+Implementing Common Core

State Standards in the

Classroom

High SchoolDay 1

+Overall Outcomes

Recognize the interconnectedness of the Standards for Mathematical Practice and content standards in developing student understanding and reasoning.

Illuminate practices that establish a culture where mistakes are a springboard for learning, risk-taking is the norm, and there is a belief that all students can learn.

+Effective Classrooms

+What research says about effective classrooms

The activity centers on mathematical under-standing, invention, and sense-making by all students.

The culture is one in which inquiry, wrong answers, personal challenge, collaboration, and disequilibrium provide opportunities for mathematics learning by all students.

The tasks in which students engage are mathematically worthwhile for all students.

A teacher’s deep knowledge of the mathematics content she/he teaches and the trajectory of that content enables the teacher to support important, long-lasting student understanding

+Effective implies:

Students are engaged with important mathematics.

Lessons are very likely to enhance student understanding and to develop students’ capacity to do math successfully.

Students are engaged in ways of knowing and ways of working consistent with the nature of mathematicians ways of knowing and working.

+Outcomes Day 1:

Reflect on teaching practices that support the shifts (Focus, Coherence, & Rigor) in the Common Core State Standards for Mathematics.

Understand the four SBAC Assessment Claims for Mathematics.

Deepen understanding of the progression of learning and coherence around the CCSS-M Conceptual Category Functions

+Common Core State

Standards: Mathematics

+Why CCSS?

Greta’s Video Clip

+What We are Doing Doesn’t Work

Almost half of eighth-graders in Taiwan, Singapore and South Korea showed they could reach the “advanced” level in math, meaning they could relate fractions, decimals and percents to each other; understand algebra; and solve simple probability problems.

In the U.S., 7 percent met that standard.

Results from the 2011 TIMMS

+Theory of Practice for CCSS Implementation in WA

2-Prongs:

1. The What: Content Shifts (for students and educators) Belief that past standards implementation efforts have

provided a strong foundation on which to build for CCSS; HOWEVER there are shifts that need to be attended to in the content.

2. The How: System “Remodeling” Belief that successful CCSS implementation will not take

place top down or bottom up – it must be “both, and…” Belief that districts across the state have the conditions

and commitment present to engage wholly in this work. Professional learning systems are critical

+ WA CCSS Implementation Timeline

2010-11 2011-12 2012-13 2013-14 2014-15

Phase 1: CCSS Exploration

Phase 2: Build Awareness & Begin Building Statewide Capacity

Phase 3: Build State & District Capacity and Classroom Transitions

Phase 4: Statewide Application and Assessment

Ongoing: Statewide Coordination and Collaboration to Support Implementation

+Transition Plan for Washington State

 K-2 3-5 6-8 High School

 Year 1- 22012-2013

School districts that can, should consider adopting the CCSS for K-2 in total. K – Counting and Cardinality (CC); Operations and Algebraic Thinking (OA); Measurement and Data (MD) 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); Operations and Algebraic Thinking (OA) 4 – Number and Operations – Fractions (NF); Operations and Algebraic Thinking (OA)  5 – Number and Operations – Fractions (NF); Operations and Algebraic Thinking (OA) 

and remaining 2008 WA Standard

6 – Ratio and Proportion Relationships (RP); The Number System (NS); Expressions and Equations (EE)  7 – Ratio and Proportion Relationships (RP); The Number System (NS); Expressions and Equations (EE) 8 – Expressions and Equations (EE); The Number System (NS); Functions (F) and remaining 2008 WA Standards

Algebra 1- Unit 2: Linear and Exponential Relationships; Unit 1: Relationship Between Quantities and Reasoning with Equations and Unit 4: Expressions and Equations 

Geometry- Unit 1: Congruence, Proof and Constructions andUnit 4: Connecting Algebra and Geometry through Coordinates; Unit 2: Similarity, Proof, and Trigonometry andUnit 3:Extending to Three Dimensions and remaining 2008 WA Standards

+Focus, Coherence & Rigor

+The Three Shifts in MathematicsFocus: Strongly where the standards focus

Coherence: Think across grades and link to major topics within grades

Rigor: Require conceptual understanding, fluency, and application

+Focus on the Major Work of the Grade

Two levels of focus ~• What’s in/What’s out• The shape of the content

+Focus in International Comparisons

TIMSS and other international comparisons suggest that the U.S. curriculum is ‘a mile wide and an inch deep.’

