Common Core State Standards for Mathematics 2011

— SAMPLER — Common Core State Standards for Mathematics, Foundational Overview of the Common Core State Standards for Mathematics, Facilitator Handbook

Published by Pearson School Achievement Services, a division of Pearson, Inc. 1900 E. Lake Ave., Glenview, IL 60025

ISBN 115469

Contents

Materials Checklist...... 3 Facilitator Agenda...... 5 Preparation and Background...... 8 Introduction...... 11 Section 1: Along the Way to Common Standards...... 13 Section 2: Teach Less, Learn More...... 24 Section 3: From Standards to Classroom Practice and Assessment...... 41 Reflection and Closing...... 51 References...... 53

Materials Checklist

Item ISBN Special Instructions Participant Trainer Quantity Consumable Computer N/A Note 1 X X 1 each No Projector N/A X X 1 total No Speakers N/A X 1 total No PowerPoint N/A X 1 total No Videos N/A Note 2 X 3 total No Participant Workbook N/A X X 1 each Yes Posters/charts N/A Note 3 X 1 set to reuse No Common Core State 1 per Standards for Note4 X 1 per participant Yes participant Mathematics N/A Chart paper N/A 1 pad Yes Markers N/A 1 set per table 1 set per table No 1 per Highlighters 1 per participant No N/A participant Set out 4 per table for Slide 19 (Optional Activity). 3 per Index cards X 2 packs Yes Provide extras if you use them for participant N/A name tents. Sticky notes N/A Distribute 1 pad per table. X 1 pad per table Yes Tape N/A Use this item to hang charts. X 1 roll Yes Scissors N/A X 1 pair per table No Use a timer to ensure pacing Timer X No N/A during activities and break. Make (will need large paper clips) Yes or No Spinners 1 for every 2 or buy 6 section spinners. (See X (It depends if spinners are (optional) participants N/A Slide 59.) made or purchased.) Sticker dots in two X 2 dots per participant Yes different colors N/A Timeline Cards N/A Note5 X X 1 set per table No CCSSM Domain Sorting Note6 X X 1 set per table No Cards and Answer Key N/A PARCC and SBAC Note7 X X 2–3 per table No documents N/A

*Product materials must be ordered by consultant and used for on-site workshop purposes. Participants must be notified prior to workshop that they must bring suggested materials.

Note1 The school district needs to provide a workshop room with a computer for the facilitator. Prior to the workshop, the facilitator should obtain information about how to log in to the system. The facilitator should also confirm that PowerPoint is installed on the computer, and that the computer has Internet access. If the facilitator wishes to use his or her personal computer during the workshop, he or she needs to obtain permission from the district’s Technology Department. Participants can use their personal laptops to explore the Common Core State Standards for Mathematics (CCSSM) if needed.

Note2 Make sure that the videos used in this workshop are in the same folder as the PowerPoint. Be sure to watch the videos and think about possible responses prior to the workshop and check the links in the PowerPoint the morning of the workshop.  Videos o Section 1—Phil Daro: How Do You Create Better Standards in Math? o Section 2—Felisha Video o Section 3—John Van de Walle: Approach to Teaching

Note3 There is an electronic copy of each of the posters used in this workshop in the Additional Resources folder. As an alternative to creating each chart by hand, you can print them off and have them enlarged to poster size. Charts included in the Additional Resources folder are listed below:  Section 1 o K-W-L Chart o 1983 Trainer Chart  Section 2 o CCSSM Chart  Section 3 o Reflecting on Implications for Implementation Chart

Note4 The Common Core State Standards are in the warehouse and will be shipped to the workshop site prior to the workshop. Please check with [email protected] to ensure materials have been shipped. Please contact the school to ensure that materials have arrived.

Note5 The Timeline Cards can be found in the Additional Resources folder. Copy one set of the timeline cards for each table. Printing them on card stock will allow them to be reused.

Note6 The Domain Sorting Cards and Answer Key can be found in the Additional Resources folder. Copy one set of the Cards and one Answer Key for each table. The facilitator can print them on card stock for reuse.

Note7 Copy two to three sets of each document per table. If you copy them on colored paper and ask participants to return them, you can reuse them in each workshop. This will reduce the number of copies needed in the future and help the environment. If participants want their own copies, they can access them online. You can find these documents in the Additional Resources folder.

