# Building Students’ Deep Understanding through a Common Core-Aligned Unit Setting the Stage  Reflect on planning and pedagogical practices in context of.

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Building Students’ Deep Understanding through a Common Core-Aligned Unit Setting the Stage  Reflect on planning and pedagogical practices in context of the CCLS instructional shifts in mathematics Rigorous Tasks as Unit Drivers  Evaluate and strengthen the alignment of a unit’s culminating task  Evaluate and adjust the rigor of a unit’s culminating task Planning with the Instructional Shifts in Mind  Analyze the coherence of tasks within a unit  Study the elements of a Common Core-aligned lesson plan  Create or revise a lesson plan for an instructional task Supporting the Instructional Shifts through Mathematical Talk  Participate in a text-based discussion about mathematical talk and analyze a video of mathematical talk in action Bringing it all Together  Watch video of classroom practice and analyze teacher moves and student knowledge and skills  Determine next steps for unit outline  Reflect on own practice in the context of course learnings  Create an action plan for building school-wide capacity 1

Building Students’ Deep Understanding through a Common Core-Aligned Unit Session 2: Rigorous Tasks as Unit Drivers 1.Introduction, Logistics, review of Bridge to Practice from Session 1 2.Activity #1: Aligning a Unit’s Culminating Task to the CCLS 3.Introduction to Depth of Knowledge 4.Activity #2: Using Depth of Knowledge to Assess the Rigor of a Sample Mathematics Task 6.Reflection, Strategies for Sharing, Bridge to Practice, and Feedback Forms 2

Reflecting on Bridge To Practice from Session 1  What unit did you choose for this course?  Why did you choose it?  What have you already developed for this unit? (lesson plans, formative assessments, rubrics, etc.) 3

ACTIVITY #1 ALIGNING A UNIT’S CULMINATING TASK WITH THE CCLS 4

What do you consider to be the important components of a unit plan in math? 5

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Unit Outline Components Overarching Questions: The big inquiries of a unit. These questions reach across and connect content and skill in the unit. Each experience allows students to deepen responses to the overarching questions. Primary CC Content Standards addressed in the Unit: What content, skills, and performances will be the major focus for this unit? Primary CC Mathematical Practices addressed in the Unit: Which Practices lend themselves to deepening conceptual understanding and fluency in math for this unit? 7

Unit Outline Components  Sequenced Activities: Activities cohere around the same content/performances as assessment task. Activities a) allow for CCLS-based work that parallels assessments in smaller chunks; b) are sequenced to prompt retrospective work; and c) provide a model of the kind of writing, skills, and performances required by the culminating assessment.  Instructional Tasks: Provide opportunities for students to a) learn/experience/build their content knowledge b) develop skills embedded in the Math Practices; c) are sequenced to move learners from basic procedural knowledge to higher level thinking about math; and d) mirror the assessment tasks in order to provide support for students to learn the content, habits, and skills they need to successfully and independently complete the unit's culminating task. 8

Unit Outline Components  Embedded Assessments: List the ways in which you will assess student learning during and after the instructional task.  Culminating Assessment Task: How can the content, skills, and performances in the unit be combined to elicit student responses that demonstrate a deep understanding of the unit standards? 9

Performance Tasks  What comes to mind when you hear the term “performance task?” 10

Step 1. Work the task thoroughly. Step 2. Compare your work with the answer key/rubric and other instructional support materials. Step 3. Identify the content and performances required. Step 4. Match the content and performances to the CCLS. Step 5. Rate the alignment of content. Step 6. Rate the alignment of performances. Step 7. Additional considerations. 11 SEVEN STEPS FOR ALIGNING MATHEMATICS TASKS TO THE CCLS

Step 5: CCLS Mathematics Content Standards: Content vs. Performance 12 CCLSContentPerformance 4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

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DEBRIEF CAROL’S NUMBERS What was your solution? What content was required to solve the task? What performances were required to solve the task? 17

DEBRIEF CAROL’S NUMBERS: SOLUTION AND CONTENT AND PERFORMANCES Solution: 1) 742 2) 247; Put the smallest number on the left, the next smallest number in the middle and the largest number last. 3-5) See number line and discuss. Content: Place value, three-digit numbers, number line Performances: Represent, compare, read and write, understand 18

DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH MATH PRACTICES  MP.1 Make sense of problems and persevere in solving them.  MP.3 Construct viable arguments and critique the reasoning of others.  MP.6 Attend to precision. 19

DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH THE CCLS CONTENT STANDARDS  2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.  2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.  2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.  2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. 20

DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH MATH PRACTICES  MP.1 Make sense of problems and persevere in solving them. (Rating – Performance: 3)  MP.3 Construct viable arguments and critique the reasoning of others. (Rating – Performance: 2)  MP.6 Attend to precision. (Rating – Performance: 3) 21

DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH THE CCLS CONTENT STANDARDS  2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. (Rating – Content: 3, Performance: 3)  2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. (Rating – Content: 3, Performance: 2)  2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. (Rating – Content: 3, Performance: 2)  2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. (Rating – Content: 3, Performance: 2) 22

INTRODUCTION TO DEPTH OF KNOWLEDGE 23

How does DOK fit into the Citywide Instructional Expectations for 2012-13?  A key component of the Citywide Instructional Expectations is strengthening student work by examining and refining curriculum, assessment and instruction.  Rigorous questions, tasks and assessment are essential to driving the higher-order thinking and skills students need to become college and career-ready  Depth of Knowledge is a framework that helps educators examine the level of rigor to ensure students are being pushed to meet the demands of the new standards. 24

Surfacing Definitions of Rigor  What is your current definition of rigor?  Please record it in your note-taking guide 25

DOK Video Guiding Questions  http://schools.nyc.gov/Academics/CommonCoreLibrar y/ProfessionalLearning/DOK/default.htm http://schools.nyc.gov/Academics/CommonCoreLibrar y/ProfessionalLearning/DOK/default.htm  After watching the video, think about rigor in terms of your own practice. >What sounded familiar to you? >What sounded new? 26

27 19562001 Knowledge - Define, duplicate, label, list, name, order, recognize, relate, recall Remember - Retrieve knowledge from long- term memory, recognize, recall, locate, identify Comprehension - Classify, describe, discuss, explain, express, identify, indicate, locate, recognize, report, review, select, translate Understand - Construct meaning, clarify, paraphrase, represent, translate, illustrate, give examples, classify, categorize, summarize, generalize, predict… Application - Apply, choose, demonstrate, dramatize, employ, illustrate, interpret, practice, write Apply - Carry out or use a procedure in a given situation; carry out or use /apply to an unfamiliar task Analysis - Analyze, appraise, explain calculate, categorize, compare, criticize, discriminate, examine Analyze - Break into constituent parts, determine how parts relate Synthesis - Rearrange, assemble, collect, compose, create, design, develop, formulate, manage, write Evaluate - Make judgments based on criteria, check, detect inconsistencies/fallacies, critique Evaluation - Appraise, argue, assess, choose, compare, defend, estimate, explain, judge, predict, rate, core, select, support, value Create - Put elements together to form a coherent whole, reorganize elements into new patterns/ structures Bloom – 1956 to 2001

Webb’s Depth of Knowledge Levels  DOK 1 - Recall & Reproduction - Recall a fact, term, principle, or concept, perform a routine procedure  DOK 2 - Basic Application of Skills/Concepts - Apply information or conceptual knowledge to routine situations or problems, select appropriate procedures for a task, complete two or more steps with decision points along the way, organize/display data, interpret/use simple graphs  DOK 3 - Strategic Thinking - Use reasoning to develop a plan or sequence of steps to approach a problem, make a claim and justify it using evidence, solve abstract, complex, or non-routine problems with more than one possible solution or solution path  DOK 4 - Extended Thinking – Investigate multi-faceted real-world problems, use multiple sources or an interdisciplinary approach to create new understanding of a topic 28

Curriculum DOK 1-4 DOK 1-4 DOK 1-4 SeptemberJune Unit of Study Weaving DOK into our current units of study and curriculum maps can help schools transition to the CCLS… College & Career Trajectory

ACTIVITY #2 USING DEPTH OF KNOWLEDGE TO ASSESS THE RIGOR OF A MATHEMATICS TASK 30

Assessing Rigor Using DOK 1.Work the task 2.Analyze the rigor of the task using the Cognitive Rigor Matrix 3.Suggest changes to modify the rigor of the task, when appropriate 4. Consider instructional supports that would need to be included in the unit that builds towards this task 31

Reflection  When can you use DOK throughout the school year?  How can this process apply to other aspects of curriculum, assessment, and instruction in addition to culminating tasks?  What further support do you need in using DOK to assess and increase rigor in your classroom? 32