“…On average, the U.S. curriculum omits only 17 percent of the TIMSS grade 4 topics compared with an average omission rate of 40 percent for the 11 comparison countries.

The United States covers all but 2 percent of the TIMSS topics through grade 8 compared with a 25 percent noncoverage rate in the other countries.

High-scoring Hong Kong’s curriculum omits 48 percent of the TIMSS items through grade 4, and 18 percent through grade 8.” – Ginsburg et al., 2005

ALGEBRA 1 The Real Number System (N-RN)

Use properties of rational and irrational numbers (3)

Quantities(N-Q) Reason quantitatively and use units to solve problems (1,

2, 3)

Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions (1, 2)

Write expressions in equivalent forms to solve problems (3)

Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials (1)

Understand the relationship between zeros and factors of polynomials (3)

Creating Equations (A-CED) Create equations that describe numbers or relationships (1, 2, 3, 4)

Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning

and explain the reasoning (1) Solve equations and inequalities in one variable (3, 4)

Solve systems of equations (5, 6) Represent and solve equations and inequalities

graphically (10, 11, 12)

Interpreting Functions (F-IF) Understand the concept of a function and use function notation (1, 2, 3)

Interpret functions that arise in applications in terms of the context (4, 5, 6)

+Engaging with the HS Content

How would you summarize the major work of HS?

What would you have expected to be a part of the major work that is not?

Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate, discrete topic.

+Coherence Across and Within GradesIt’s about math making sense.

The power and elegance of math comes out through carefully laid progressions and connections within grades.

+Coherence Think across grades, and link to major topics within gradesCarefully connect the learning within and

across grades so that students can build new understanding onto 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.

+How do students perceive mathematics?

• Doing mathematics means following the rules laid down by the teacher.

• Knowing mathematics means remembering and applying the correct rule when the teacher asks a question.

• Mathematical truth is determined when the answer is ratified by the teacher.

-Mathematical Education of Teachers report (2012)

+How do students perceive mathematics? Students who have understood the mathematics

they have studied will be able to solve any assigned problem in five minutes or less.

Ordinary students cannot expect to understand mathematics: they expect simply to memorize it and apply what they have learned mechanically and without understanding.

-Mathematical Education of Teachers report (2012)

+Looking For Coherence Within Grades Examples:

1st grade – 5th grade: Represent and Interpret Data 3rd grade & 5th grade: “Relate area (volume) to

multiplication and to addition.” 6th grade: Solve problems by graphing in all 4

quadrants. (1st year of rational numbers) 8th grade: “Understand the connections between

proportional relationships, lines and linear equations.”

HS: “Understand that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.”

+Coherence Within A Grade

Functions – Connections to Expressions, Equations, Modeling and Coordinates

Determining an output value for a particular input involves evaluating a an expression; finding inputs that yield a given output involves solving an equation. Questions about when two functions have the same value for the same input lead to equations, whose solutions can be visualized from the intersection of their graphs. Because functions describe relationship between quantities, they are frequently used in modeling. Sometimes functions are defined by a recursive process, which can be displayed effectively using a spreadsheet or other technology.

+Looking for Coherence Across Grades

Coherence is an important design element of the standards.

“The Standards are not so much built from topics as they are woven out of progressions.”

Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix

+Rigor: Illustrations of Conceptual Understanding, Fluency, and Application

Here rigor does not mean “difficult problems.”

It’s a balance of three fundamental components that result in deep mathematical understanding.

There must be variety in what students are asked to produce.

+Some Old Ways of Doing Business • Lack of rigor

Reliance on rote learning at expense of concepts

Lack of or excessive use of repetitious practice

Severe restriction to stereotyped problems lending themselves to mnemonics or tricks

Lack of quality applied problems and real-world contexts

Lack of variety in what students produce

E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.