District- and Teacher-Provided Materials Ask the district to provide the following materials:  Workshop room with a computer for the facilitator (if necessary)  One copy of the CCSSM for each participant

Facilitator Agenda Foundational Overview of the Common Core State Standards for Mathematics Section Time Agenda Items Introduction 15 minutes Slides 1–3  Introduction and Welcome  Outcomes  Agenda 1: Along the Way to Common 90 minutes Slides 4–20 Standards  Section 1 Big Questions  Introduction o Activity: K-W-L Chart o Activity: 1983 Chart o Activity: Critical Documents Timeline  Common Ground for the Common Core o Activity: Partner Talk  Making Sense of Mathematics o Activity: Math Tasks (K–5 example and 6–12 example)  Long-Standing Importance  Mathematical Proficiency Reflection o Activity: Jigsaw  International Benchmarking  College and Career Readiness  Phil Daro on Common Core Standards o Video: Phil Daro—Creating Better Standards in Math  Review Section 1 Big Questions Break 15 minutes 2: Teach Less, Learn More 75 minutes Slides 21–38  Section 2 Big Questions

 Overview of the Common Core Standards for Mathematics o Activity: CCSSM Chart o Activity: The CCSSM Are/Are Not  Toward Greater Focus and Coherence  Grade-Level Standards o Activity: Standards Card Sort Activity  Bloom’s Taxonomy and Depth of Knowledge (DOK) o Optional Activity: Identify the DOK Level Lunch 30 minutes 2: Teach Less, Learn More 60 minutes Slides 39–48 (continued)  Toward Greater Fluency and Understanding o Activity: Fair Share o Video: Felisha  The Standards for Mathematical Practice o Revisit the Felisha Video  Model with Mathematics  NCTM Process Standards and the Standards for Mathematical Practice o Revisit the K-W-L chart  Review Section 2 Big Questions 3: From Standards to Classroom 45 minutes Slides 49–53 Practice and Assessment  Section 3 Big Questions  From Standards to Classroom Practice and Assessment o Video: John Van de Walle: Approach to Teaching  A Culture of Thinking and Learning  The Three-Phase Lesson Structure o Activity: Modeling the Three-Phase Lesson Structure  Mathematics Worth Doing Break 15 minutes 3: From Standards to Classroom 60 minutes Slides 54–63 Practice and Assessment  Assessment (continued) o Activity: Comparing PARCC and SBAC  Next-Generation Assessments o Activity: Assessment Samples  Mathematical Practices within a Rich Content o Activity: Integrating the Mathematical Practices into Classroom Instruction  Modeling Tasks within the Content

 Reflecting on Implications for Implementation o Activity: Implications for Implementation  Revisit the K-W-L Chart  Review Section 3 Big Questions Reflection and Closing 15 minutes Slides 64–68  Reflection Questions  Review Workshop Outcomes  Closing  References Total 6 hours

© 2011 Pearson, Inc. All rights reserved. 9 Common Core State Standards for Mathematics, Foundational Overview of the Common Core State Standards for Mathematics, Facilitator Handbook Preparation and Background Content Information Note to Facilitator: Please check if the state or district in which you will be leading the workshop has created its own state documents. States such as Arizona and New York already have already released state-specific versions of the CCSSM. You should become familiar with the state-specific documents and adapt the workshop materials to use the state-specific CCSSM. Tell participants that their work does not end here. Emphasize this especially for Hawaii. They should continue to look at each unit to determine which lessons and resources will help them meet the CCSSM and where they may need to supplement instruction to achieve a standard. By doing this for all units, they will learn when each standard is met in a program and determine if more support is needed for a specific standard. A suggestion could be to divide the units up between grade level teams and use the correlations documents as a guide.

The Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO).

These standards were developed for three reasons. First is to provide consistency across states. A set of common standards allows for consistent and quality education across all 50 states. Second, they align with international standards. To compete in global markets, students in the United States cannot lag behind their peers in other countries. The Common Core State Standards for Mathematics (CCSSM) are benchmarked against international standards so that students can compete in a global economy. Last, the standards help prepare students for college and work. Colleges and universities expect students to read complex texts independently, and employers look for workers who have the skill set to solve problems and the ability to integrate new knowledge. Elementary and secondary education need to prepare students for these challenges.

The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our students for college and the workforce. The NGA Center and CCSSO received initial feedback on the draft standards from national organizations representing, but not limited to, teachers, postsecondary educators (including community colleges), civil rights groups, English language learners, and students with disabilities. Following the initial round of feedback, the draft standards were opened for public comment, receiving nearly 10,000 responses.

