PUTTING THE COMMON CORE MATH STANDARDS INTO ACTION Sandy Christie Craig Bowman Spring 2012

Implementing the Common Core State Standards in Washington State Our Vision: Every student will have access to the CCSS standards through high quality instruction aligned with the standards every day; and that all English language arts and mathematics teachers are prepared and receive the support they need to implement the standards in their classrooms every day. Our Purpose: To develop a statewide system with aligned resources that supports all school districts in their preparation of educators and students to implement the CCSS. This includes building system-wide capacity for sustained professional learning that can support CCSS implementation now and be applied to other initiatives in the future. March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 2 Our Core Values: This vision can only occur through core values of clarity, consistency, collaboration, coordination, and commitment from classrooms, schools, and communities to the state level.

Objectives Awareness of history of CCSS and SBAC Understand the language/content of a grade specific CCSS Domain/Cluster at a deeper level Analyze a CCSS Domain learning progression for a grade band Connect Cognitive Complexity to Mathematical Practices and depth of content standards Strategies to support implementation of Mathematical Practices to increase content depth

A BRIEF REVIEW OF THE COMMON CORE STATE STANDARDS CCSS – Mathematics 4

July 20, 2011 Washington confirmed its commitment to student success with the adoption of Common Core State Standards (CCSS) 5

Where did they come From? State-led effort coordinated by National Governors' Association (NGA) Council of Chief State School Officers (CCSSO) A national set of standards but not a federal government product or directive Written by a consortium of content experts, teachers, and administrators Why now and not before? Race To the Top educational reform being funded by the U.S. Department of Education 6

WHO ELSE HAS ADOPTED?

What Did We Get? Two sets of standards K-12 English – Language Arts & Literacy includes integrated reading and writing standards for History/Social Studies, Science, and Technical Subjects Mathematics Created by nationally recognized experts in each field An evolution of our current standards – not a replacement 8

Progression of Standards

Building a foundation 10

SMARTER BALANCED ASSESSMENT SYSTEM New Assessment System: What We Know So Far

A National Consortium of States 28 states representing 44% of K-12 students 21 governing, 7 advisory states Washington state is fiscal agent March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 12

Key Assessment Activities

Grades Supported Through Smarter Balanced GradesSummativeInterim (Optional) Formative Tools and Professional Learning (Optional) ✔✔✔ 1-2 Performance Tasks as Required to Cover CCSS ✔ EOC and Comprehensive ✔ ✔✔ EOC and Comprehensive ✔ Optional ✔ EOC and Comprehensive ✔ March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 14

Time and format Summative: For each content area - ELA & Math Computer Adaptive Testing Selected response (MC), Constructed Response (open- ended), Technology enhanced (e.g., drag and drop, video clips, limited web-interface) Paper/pencil summative offered for three years (transition period) Performance Tasks (like our CBAs) Up to 2 per content area in grades 3-8 Up to 6 per content area in High School March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 15

Time and format Summative: - Administration window is last 12 weeks of school - For each content area - ELA & Math Shorter option for states (~3 hours ELA, ~2 hours Math) Scale score on comprehensive test (met/not met determination) Longer option for states (~5 hours ELA, ~3 hours Math) Able to report data on claims for individual students March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 16

Time and format Interim assessments Can be used as often as needed Can be customized by districts/schools To focus on selected strands To clone summative test Will use Computer Adaptive Technology Released items from summative item bank March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3 17

Washington’s Context… Proposed Summative Assessments in 2014–15 English/LAMathematicsScience Grade 3SBAC Grade 4SBAC Grade 5SBAC MSP Grade 6SBAC Grade 7SBAC Grade 8SBAC MSP Grades 9-10HSPE Rdg & Writing ??? EOC Algebra/Geometry ??? EOC Grade 11SBAC SBAC=SMARTER Balanced Assessment Consortium MSP= Measurements of Student Progress HSPE = High School Proficiency Exams EOC= End of Course exams March 20, OSPI CCSS Mathematics Webinar - Part 3

Many details still to be worked out. For more info: Check out CCSS Math Webinar Part 3 on OSPI website. Smarter Balanced Assessment Consortium

DEEPEN UNDERSTANDING OF THE COMMON CORE MATH STANDARDS

Major Shifts within Mathematics CCSS Focus Fewer big ideas --- learn more Learning of concepts is emphasized Coherence Articulated progressions of topics and performances that are developmental and connected to other progressions Application Being able to apply concepts and skills to new situations

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. 23

Structure of the CCSS

Transitioning… Year 1 Grade level Focus D omains K High School Year School districts that can, should consider adopting the CCSS for K-2 in total. K – Counting and Cardinality (CC); Operations and Algebraic Thinking (OA) 1 – Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT) 2 – Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT) and remaining 2008 WA Standards 3 – Number and Operations – Fractions (NF) 4 – Number and Operations – Fractions (NF) 5 – Number and Operations – Fractions (NF) and remaining 2008 WA Standards 6 – Ratio and Proportion Relationships (RP) 7 – Ratio and Proportion Relationships (RP) 8 – Expressions and Equations (EE) and remaining 2008 WA Standards Teach all of the 2008 WA Mathematics Standards for each course and prepare for Algebra 1- Unit 2: Linear and Exponential Relationships Geometry- Unit 1: Congruence, Proof and Constructions and Unit 4: Connecting Algebra and Geometry through Coordinates

OSPI Grade Level Transition Documents What does this document tell you? What doesn’t this document tell you? How might you use this document?