+A.SEE Interpret the structure of expressions.

Suppose P and Q give the sizes of two different animal populations, where Q>P.

In (a)–(d), say which of the given pair of expressions is larger. Briefly explain your reasoning in terms of the two populations.

28

Some New Ways of Doing Business

+Instructional order leads to concept development which leads to flexible thinking about models

Conceptual and Procedural Understanding

+Frequently Asked Questions

How can we assess fluency other than giving a timed test?

Is it really possible to assess conceptual understanding? What does it look like?

Are the Common Core State Standards for Math all about application and meaningful tasks?

+Standards for Mathematical Practice and Depth of Knowledge

+Lets’s Do Some Math!

Figure Height

Write an equation that solves for the height, h, in terms of b. Show all work necessary to justify your answer.

+Whole group discussion

Share solutions

Identify domain(s) and cluster(s)

+Standards for Mathematical Practices (SMP)

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.

+Standards for Mathematical Practices (SMP)What Standards for Mathematical Practice (SMP) could be promoted with the Figure Height Task?

+Cognitive Rigor and Depth of Knowledge (DOK) The level of complexity of the cognitive demand.

Level 1: Recall and Reproduction Requires eliciting information such as a fact, definition, term,

or a simple procedure, as well as performing a simple algorithm or applying a formula.

Level 2: Basic Skills and Concepts Requires the engagement of some mental processing beyond

a recall of information. Level 3: Strategic Thinking and Reasoning

Requires reasoning, planning, using evidence, and explanations of thinking.

Level 4: Extended Thinking Requires complex reasoning, planning, developing, and

thinking most likely over an extended period of time.

+

+Depth of Knowledge

What is the depth of knowledge (DOK) of the Figure Height task?

+DOK Distribution on SBAC

DOK 1

DOK 2 DOK 3

DOK 4

Grade 4 25% 40% 26% 9%

Grade 8 18% 43% 27% 12%

High School

27% 41% 23% 9%

+BREAK TIME!!!

15 minutes….Go

+Smarter Balanced Assessment Consortium

aka ….SBAC

+

Note: 10th grade exams measure high school proficiency with passage required for graduation; 11th grade exams measure career and college-ready standards.* 10th grade math exams could be separate Algebra and Geometry EOC exams.

Grade

Subject Tested

2012–13 and 2013–14

Measure current Reading, Writing, Algebra, Geometry ,

and Biology Standards

2014–15 and BeyondMeasure Common

Core State Standards and current

Biology Standards

10 Reading HSPE  

10 Writing HSPE  

10 E/LA   SBAC

10 Algebra EOC  

10 Geometry EOC  

10 Math   SBAC

10 Biology EOC EOC

11 E/LA   SBAC

11 Math   SBAC

Using SBAC for High School Graduation Tests – Policy Questions Abound…

*

+A Balanced Assessment System

43

School Year Last 12 weeks of the year*

DIGITAL CLEARINGHOUSE of formative tools, processes and exemplars; released items and tasks; model curriculum units; educator training; professional development tools and resources; scorer training modules; and teacher collaboration tools.

English Language Arts/Literacy and Mathematics, Grades 3-8 and High School

Computer Adaptive

Assessment andPerformance

Tasks

Computer Adaptive

Assessment andPerformance

TasksScope, sequence, number and timing of interim assessments locally determined

*Time windows may be adjusted based on results from the research agenda and final implementation decisions.