The Common Core State Standards Initiative (2010a) states the following: The standards are informed by the highest, most effective models from states across the country and countries around the world, and provide teachers and parents with a common understanding of what students are expected to learn. Consistent standards will provide appropriate benchmarks for all students, regardless of where they live. These standards define the knowledge and skills students should have within their K–12 education careers so that they will graduate from high school able to succeed in entry-level, credit-bearing academic college courses and in workforce training programs. The standards  are aligned with college and work expectations;  are clear, understandable, and consistent;  include rigorous content and application of knowledge through high-order skills;  build upon strengths and lessons of current state standards;  are informed by other top-performing countries, so that all students are prepared to succeed in our global economy and society; and

 are evidence-based. Workshop Information

Big Ideas  Teaching less, learning more: Toward greater focus and coherence has two main ideas: o There are only three or four mathematics “critical areas” for most grades. o There are progressions of mathematics concepts across multiple grade levels (instead of grades in isolation).  Mathematical proficiency is more than “getting the answer;” it includes the process of using mathematical concepts effectively as identified in the Common Core State Standards for Mathematics’ (CCSSM) Standards for Mathematical Practice.  The Standards for Mathematical Practice are consistent for all the grade levels even though they manifest themselves differently as students grow in mathematical maturity.  Students need to engage in learning tasks that support the deep learning identified in the CCSSM.  Key features of these learning tasks include o encouraging productive struggle by using challenging problems; o connecting the current problems to students’ prior learning; o highlighting important mathematics in the teacher’s verbal introductions to the lesson and summarization at the end; o asking questions that emphasize the useful mathematical concepts; and o providing coherence between current learning and future learning.

Essential Questions  What are the CCSSM and how are they different from previous standards?  What are the CCSSM Standards for Mathematical Practice and why are they important for mathematical proficiency?  What kinds of learning tasks allow students the opportunity to demonstrate their mathematical proficiency?

Activities within the Workshop  Write about current knowledge about the CCSSM using the K-W-L chart.  Listen to background information about how CCSSM differs from other standards.  Discuss the introduction material of the CCSSM (pages 3–5) with a focus on surprises and how to identify differences between CCSSM and prior standards.  Perform a card sort to examine progressions and specific grade level changes/implications for instruction.  Write initial thoughts about the mathematical practices.  Watch the video of Phil Daro describing the Standards for Mathematical Practice.  Solve a problem about sharing a cookie with four, then three people.  Watch a video example of “Felisha” solving the Fair Share Problem.  Rewatch the “Felisha” video to find mathematical practices.  Reflect on the implications for implementation.

 Connect to assessments and then compare the Partnership for Assessment of Readiness for College and Careers (PARCC) and SMARTER Balanced Assessment Consortium (SBAC) assessments.

Assessments of Participants’ Learning during the Workshop  Show interest in the goals of the CCSSM by participating in workshop activities and sharing ideas.  Describe the key differences in CCSSM including comparisons between the standards they have been using and CCSSM.  Successfully identify the mathematical practices in the video examples or in their own group discussion while solving a mathematics problem.  Identify effective methods for promoting student understanding both in the facilitator’s modeling and in their own work on the mathematics problems.  Reflect on concrete changes that they can make next week that will better align students’ learning with what is expected under CCSSM.

Assessment Back in the School/Classroom  Describe the features of the CCSSM for their colleagues.  Correct others’ incorrect statements about the CCSSM.  Effectively navigate the CCSSM document across multiple grade levels.  Discuss the importance of mathematical practices with their colleagues.  Recognize and reinforce mathematical practices when they are exhibited by their students.  Intentionally model and support the practices when planning and facilitating lessons.  Select tasks that require students to engage in productive struggle and use methods to support students through the struggle to the important math concepts.

Outcomes By the end of the workshop, participants will be able to do the following:  Identify the domains and concept categories included in the K–12 Standards for Mathematical Content.  Connect the K–12 Standards for Mathematical Practice to the National Council of Teachers of Mathematics’ (NCTM) Process Standards and Proficiencies as detailed in Adding It Up: Helping Children Learn Mathematics.  Identify ways to promote classroom discourse that help students develop mathematical proficiency.  Identify aspects of the mathematical practices that bring teaching closer to assessment.  Connect current practice and articulate the changes needed to implement the CCSSM.

