reasoning to solve problems. 1.Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 2.Understand the concept of a unit rate a/b associated with a ratio a:b with b  0, and use rate language in the context of a ratio relationship. 3.Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a.Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b.Solve unit rate problems including those involving unit pricing and constant speed. c.Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d.Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Concepts, Skills and Procedures Understand ratio concepts and use ratio reasoning to solve problems. 1.Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 2.Understand the concept of a unit rate a/b associated with a ratio a:b with b  0, and use rate language in the context of a ratio relationship. 3.Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a.Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b.Solve unit rate problems including those involving unit pricing and constant speed. c.Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d.Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

CONCEPTS vs SKILLS Concepts are learned through inquiry and hands-on experience. Skills are learned through repeated practice. Concepts must be mastered in the concrete prior to skill drill.

Model Curriculum

Instructional Strategies Instructional Resources and Tools Common Misconceptions

Activity 4 Look at the Model Curriculum for your grade level or subject. Look closely at content and resources available. Be ready to share out on what is there and what is not. What is the most helpful information/resource?

CCSS Support Materials - Future Development Pod Casts –Common Core State Standards – 101 –Ohio’s CCSS Model Curriculum – 102 –Standards for Mathematical Practice and the Critical Areas of Focus – 103 Resource Alignment Tool Eye of Integration

External Resources for CCSSM CCSSO – Achieve – NCTM – Center for K-12 Assessment & Performance Management at ETS – YouTube Video Vignettes explaining the CCSS –

Activity 5 Video Dan Meyer: Math Class Needs a Makeover

Resources: Click on “My Curriculum” Dan Meyer’s curriculumhttp://blog.mrmeyer.com/ MARS, Math Assessment Resource Servicewww.insidemathematics.org

Resources for H.S. Improvement NCTM’s high school reports –Focus on Reasoning and Sense MakingFocus on Reasoning and Sense Making Use the Common Core State Standards –Identify A2E content for all students Use Pathways and Standards Progressions –Reduce redundancy and incoherence –Use previous mathematics in service of new ideas Ohio’s Model CurriculumModel Curriculum –Adopted in March 2011

What Should Districts Do Now? Deepen your understanding of the CCSSM in Professional Learning Communities through: –the Standards for Mathematical Practice –the Critical Areas –the Model Curriculum –the Standards Progressions –the Comparative Analysis Begin focusing instruction around: – the Mathematical Practices –The Critical Areas Develop support structures for reaching all students –Use previous mathematics in service of new ideas –Provide all students access to the regular curriculum; RtI

1 CCSS, 2010, p. 5 2 PARCC – Draft Content Framework

ODE Mathematics Consultants Brian Roget Anita Jones Ann Carlson Yelena Palayeva