PERFORMANCE TASKS

•ELA/Literacy•Mathematics

Re-take option

COMPUTER ADAPTIVE

TESTS

•ELA/Literacy•Mathematics

Optional Interim

Assessment

Optional Interim

Assessment

+Time and formatSummative:

For each content area - ELA & Math Computer Adaptive Testing (CAT)

Selected response (SR), Constructed Response (open-ended—CR, ECR), Technology enhanced (e.g., drag and drop, video clips, limited web-interface)

Performance Tasks (like our CBAs) (PT) 1 per content area in grades 3-8 Up to 3 per content area in High School

44

+

+

+Section 4

THE CLAIMS

+ SBAC Assessment Claims for Mathematics

Overall Claim (Gr. 3-8)

Overall Claim (High School)Claim 1

Concepts and Procedures

Claim 2

Problem SolvingClaim 3

Communicating Reasoning

Claim 4

Modeling and Data Analysis

+What is a claim? “Claims” are the broad statements of the

assessment system’s learning outcomes, each of which requires evidence that articulates the types of data/observations that will support interpretations of competence towards achievement of the claims.

“assessment targets” describe the expectations of what will be assessed by the items and tasks within each claim.

+Claim 1Concepts and Procedures

Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

Grade Level

Number of Assessment

Targets

3 11

4 12

5 11

6 10

7 9

8 10

11 17

Assessment Targets =

Clusters

+Claim 1 Targets

Number and Quantity (9-12.N) Target A: Extend the properties of exponents to rational exponents. (DOK 1, 2) [a/s] Target B: Use properties of rational and irrational numbers. (DOK 1, 2) [a/s] Target C: Reason quantitatively and use units to solve problems. (DOK 1, 2) [m] Algebra (9-12.A) Target D: Interpret the structure of expressions. (DOK 1) [m] Target E: Write expressions in equivalent forms to solve problems. (DOK 1, 2) [m] Target F: Perform arithmetic operations on polynomials. (DOK 1) [a/s] Target G: Create equations that describe numbers or relationships. (DOK 1, 2) [a/s] Target H: Understand solving equations as a process of reasoning and explain the reasoning. (DOK 1, 2) [m] Target I: Solve equations and inequalities in one variable. (DOK 1, 2) [m] Target J: Represent and solve equations and inequalities graphically. (DOK 1, 2) [m] Functions (9-12.F) Target K: Understand the concept of a function and use function notation. (DOK 1) [m] Target L: Interpret functions that arise in applications in terms of a context. (DOK 1, 2) [m] Target M: Analyze functions using different representations. (DOK 1, 2, 3) [m] Target N: Build a function that models a relationship between two quantities. (DOK 1, 2) [m] Geometry (9-12.G) Target O: Prove geometric theorems. (DOK 2) [m] . Statistics and Probability (9-12.SP) Target P: Summarize, represent and interpret data on a single count or measurement variable. (DOK 2) [m]

+

+

+Claims Task Analysis Jigsaw3 Rounds: Claims

At your current table: Count off by 3 –move to numbered tables for “focus group”

Each Round, we will focus on a Claim. Focus groups will rotate their focus: SMP, CCSS or DOKDo tasks togetherAnalyze tasks focusing on assigned aspect for that roundBriefly Share after each round

Return to “home” table at end of all 3 rounds to more fully share ideas from your groups and complete Task Analysis Form

Please Count off and Move: 1’s, 2’s, 3’s

+Task Analysis Protocol Sheet

+Task Analysis Round 1 (Claim 1)Do “New Computers” task on claims

handout. Discuss and justify the SBAC details listed: 1’s: What content domain/cluster does the task

address? 2’s: What is the depth of knowledge (DOK) of the

task? 3’s: What Standards for Mathematical Practices (SMP)

can it promote?

Do “Rewrite Functions” task. Determine and justify the same SBAC aspect your group focused on for “New Computers”

+New Computers

1’s: Domain/Cluster 2’s: DOK 3’s: SMP

+Rewrite Functions

1’s: Domain/Cluster 2’s: DOK 3’s: SMP

+Share & justify! 1’s: Domain/Cluster

2’s: DOK3’s: SMP

+Claim 2 – Problem Solving

A. Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace

B. Select and use tools strategically

C. Interpret results in the context of the situation

D. Identify important quantities in a practical situation and map their relationships.

Claim 2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

+

+Claim 2 Item SpecsTask Types

+Task Analysis Round 2Review “Figure Height” task on claims

handout. Discuss and justify (also a review from earlier!) the SBAC details listed: 1’s: What is the depth of knowledge (DOK) of the task? 2’s: What Standards for Mathematical Practices (SMP)

can it promote? 3’s: What content domain/cluster does the task

address?