Facilitator Goals  Explain the organization of the CCSSM and the key features in their approach.  Convey the importance of the Standards for Mathematical Practice for building students’ mathematical proficiency.  Support teachers in selecting tasks that improve students’ mathematical proficiency and practices.  Use active learning techniques and movement to facilitate activities and engage learners.

© 2011 Pearson, Inc. All rights reserved. 12 Common Core State Standards for Mathematics, Foundational Overview of the Common Core State Standards for Mathematics, Facilitator Handbook Section 3: From Standards to Classroom Practice and Assessment (Slides 49–63) Time: 105 minutes Big Questions  What kinds of learning tasks allow students the opportunity to demonstrate their mathematical proficiency?  How can you establish a classroom culture of thinking and learning that supports the vision of the CCSSM? Workshop Objectives  Participants will develop connections between classroom practice and success in implementing the CCSSM.  Participants will discuss ways in which teachers can establish a classroom culture of thinking and learning that support the vision of the Common Core.  Participants will identify assessments associated with the Standards for Mathematical Practice. Materials per Section  Chart paper and markers as needed  John Van de Walle Video: Approach to Teaching  CCSSM document  PARCC and SBAC documents—two to three copies per table (available in the Additional Resources folder)

Topic Presentation Points Presentation Preview Section 3 Big Display Slide 49. Questions  Highlight the Big Questions for this section: o What kinds of learning tasks allow students the opportunity to demonstrate their mathematical proficiency? o How can you establish a classroom culture of thinking and learning that supports the vision of the CCSSM?

PW: Page 24: Section 3 Big Questions

Topic Presentation Points Presentation Preview From Standards to Display Slide 50. Classroom Practice  Explain that this part of the session takes a more focused look at what will and Assessment likely need to change about classroom practice in order for instruction to meet the rigor of the CCSSM.  Much of the discussion during this part of the workshop will be on identifying the probable implications for classroom practice—teaching, learning, and assessment.  Play the John Van de Walle video for participants. o To debrief, have participants discuss points made in the video that speak to instructional practice. o Chart these, and then spend several minutes making connections between Van de Walle’s approach to teaching and classroom practices that support the vision of the Common Core. PW: Page 24: John Van de Walle on Approach to Teaching A Culture of Thinking Display Slide 51. and Learning  Take participants back to the earlier conversation regarding understanding in Section 2. Connect these ideas not only to Van de Walle’s approach but to the expectations of the content standards and the Standards for Mathematical Practice of the Common Core.  Explain that research shows that the following three attributes of a classroom environment (on page 25 in the Participant Workbook) have been shown to increase mathematical proficiency (from Chapter 6 of Teaching and Learning Mathematics: Translating Research for Elementary School Teachers by Jennifer Bay-Williams): o Classroom Discourse: This is the way in which teachers and students talk about mathematics. o Classroom Norms: These are the principles of appropriate action the PW: Page 25: A Culture of Thinking and teacher establishes, which in turn establish (or do not establish) a Learning culture for thinking and learning. o Classroom Relationships: These are the ways in which the teacher builds relationships.  Each of these attributes could be the basis for a stand-alone professional development workshop. However, for the purposes of this workshop, let participants know that discussion in this last Section will focus on classroom discourse—the exchange between teacher and students when they talk about mathematics.

Topic Presentation Points Presentation Preview The Three-Phase Display Slide 52. Lesson Structure  The Three-Phase Lesson Structure provides a structure for the classroom discourse noted above.  Van de Walle labels the phases Before-During-After; others label the model Opening-Work Time-Closing. o During the first phase of the lesson—Before or Opening—the teacher may set the problem, introduce new ideas/concepts, clarify definitions, spiral/review concepts, or connect to past experiences without lowering the challenge of the task, which is designed to address one or more standards. o During the second phase—During or Work Time—students work independently or in small groups on the math task to gather data, share ideas, look for patterns, and make conjectures. PW: Page 26: The Three-Phase Lesson o In the final phase—After or Summary—students present and discuss Structure their solution paths as well as the strategies they used. The teacher guides them to reach the mathematical goal of the class and to connect their new understanding to prior knowledge.  The three-phase lesson structure helps teachers and students understand the expectations for work and performance for each grade. It also gives teachers and students the tools to reach and surpass those expectations. Predictable classroom management structure is essential to ensure that class time is productive and promotes a mathematics community of learning.  Briefly model the Before-During-After structure for the K–5 or 6–12 mathematical task the participants did earlier (in Section 1). Have them reflect on the roles of the teacher and student in that task.

