Alum Rock Union Elementary School District CCSS-Mathematics Grade 4 February 2014

WELCOME AND INTRODUCTION

Outcomes Understand the background, rationale and organization of the Common Core State Standards-Mathematics (CCSS-M). Increase understanding of number talks and how they can be implemented in the third grade classroom. Identify how the new mathematics assessment will measure student understanding

Outcomes Become familiar with the CCSS-M instructional shifts Engage in Problem of the Month and learn strategies to support all students accessing rich tasks

Agenda Welcome and Introduction CCSS Overview CCSS Standards for Mathematical Practice CCSS Mathematics Content Standards Assessment Instructional Shifts in Mathematics Mathematics Discourse Closing and Feedback

Norms “No one is as smart as all of us are together.” Respect Individual think time Everyone participates Everyone helps Leave no one behind Take responsibility Be positive Technology courtesy (cell phones and computers)

CCSS-M OVERVIEW Overview and Structure of the CCSS Mathematics Content Standards

States that have Adopted the Common Core State Standards

Why the Common Core State Standards? Ensure that our students are:  Meeting college and work expectations;  Provided a vision of what it means to be an academically literate person in the twenty-first century;  Prepared to succeed in our global economy and society; and  Provided with rigorous content and applications of higher knowledge through higher order thinking skills.

Benefits of the CCSS  Internationally benchmarked  Evidence and research-based  Expectations clear to students, parents, teachers, and the general public  Costs to the state reduced  Consistent expectations for all— not dependent on a zip code

Common Core State Standards San Jose Common Core Tech

STANDARDS FOR MATHEMATICAL PRACTICE Common Core State Standards

Underlying Frameworks National Council of Teachers of Mathematics 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Strands of Mathematical Proficiency Strategic Competence Adaptive Reasoning Conceptual Understanding Productive Disposition NRC (2001). Adding It Up. Washington, D.C.: National Academies Press. Procedural Fluency Underlying Frameworks

Standards for 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.

CCSS Standards for Mathematical Practice Please examine the first three words of each of the 8 mathematical practices…what do you notice? Mathematically Proficient Students…

CCSS Standards for [Student] Mathematical Practice What are the verbs that illustrate the student actions for your assigned mathematical practice? Circle, highlight or underline them for your assigned practice. Please select a spokesperson.

Notetaking Guide Standards for Mathematical Practice

The Standards for [Student] Mathematical Practice SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Notice and pay attention to…

Rigor of the Standards Revised Bloom’s Taxonomy

Standards for Mathematical Practice  Each group will be assigned to read one of the Standards for Mathematical Practice.  What will your classroom look like/sound like as this standards is being implemented  Use your note taking guide to capture shared ideas. Jigsaw

Table Talk To what extent is your school promoting students’ proficiency in the Standards for Mathematical Practice you just examined?

CCSS Mathematical Practices OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Website: Inside Mathematics For classroom videos of the CCSS Standards for Mathematical Practice in action.

CCSS-M CONTENT STANDARDS

Common Core State Standards for CA DOMAINS California Standards Grades K-7 STRANDS K-5 Counting and Cardinality (K only) Operations and Algebraic Thinking Number and Operations in Base 10 Number and Operations-Fractions Measurement and Data Geometry 6-8 Ratio and Proportional Relationships (grade 6-7) The Number System Expressions and Equations Functions (Grade 8) Geometry Statistics and probability Number Sense Algebra and Functions Measurement and Geometry Statistics, Data Analysis and Probability Mathematical Reasoning California Comparison 26

CCSS Domains and Conceptual Categories K HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

Overview Page- Fourth Grade

How to Read the Grade Level Standards Domain

How to Read the Grade Level Standards Cluster Heading

How to Read the Grade Level Standards Cluster

How to Read the Grade Level Standards Abbreviations

Reviewing CCSS-M Structure Domain Cluster Heading Cluster Standards Mark and label your standards. CCSS First Grade Overview

CCSS Content Standards Overview Review your grade level content. What are the big ideas for your grade level? – What new content will you be teaching this year? – What content is no longer part of your grade level? – What content are you still teaching? Use the content analysis form to record your ideas. CCSS First Grade Overview

ASSESSMENT

Assessment: What We Know Assessments will be given to students as a field test in Students will receive scores in California is a governing state in the SMARTER Balanced Assessment Consortium. Assessments will include: – Computer Adaptive Assessments (interim & summative) – Selected Response – Performance Assessments (interim & summative) Technology Enhanced Constructed Response Performance Task Extended Performance Event

SBAC’s Four Major Claims #1 Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. #2 Students can frame and solve a range of complex problems in pure and applied mathematics #3 Students can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. #4 Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

Smarter Balanced: New Website

Traditional Selected Response CST Example A company has 6 big trucks. Each truck has 18 wheels. How many wheels is this in all? A 24 B 96 C 108 D California Standards Test Released Test Question pg. 14, #34

Non-Traditional Selected Response

Non-Traditional Selected Response Rubric

Performance Task

Performance Task Rubric

The main point in mathematics teaching is to develop the tactics of problem solving. George Polya

CCSS-M Assessments (Claim 4) View the Robot Maker Task. What skills will students need in order to complete the task?

DEPTH OF KNOWLEDGE (DOK) Common Core State Standards

DOK is NOT... a taxonomy (Bloom’s) the same as difficulty about using “verbs”

Verbs are not always used appropriately... Words like explain or analyze have to be considered in context. “Explain to me where you live” does not raise the DOK of a simple rote response. Even if the student has to use addresses or landmarks, the student is doing nothing more than recalling and reciting.

DOK is about what follows the verb... What comes after the verb is more important than the verb itself. “Analyze this sentence to decide if the commas have been used correctly” does not meet the criteria for high cognitive processing.” The student who has been taught the rule for using commas is merely using the rule.