Do “Graph Inverse” task. Determine and justify the same SBAC aspect your group focused on for “Figure Height”

+Figure Height

1’s: DOK 2’s: SMP 3’s: Domain/Cluster

Write an equation that solves for the height, h, in terms of b. Show all work necessary to justify your answer.

+Graph Inverse

1’s: DOK2’s: SMP3’s: Domain/Cluster

+Share & justify! 1’s: DOK

2’s: SMP3’s: Domain/Cluster

+Claim 3 – Communicating Reason

A. Test propositions or conjectures with specific examples.

B. Construct, autonomously, chains of reasoning that justify or refute propositions or conjectures.

C. State logical assumptions being used.

D. Use the technique of breaking an argument into cases.

E. Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in the argument—explain what it is.

F. Base arguments on concrete referents such as objects, drawings, diagrams, and actions.

G. Determine conditions under which an argument does and does not apply.

Claim 3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

+

+Task Analysis Round 3Review “Parking Lot” task on claims

handout. Discuss and justify the SBAC details listed: 1’s: What Standards for Mathematical Practices (SMP)

can it promote? 2’s: What content domain/cluster does the task

address? 3’s : What is the depth of knowledge (DOK) of the task?

Review “Decibels” task. Determine and justify the same SBAC aspect your group focused on for “Figure Height”

+ 1’s: SMP2’s: Domain/Cluster3’s:DOK

+DECIBELS The noise level at a music concert must be no more than 80

decibels (dB) at the edge of the property on which the concert is held.

Melissa uses a decibel meter to test whether the noise level at the edge of the property is no more than 80 dB.

Melissa is standing 10 feet away from the speakers and the noise level is 100 dB.

The edge of the property is 70 feet away from the speakers.

Every time the distance between the speakers and Melissa doubles, the noise level decreases by about 6 dB.

Rafael claims that the noise level at the edge of the property is no more than 80 dB since the edge of the property is over 4 times the distance from where Melissa is standing. Explain whether Rafael is or is not correct.

1’s: SMP2’s: Domain/Cluster3’s:DOK

+Share & justify! 1’s: SMP

2’s: Domain/Cluster3’s:DOK

+Return to Original groups

Jigsaw debrief

+

+ Functions Progression of Learning:

How does coherence manifest itself in the standards?

+Common Core Format

K-8

Grade

Domain

Cluster

Standards

(There are no preK Common Core Standards)

High School

Conceptual Category

Domain

Cluster

Standards

+Conceptual Category: Functions

(Function) Domains: F-IF: Interpreting Functions

(3 clusters under Interpreting Functions domain)

F-BF: Building Functions (2 clusters) F-LE: Linear, Quadratic, and Exponential

Models* (2 clusters) F-TF: Trigonometric Functions (3 clusters)

+FunctionsAssign one Domain to each table group1. Interpret Functions 2. Build Functions or 3. Linear, Quadratic,& Exp

Models

Think: Individually read the Conceptual Category

- Functions overview from CCSS

In Pairs: Brainstorm: What do students need to

know for each of the clusters in your assigned Functions Domain?

Share: In table groups, share your lists with each other & create a “group list”

+Functions: Grade 8

What do students learn about functions in grade 8?

Read Functions Progression, Grade 8 Section

Compare with your group list Notate any items on your group list that are

addressed in grade 8

+Grade 8 Functions Clusters

Major: Define, evaluate and compare functions

Supporting: Use functions to model relationships between quantities

+Functions: ConnectionsWhat connections are there between the Functions domains/clusters and the other high school conceptual categories?

Read the CCSS document for assigned function domain Find & enhance details for aligned items on your group list

Look for connections to other high school conceptual categories in the CCSS document—where are the other items from your list? Notate on your list the cluster(s)/standard(s) where these

related items are located in the CCSS

+Functions Domain Poster & Presentation

Meet with other tables working on the same domain.