Topic Presentation Points Presentation Preview Mathematics Worth Display Slide 53. Doing  Discuss each of the points on the slide, which will likely evolve into a dialogue about some of the challenges teachers are currently facing in their own classrooms. Remind them that the three-phase lesson structure is one good way to address their current challenges. o Choose high-level learning tasks. o Consider the language and the context of the problems being chosen. This is beneficial for English language learners (ELLs). o Encourage students to work independently of the teacher either individually or cooperatively in groups. o Encourage students to analyze situations and pose questions, because this is directly related to students’ demonstrating higher- order thinking skills (Bloom’s Revised Taxonomy and DOK) and the PW: Page 27: Mathematics Worth Doing eight Standards for Mathematical Practice. Having students pose questions also allows the teacher the opportunity to uncover misconceptions. . Restate student comments. Doing this allows the teacher to replace common language with mathematics vocabulary. Again, this is especially helpful for ELLs, and it is a critical element of the practice of precision. o By focusing on student approaches, the teacher shows willingness to understand the student’s approach and to help all students focus on the important mathematics—not just the approach.

Wrap up this part of the discussion by connecting back to Van de Walle’s notion of students—not teachers—being the ones that should make sense of the mathematics. Additionally, Daro (2010) stated that answer getting (students working a problem only for the purpose of getting the answer) is a black hole for the following reasons: o It short-circuits math learning. o It prevents students from making sense of the problem situation. o Students tend to use only math that they already know. o Teachers believe it’s good for classroom management (maintains a fairly quiet class). BACKGROUND INFORMATION: Consider the following alternatives:  Encouraging teachers to think, "How can I use this problem to teach the

Topic Presentation Points Presentation Preview mathematics of this unit?" Not, "How can I ensure my students can answer these questions?"  Encouraging teachers to go for robust understanding (understanding different ways of thinking about the problem): o The first response in the classroom should be to make the different ways of thinking that students bring to the lesson visible to all. o Students should be expected to share their thinking with others. o Use three or four different ways of thinking that students bring as starting paths to grade-level math targets. Assessment Display Slide 54.  Use the discussion above focused on student learning and understanding to transition to the quote presented on the slide.  Use the continuum to introduce some of the assessment language being used by the two consortia (SBAC and PARCC).  NOTE TO FACILITATOR: The Additional Resources folder contains documents on the Partnership for Assessment of Readiness for College and Careers (PARCC) and the SMARTER Balanced Assessment Consortium (SBAC). o Depending on the state you are working with, use the PARCC or SBAC information. o The continuum is simply a conversation starter to begin to frame the discussion on assessment that follows. PW: Page 28: Assessment  If time permits, have one half of the participants read the PARCC document and identify some of the assessment language.  Have the other half of the participants do the same with the SBAC document  When participants are finished, have them share their responses with the group.

Topic Presentation Points Presentation Preview Next-Generation Display Slide 55. Assessments  Associate the concept of "next-generation" assessments with the PARCC or SBAC.  Encourage participants to discuss how the examples on page 28 of the Participant Workbook differ from the ones they currently administer.  Discuss what type of learning is required for each task and at what level of knowledge (DOK) the assessment is written.  Example 1 is known as a completion item for assessing 3.MD.4. Ask participants to find 3.MD.4 in the CCSSM document. Are any of the mathematical practices embedded in the assessment of the content standard? If so, which ones? PW: Page 28: Next-Generation Assessments  What type of high-level learning task for a third-grade classroom would support students being able to successfully complete this sample assessment and assess some of the other mathematical practices?

Display Slide 56.  Example 2 is an item created to assess 6.RP.2 and 6.RP.3b. Ask participants to find these standards in the CCSSM. Which of the eight Standards for Mathematical Practice are embedded in the assessment of these content standards?  How is this problem similar to or different from the typical “textbook-like” problem?

PW: Page 28: Next-Generation Assessments

Topic Presentation Points Presentation Preview Mathematical Practices Display Slide 57. within a Rich Content  As the previous examples demonstrate, embedding the Standards for Mathematical Practice into content standards should bring teaching closer to assessment.

