#### Transcript Assessment Literacy on Steroids

Common Core Lite Mathematics Brought to you by…. 1 Provide an overview of the Common Core State Standards for Mathematics. Conduct this workshop with a process that you can replicate with large or small groups of teachers. Provide you with the materials necessary to get all K-12 teachers ‘dipped’ into the standards. 2 3 1. Our focus today is to learn HOW to investigate the Common Core State Standards for math. 2. You will not investigate all of the standards today. You will be given a process and materials to duplicate today’s process in your school. 3. WI has Early Learning Standards that address expectations for children birth to the beginning of first grade. When developing curriculum and assessment practices for 4K and 5K, the WMELS need to be considered along side the CCSS 4 1. An open and willing mind 2. The materials at your table 5 Practices Understandings Connections 6 The CCSS mandates the student learning outcomes for every grade level/grade band. Students will be tested and instructional effectiveness will be measured based on CCSS (beginning 2015). Federal funding is tied to CCSS adoption, implementation, and accountability. ELA and Mathematics CCSS are just the beginning. Science and Social Studies are in the draft stage…more subject area standards are being developed. CCSS create an opportunity for educators to talk and share knowledge across state lines. 7 …the acquisition of the knowledge and skills a student needs to enroll and succeed in creditbearing, first-year courses at a postsecondary institution (such as a two- or four-year college, trade school, or technical school) without the need for remediation. (ACT) The standards were built on this vision for every single student who graduates from high school. 8 Activity 1 ◦ Foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals ◦ Procedural as well as conceptual ◦ Hands-on ◦ Apply mathematical ways of thinking to real world issues and challenges ◦ Rigorous definition of college and career readiness ◦ Emphasize mathematical modeling 9 Standards for Mathematical Practice Carry across all grade levels Standards Describe habits of mind of a Document – mathematically expert student page 6 1. 2. 3. 4. 5. 6. 7. 8. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments & 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 10 Refer to the Standards Documents K-8 standards presented by grade level Organized into domains that progress over several grades Grades K-8 introductions give 2 to 4 domains at each grade level High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability) 11 Provide a sense of … ◦ the sophistication for mathematical understanding at the grade level. ◦ the learning progressions for the grade. ◦ extensions from prior standards. ◦ what’s important at the grade level. 12 Grade 1 Narrative 13 The Math Structure is Like a File Cabinet Intent - File Cabinet Cluster- Hanging Files Domain- Drawer File Folders – Grade Level Standards 14 Activity 2 Task: Note the descriptions of domains described. Divide the grade level focus areas among table partners and read the descriptions. Use the organizers provided to note what you discover and think about the standard’s intent. Discuss your thinking with your table partners about all of the critical focus areas. 15 Standards for Mathematical Practice are provided in detail. The Practices are also listed at the beginning of each grade level 16 Domains are larger groups that progress across grades Grade Level Standards define what students should understand and be able to do Clusters are groups of related standards Domain Operations and Algebraic Thinking Grade Level Standards 1.0A Cluster 17 Simple…Like a File Cabinet Intent - File Cabinet Cluster- Hanging Files Domain- Drawer File Folders – Grade Level Standards 18 Activity 3 Task: Find the Grade 8 Mathematics Standards. Examine the standards provided in the activity. Find all the elements Grade/Domain/Cluster), and note them in the chart. 19 Activity 3 Investigating the Content Standards’ Structure Task: Grade Go to the Mathematics Standards to review the components of the content standards structure. See the standards provided in the table below. Scavenger Hunt for each standard, find all the elements (Cluster, Domain and Grade/Conceptual Category), and note them in the table below. Domain Cluster Standard Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distancetime equation to determine which of two moving objects has greater speed. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 20 “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.” CCSS page 6 21 1. 2. 3. 4. 5. 6. 7. 8. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments & critique the reasoning of others Refer to the Model with mathematics standards Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning 22 Investigating the Standards for Mathematical Practice What is it? How can you use it? 23 Grad eK Counting & Cardinality Grad e1 Grad Grade Grade Grade Grade Grade Grade 3 4 5 6 7 8 e2 The Number System Operations & Algebraic Thinking Number & Operations in Base 10 Number Operations – Fractions Measurement & Data Geometry Ratios & Proportional Relationships Function s Expressions & Equations Statistics & Probability Vertical Connections All Standards in mathematics have a connection to early and subsequent concepts and skills The flow of those connections is documented by how a student develops the concepts Future Standards Future Standards Current Standard Prior Standards Prior Standards 25 TEAM TAKE AWAY 2 Investigating Vertical Connections Investigating Vertical Connections Task: Find a standards to insert in the chart , find corresponding prior and future standards that focus on the learning progressions one level above or below the given standard (if they exist). Note that you will be looking for standards prior to the given grade level and after the given the grade level. Discuss and note these connected standards in the chart below. EXAMPLE: Prior Standard Cluster/ Grade Level Standard Future Standard th 7 Grade. Ratios & Proportional Relationships. 2. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost ( t) is proportional to the number (n) of items purchased at a constant price (p), the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 8th Grade Functions. 4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 26 Investigating the Standards Through Vertical Connections 27 Properties of operations: their role in arithmetic and algebra Mental math and algebra vs. algorithms (Inspection) Units and unitizing Operations and the problems they solve Quantities Variables Functions Modeling (As a sequence across grades) Number Operations Expressions Equations (As a sequence across grades) Modeling Practices (from Phil Daro, one of three lead writers on the Common Core Standards for Mathematics) 28 So how will you use this in your school or district? PowerPoint Activities 1 - 4 2 Takeaway Activities Today’s Materials are all Available at: http://www.cesa4.k12.wi.us/ 29 (Today’s slides and materials were adapted from Investigating the Standards, ©2010 Wisconsin Cooperative Educational Service Agencies (CESAs) School Improvement Services statewide roll-out initiative) 30 Please complete your Exit Ticket. Nicki Pope Thanks for coming! Sherri Torkelson Billie Finco Julie Jensen 31