Poster: Create a poster to represent the information you gathered for your Functions Domain, making sure to include: Key cluster and standard language in the domain Progression of learning from 8th grade Connections to other high school conceptual

categories

Presentation: Select one person to talk about each of the above bullets for @ 2 minutes each

+BREAK TIME!!!

10 minutes….Go

+Instructional Shifts to Develop the Standards for Mathematical Practices

+Mathematical Practices1. 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.

+Standards of Student Practice in Mathematics Proficiency Matrix

+Digging Deeper: Constructing Viable Arguments & Critiquing Reasoning of Others and Modeling with MathematicsIn groups of 4

Each person reads one side of the Mathematical Practices (#3 & #4) handouts.

Highlight three new ideas found in your assigned reading

Share in your group and use the ideas to “enhance” the Proficiency matrix using the blank matrix

+Planning for Instructional Action

+Implications for your students

Consider your lessons over the next few weeks

Develop an instructional action intended to improve your instructional practice for critiquing the reasoning of others.

Use think-pair-share as one of your strategies.

+Homework

Use one of the 2 given tasks as a learning activity in at least 1 class before next session.

Complete the Rich Task Classroom Implementation Preplanning worksheet before doing the lesson – be sure to include using Think-Pair-Share

Capture evidence of several students development of SMP 3&4 during the lesson using the Proficiency Matrix

Reflect on instructional strategies you implemented during lesson to support MSP 3&4 (including those on preplanning worksheet)

Select 3 samples of student work to share at next class: 1 high, 1 low

Bring back all handouts to next session

+Top Resources for Math Educators Inside Mathematics Video excerpts of mathematics lessons correlated with the

practice standards, resources on content standards alignment, and videos of exemplary lessons in both elementary and secondary settings.

Illustrative Mathematics Guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards.

Progressions Documents for the Common Core Math Standards Narrative documents describing the progression of a topic across a number of grade levels.

Publishers Criteria Provides criteria for aligned materials to CCSS. Based on the two major evidence-based design principles of the CCSSM, focus and coherence, the document intends to guide the work of publishers and curriculum developers, as well as states and school districts, as they design, evaluate, and select materials or revise existing materials.

Achieve The Core Guidance and templates on how to begin implementing the shifts, assembled by the nonprofit Student Achievement Partners.

+Reflections

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+Wrap up Activity

Feedback

Thank You!

See you next session…………..

+

Day 2

+Outcomes Day 2 & 3:

Analyze student work with the Standards for Mathematical Practice and content standards.

Analyze, adapt, and implement a task with the integrity of the Common Core State Standards.

+Welcome Back Activity

Success, challenge, barrier, breakthrough

Reflect on your experience using one of the assigned tasks in your classroom.

Use separate post-it notes to capture your successes, challenges, barriers, and/or breakthroughs

Post on appropriate poster

Read post-it notes on all posters and select one that resonates with you.

Quick share of selected post-its.

+

Homework Review

+Collaboration Protocol-Looking at Student Work (55 minutes)

Select one group member to be today’s facilitator to help move the group through the steps of the protocol.

Teachers bring student work samples with student names removed.

1. Individual review of student work samples (10 min)

• All participants observe or read student work samples in silence, making brief notes on the form “Looking at Student Work”

2. Sharing observations (15 min)

The facilitator asks the group

• What do students appear to understand based on evidence?

• Which mathematical practices are evident in their work?

• Each person takes a turn sharing their observations about student work without making interpretations, evaluations of the quality of the work, or statements of personal reference.

3. Discuss inferences -student understanding (15 min)

• Participants, drawing on their observation of the student work, make suggestions about the problems or issues of student’s content misunderstandings or use of the mathematical practices.

Adapted from: Steps in the Collaborative Assessment Conference developed by

Steve Seidel and Project Zero Colleagues

4. Discussing implications-teaching & learning (10 min)

• The facilitator invites all participants to share any thoughts they have about their own teaching, students learning, or ways to support the students in the future.