Let’s do some math… Individually work your grade level problem… Discuss how you solved it with your table partners Identify what mathematical practices you used Determine the cluster/standard the problem addresses Whole group discussion

CCSS Grade Overview Grade level overview… Read Where does the task that you just solved fit? What else do you notice? Share with partners

Focusing on the Domain Individual… Read and Highlight As you read, what language might someone (parent or colleague) have trouble understanding? Highlight those areas on the Domain Illustration Sheet Whole group… Discuss areas of concern

Creating Personal Connections On the provided Domain Illustration… Personal description or definition /Example Non-example or misconception Whole group… share out Finished Early?? – listen in and/or contribute to other teams conversations

31 Grade Level Progression Problems In grade bands (K-2, 3-5, 6-8, HS): Each partner group has a set of grade band problems Order the problems in a learning progression for each grade Combine into a grade band progression Compare with other same grade band partner teams Review “answers”

Martha’s Carpeting Task Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

The Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? How long would each of the sides of the pen be if they had only 16 feet of fencing? How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Comparing Two Mathematical Tasks Think privately about how you would go about solving each task (solve them if you have time) Talk with your neighbor about how you did or could solve the task – Martha’s Carpeting – The Fencing Task

Solution Strategies: Martha’s Carpeting Task

Martha’s Carpeting Task Using the Area Formula A = l x w A = 15 x 10 A = 150 square feet

Martha’s Carpeting Task Drawing a Picture 10 15

Solution Strategies: The Fencing Task

The Fencing Task Diagrams on Grid Paper

The Fencing Task Using a Table LengthWidthPerimeterArea

The Fencing Task Graph of Length and Area

Comparing Two Mathematical Tasks How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

Similarities and Differences Similarities Both are “area” problems Both require prior knowledge of area Differences The amount of thinking and reasoning required The number of ways the problem can be solved Way in which the area formula is used The need to generalize The range of ways to enter the problem

Mathematical Tasks: A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

Level 1 (Recall) ….includes the recall of information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one‐step, well‐defined, and straight algorithmic procedure should be included at this lowest level. 45

Level 2 (Skill/Concept) ….includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a rote response, perform a well‐known algorithm, follow a set procedure (like a recipe), or perform a clearly defined series of steps. 46

Level 3 (Strategic Thinking) ….requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. This may require a student to explain their thinking or make conjectures. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning. 47

Level 4 (Extended Thinking) ….requires complex reasoning, planning, developing, and thinking most likely over an extended period of time. 48

Refer to the Carpeting and Fencing Tasks- What are their levels of cognitive complexity? 49

Sorting Activity Individually: Categorize tasks into Level 1, 2, 3, or 4 using Cognitive Complexity Levels for Grade 7. Record your responses on the provided worksheet. In table teams: Share your results and come to consensus at your table. Whole group: Share results and review criteria groups used for low and high levels. 50

Sorting Questions to ponder…… How did you determine between levels 2 & 3? Does a task presented as a word problem always have a high level of cognitive complexity? Does using a manipulative indicate a higher level of cognitive complexity? If a task requires an explanation, does it have a high level of cognitive complexity?

Changing the Cognitive Complexity Level Each team member picks out a task that was placed in level 1 or 2. Individually determine how you would modify your task to be a level 3 task. Share out with your team & determine which task you will share with the entire group. Share out entire group.

Cognitive Complexity & Mathematical Practices Which levels of cognitive complexity allow students to develop the mathematical practices? Update your Domain Illustration column 5. 53

Are there various levels of Cognitive Complexity in Your Instructional Materials? Review several types of problems/tasks found in your instructional materials. What level of cognitive complexity are these tasks? Level 1 (Recall) Level 2 (Skill/Concept) Level 3 (Strategic Thinking) Level 4 (Extended Thinking) 54

Share at your table the types of problems/ tasks you found : What are the prevalent levels of complexity in your instructional materials? How will this impact meeting the standards for mathematical practice? Whole group share out 55

Gas Mileage Activity Complete the Gas Mileage Activity Discuss responses Review “original” Gas Mileage Activity Compare/contrast both versions 56

Who’s Doing the Thinking? Watch Dan Meyer video 57

Video Debrief How much is too much support, how much is too little? How does scaffolding interfere/promote the standards for mathematical practice? 58

Impact of Teachers Read case studies (scenarios) of how Fencing Task was implemented. Use worksheet to write your thoughts on cognitive complexity students experience. Share out in table teams Whole group share out

Who’s Doing the Thinking? Brainstorming Session: What instructional strategies can be used to promote student thinking and develop mathematical practices? How does this relate to content depth? Shifts in Classroom Practice Handout 60

If time………………….. Watch Annenberg Video for Mathematical Practices: Partner 1: Look for Mathematical practices students are exhibiting. What are they doing/saying? Partner 2: Look for teacher “moves” that encourage student development of mathematical practices. Partner Shareout…………………Whole Group Shareout

Objectives Revisited Awareness of history of CCSS and SBAC Understand the language/content of a grade specific CCSS Domain/Cluster at a deeper level Analyze a CCSS Domain learning progression for a grade band Connect Cognitive Complexity to Mathematical Practices and depth of content standards Strategies to support implementation of Mathematical Practices to increase content depth

Resources Common Core Tools

Thank you………… Clock hours reminder– turn in forms