PW: Page 29: Mathematical Practices within a Rich Content

Display Slide 58.  Pose the following questions to continue the discussion around the need for classroom practice to integrate content and the Standards for Mathematical Practice. o What content standard is being assessed? o What Standards for Mathematical Practice are addressed? o How will you prepare students for this type of questioning? o Will computer-adapted assessment formats change classroom practice? If so, how?  These are the types of conversations that districts, teams, grade levels, vertical teams, and so forth will want to have in the coming months. PW: Page 29: Mathematical Practices within a Rich Content

Topic Presentation Points Presentation Preview Display Slides 59–60.  Have participants meet with their 9 o’clock partners to discuss the following: o To what extent do your current benchmark or cluster/unit tests, district summative tests, state tests, and so forth resemble this type of assessment (whether they are hard copy or computer adaptive assessments)? o Discuss how technology enhances this type of assessment as shown in Example 2 on pages 30–31 in the Participant Workbook.

 Important note: Currently PARCC is planning to administer only Grades 6–12 on the computer, while Grades 3–5 in the short term will involve paper and pencil administration.

PW: Pages 30–31: Example #2

Topic Presentation Points Presentation Preview Modeling Tasks within Display Slide 61. the Content  The previous example gives some indication of how the full modeling cycle is possible with technology. Participants should add the following bullet points to page 31 of the Participant Workbook: o recognize the mathematics; o find, analyze and use data; o employ mathematical procedures as appropriate o explain and/or defend their response. (Partnership for Assessment of Readiness for College and Careers 2010a)  Bring the discussion to a close by highlighting that assessment is one of many activities (curriculum instruction, accountability, and so on) that will merit time, energy, and resources.  BACKGROUND INFORMATION PW: Page 31: Modeling Tasks within the o For the past ten years, the No Child Left Behind (NCLB) federal Content statute has required annual state testing as a means of gauging student achievement. The adage, "what gets measured signals what is important," rings true in education. o Students regularly ask their teachers, "Will this be on the test?" If the answer is "no," they are less likely to pay attention to it. o Teachers and administrators pay close attention to what is tested on state and provincial assessments since their results can have high- stakes consequences. o If something is not assessed, it can quickly diminish in importance and receive less instructional emphasis. Important academic learning outcomes are falling through the cracks of the current large-scale assessment system. o Selected-response items are simply incapable of measuring students’ responses to open-ended problems and issues, discussion and debate, extended writing for real audiences and purposes, or substantive research and experimental inquiry, yet these are surely vital outcomes. o Selected-response and brief constructed-response item formats are limited in what they can appropriately assess. o Performance tasks call for students to apply their learning to new situations in context. Accordingly, they are better suited to assess

Topic Presentation Points Presentation Preview more complex aspects of CCSSM.

Reflecting on Display Slide 62. Implications for  To wrap up the discussions on implementation, have participants spend some Implementation time completing the chart on page 32 in the Participant Workbook.

OPTIONAL ACTIVITY:  Trainer Chart—As time permits, have participants share their answers by placing sticky notes on an enlarged version of the graphic in their Participant Workbooks (template in the Additional Resources folder).  Try to have a sampling of people share their thoughts so that different perspectives are provided.

Trainer Chart (optional) PW: Page 32: Reflecting on Implications for Implementation

Review Section 3 Big Display Slide 63. Questions  Revisit the K-W-L Chart: o Ask participants to reflect on the activities of this session and add to the “What I Learned” section on their K-W-L chart on page 7 of the Participant Workbook. o After a few minutes, invite participants to share key points of their reflection with the larger group. Chart their comments on the K-W-L chart you started at the beginning of the session. o Facilitators should also point out any of the “What I Want to Know” responses that were answered in this section.  Review the Big Questions for this section: PW: Page 7: K-W-L Chart PW: Page 24: Section 3 Big Questions o What kinds of learning tasks allow students the opportunity to

Topic Presentation Points Presentation Preview

demonstrate their mathematical proficiency?

o How can you establish a classroom culture of thinking and learning that supports the vision of the CCSSM?

© 2011 Pearson, Inc. All rights reserved. 23 Common Core State Standards for Mathematics, Foundational Overview of the Common Core State Standards for Mathematics, Facilitator Handbook Reflection and Closing (Slides 64–68) Time: 15 minutes

Reflection and Closing Display Slide 64.  Let participants know that they should address the statements on page 33 of the Participant Workbook.  Participants should discuss their responses with their groups.  After participants have finished discussing within their groups, lead a discussion about each reflection point for the larger group. Provide an opportunity for participants to ask any lingering questions.