Same Verb— Three Different DOK Levels DOK 1- Describe three characteristics of metamorphic rocks. (Requires simple recall) DOK 2- Describe the difference between metamorphic and igneous rocks. (Requires cognitive processing to determine the differences in the two rock types) DOK 3- Describe a model that you might use to represent the relationships that exist within the rock cycle. (Requires deep understanding of rock cycle and a determination of how best to represent it)

Level 1: Recalling and Recognizing Level 2: Using Procedures/Basic Application Level 3: Explaining and Concluding/ Strategic Thinking and Reasoning Level 4: Making Connections, Extending and Justifying/Creating Depth of Knowledge (DOK)

Name the capital of California.

Name the capitals of three other states.

Compare and contrast two state capitals from your list.

Evaluate the location of Sacramento as your state capital.

Theorize possible impacts of moving your state capital to San Francisco.

Metacognition What was going on inside your brain as you were trying to answer each of these questions? What was the difference in your thinking as the questions progressed?

Sentence Frames Added Support If Needed Why do you think… What would happen if… How does _____ affect _______? How is it possible that… What do you think ___________ means? What do you think ________ represents? Does ______ give you any ideas? Region 5 Afterschool Providers

Rigor of the Standards Revised Bloom’s Taxonomy and Webb’s Depth of Knowledge (DOK)

Grade 3 Mathematics Sample ER Item Claim 3 Sample Item ID:MAT.03.ER.3.000NF.B.229 Grade:03 Primary Claim:Claim 3: Communicating Reasoning Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Secondary Claim(s):Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Primary Content Domain:Number and Operations – Fractions Secondary Content Domain(s):Geometry Assessments Target(s):3 B: Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. 1 F: Develop understandings of fractions as numbers. 1 K. Reason with shapes and their attributes. Standard(s):3.NF.3, 3.G.2 Mathematical practice(s):3,6 DOK:3 Item Type:ER Score Points:2 Difficulty:M Key:See Sample Top-Score Response. Stimulus/Source: Target-Specific Attributes (e.g./ Accessibility Issues): Notes:Part of a PT Set

TOM TORLAKSON State Superintendent of Public Instruction Common Core Big Ideas Depth of Knowledge (DOKs) 63 MathematicsELA/Literacy DOK3DOK4DOK3DOK4 Current Assessments <2% 0% 20% 2% New SBAC Assessments 49% 21% 43% 25% Yuan & Le (2012); Herman & Linn (2013) from Linda Darling-Hammond, Assembly Hearing,

INSTRUCTIONAL SHIFTS IN MATHEMATICS Common Core State Standards

Focus Shift 1: Focus Coherence Shift 2: Coherence Rigor Shift 3: Fluency Shift 4: Deep Understanding Shift 5: Application Shift 6: Dual Intensity Instructional Shifts Combined

Shift #1: Focus Strongly where the Standards Focus Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra; linear functions Key Areas of Focus in Mathematics

Focus Using a highlighter, please highlight the standards that are in direct alignment with your grade level’s focus.

Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

Coherence: Think Across Grades K HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

The CCSSM require a balance of:  Procedural skill and fluency  Solid conceptual/deep understanding  Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources. Rigor

Fluency (Shift 3) The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts Rigor

Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within NBT.4Add/subtract within 1,000, NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

Fluency Please underline the standards that are in direct alignment with your grade level’s fluency standards.

Deep Understanding (Shift 4) Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application) Rigor

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Application (Shift 5) Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. Rigor

Shift 6: Dual Intensity Students are practicing and understanding. – Both occur with intensity – Fluency Practice – Extended application of math concepts – Driven by specific mathematical content; varies throughout the year. Rigor

It Starts With Focus The current U.S. curriculum is "a mile wide and an inch deep." Focus is necessary in order to achieve the rigor set forth in the standards. Remember Hong Kong example: more in-depth mastery of a smaller set of things pays off.

MATHEMATICS DISCOURSE

Norms “No one is as smart as all of us are together.” Respect Individual think time Everyone participates Everyone helps Leave no one behind Be positive

Hand Signals Solution Strategy Question Comment I agree Fractions

Hand Signals Agree Fractions Solution Strategy Question Comment

Number Talks and Time Number Talks (about 10 minutes) Mini-lesson(10 to 20 minutes) Lesson (more than 20 minutes)

Socio-mathematical Norms Errors are gifts, they promote discussion. Share a second sentence to connect your thoughts. The answer is important, but it is not the math. Build on the thinking of others. Ask questions until ideas make sense. Think with language and use language to think.

Lenses to Consider During Professional Development Sessions Learner Lens Teacher Lens

Math Talk Examples Dot Patterns Mental Math Number Strings Dilemmas True/False Statements What’s My Rule?

Dot Talk How many dots do you see? How did you see them?

Dot Talk I saw ______dots. I grouped the dots…. I also saw ___ dots, but I grouped the dots differently. I …

Dot Talk

Mental Math 70-34

Number Talk Classroom Example Third grade students solving the same problem.

Number String (Mental Math) 2 x 2 3 x 2 4 x 2

True/False 3 x 7 = 7 x 3 True or False? Why?

True/False 9 x 4= 6 x 6 True or False? Why?

Dilemma Explain the mathematical reasoning that both Kirsten & David used to solve for the unknown above. Kirsten says that 14 is the missing factor in 14 x 1 = x 2 David says that 7 is the missing factor in 14 x 1= x 2

What’s My Rule? InOut

What’s My Rule? InputOutput

What’s My Rule? XY

Standards for Mathematical Practice 1. Make sense of problems & persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments & 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.

Number Talks Online Resources for K-2 Resources for 3-5 Resources

CLOSING

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