PW: Page 33: Reflection and Closing Display Slide 65.  Review the workshop outcomes on the slide and on Participant Workbook page 5).  By the end of this workshop, participants will be able to o identify the domains and concept categories included in the K–12 Standards for Mathematical Content; o connect the K–12 Standards for Mathematical Practice to the National Council of Teachers of Mathematics’ (NCTM) Process Standards and Proficiencies as detailed in Adding It Up: Helping Children Learn Mathematics; o identify ways to promote classroom discourse that help students develop mathematical proficiency; o identify aspects of the mathematical practices that bring teaching closer PW: Page 5: Outcomes to assessment; and o connect current practice and articulate the changes needed to implement the CCSSM.

Display Slide 66.  Thank participants for coming and reference myPearsonTraining.com and PearsonPD.com.

Display Slides 67–68.  Display the workshop references if needed.

PW: Pages 34–35: References

America’s Choice. 2011. “Common Core State Standards Resources.” Accessed July 6, 2011. http://www.americaschoice.org/commoncorestandardsresources.

Bay-Williams, Jennifer M. 2010. “Effective Classroom Practices of Elementary School Teachers.” In Teaching and Learning Mathematics: Translating Research for Elementary School Teachers, 37–45. Reston, VA: The National Council of Teachers of Mathematics.

Bay-Williams, Jennifer M, and Karen S. Karp. 2008. Growing Professionally: Readings from NCTM Publications for Grades K–8. Reston: VA: National Council of Teachers of Mathematics.

Bay-Williams, Jennifer M., and Karen S. Karp. “Transforming Mathematics Classrooms, Teaching Mathematics Equitably to All Students.” Presentation given at the National Council of Teachers of Mathematics Annual Meeting, San Diego, CA, April 2010.

Bridges, William. 2009. Managing Transitions: Making the Most of Change. Philadelphia, PA: William Bridges and Associates, Da Capo Press.

California Department of Education. 2010. 2010 STAR Test Results. Accessed November 23, 2010. http://star.cde.ca.gov/star2010.

Common Core State Standards Initiative. 2010a. “About the Standards.” Accessed January 27, 2011. http://www.corestandards.org/about-the-standards.

—. 2010b. “The Standards: Mathematics.” Accessed October 20, 2010. http://www.corestandards.org/assets/CCSSI_Math %20Standards.pdf.

—. 2010c. “Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects.” Accessed January 1, 2011. http://www.corestandards.org/assets/CCSSI_ELA%20Standards.pdf.

—. 2010d. “National Governors Association and State Education Chiefs Launch Common State Academic Standards.” Accessed January 27, 2011. http://www.corestandards.org/articles/8-national-governors-association-and-state-academic-standards.

Conley, David T. 2011. Redefining College Readiness, Volume 5. Eugene, OR: Educational Policy Improvement Center. Accessed January 27, 2011 https://www.epiconline.org/files/pdf/RedefiningCollegeReadiness.pdf.

Daro, Phil. “Common Core State Standards: What’s Different?” Presentation given at Pearson, Glenview, IL, October 2010.

Daro, Phil. 2010. “How do you create better standards in math?” Pearson Education. 2 min., 55 sec. http://commoncore.pearsoned.com/index.cfm?locator=PS11Ye.

Fleischman, Howard L., Paul J. Hopstock, Maris P. Pelczar, Brooke E. Shelley, and Holly Xie. 2010. Highlights From PISA 2009: Performance of U.S. 15-Year-Old Students in Reading, Mathematics, and Science Literacy in an International Context (NCES 2011-004). Washington, DC: National Center for Education Statistics, Institute of Education Services. Accessed January 27, 2011. http://nces.ed.gov/pubs2011/2011004.pdf.

Mathematics Learning Study Committee, and National Research Council. 2001. Adding It Up: Helping Children Learn Mathematics, 1st ed. Washington, D.C.: The National Academies Press.

National Commission on Excellence in Education, The. 1983. A Nation at Risk: The Imperative for Educational Reform. No place: The National Commission on Excellence in Education.

National Council of Teachers of Mathematics. 2000. “Overview: Standards for School Mathematics: Prekindergarten through Grade 12.” Accessed October 20, 2010. http://standards.nctm.org/document/chapter3.

National Council of Teachers of Mathematics. 2010. “NCTM Action on the Common Core State Standards for Mathematics.” Accessed November 19, 2010. http://www.nctm.org/about/content.aspx?id=27076

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