• How might this task be adapted to further elicit student’s use of Standards for Mathematical Practice or mathematical content.

5. Debrief collaborative process (5 min)

• The group reflects together on their experiences using this protocol.

+Homework Strategy Sharing

How did using the Proficiency matrix work? Are there changes you’d like to make?

How did your students respond to Think-Pair-Share?

What other strategies did you try out to improve your instructional practice so that student’s had the opportunity to critiquing the reasoning of others?

Say It, Know It Structures handout – choose 1 to try

+BREAK TIME!!!

15 minutes….Go

+

Rich Tasks

What makes a rich task? 1. Is the task interesting to students?

2. Does the task involve meaningful mathematics?

3. Does the task provide an opportunity for students to apply and extend mathematics?

4. Is the task challenging to all students?

5. Does the task support the use of multiple strategies and entry points?

6. Will students’ conversation and collaboration about the task reveal information about students’ mathematics understanding?

Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al

+Environment for Rich Tasks

Learners are not passive recipients of mathematical knowledge.

Learners are active participants in creating understanding and challenge and reflect on their own and others understandings.

Instructors provide support and assistance through questioning and supports as needed.

+Is this a rich task?

In (a)–(e), determine whether the quantity is changing in a linear or exponential fashion. Be prepared to justify your answer.a. A savings account, which earns no interest, receives a deposit of $723 per month.b. The value of a machine depreciates by 17% per year.c. Every week, 9/10 of a radioactive substance remains from the beginning of the week.d. A liter of water evaporates from a swimming pool every day.e. Every 124 minutes, ½ of a drug dosage remains in the body.

Is this a rich task?

+

SBAC Claim 4

+Claim 4 – Modeling and Data Analysis

A. Apply mathematics to solve problems arising in everyday life, society, and the workplace.

B. Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem.

C. State logical assumptions being used.D. Interpret results in the context of a situation.E. Analyze the adequacy of and make improvement to an existing

model or develop a mathematical model of a real phenomenon.

F. Identify important quantities in a practical situation and map their relationships.

G. Identify, analyze, and synthesize relevant external resources to pose or solve problems.

Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

+

+Task Analysis

What content cluster is addressed in this task?

What is the depth of knowledge of this task?

What mathematical practices does it promote?

Is this a rich task?

+Planning for Instructional Action

+Deepen conceptual understanding using tasks found in your Current Materials

Change the tasks

Use richer tasks provided in your instructional materials (usually found at end of lesson or in “extras” with book)

Adjust existing tasks – raise DOK level

Change how you implement the task

Refer to Standards for Mathematical Practices Compilations for strategies

Think, Pair, Share strategies

Ask good questions: teacher to student, student to teacher, student to student

+DOK 1 Task adjusted to DOK 2 Which statement is true

about the relation shown below?

[1] It is a function because there exists one y-coordinate for each x-coordinate.[2] It is a function because there exists one x-coordinate for each y-coordinate.[3] It is not a function because there are multiple x-values for a given y-value.[4] It is not a function because there are multiple y-values for a given x-value.

Which statements are true about the relation shown below?

[1] It is a function because there exists one y-coordinate for each x-coordinate.[2] It is a function because there exists one x-coordinate for each y-coordinate.

[3] It is a function because it passes the vertical line test.[4] It is not a function.

+Change this DOK 1 task to

DOK 2 or 3

What type of function is shown by the graph at the right?

[1]  linear[2]  exponential[3]  quadratic[4]  absolute value 

+Planning to apply learning

Review upcoming lessons for mathematical content

Find or create or adapt a rich task to use with one of these lessons.

Develop an instructional action intended to improve your instructional practice for critiquing the reasoning of others.

+ Homework Complete the Rich Task Classroom Implementation

Preplanning worksheet before doing the lesson – include your new Think-Pair-Share strategy.

Capture evidence of several students development of SMP 3&4 during the lesson using the Proficiency Matrix

Reflect on instructional strategies you implemented during lesson to support MSP 3&4

Bring a copy of the task you used (both before and after, if you adapted the task)

Select 10-12 samples of student work to share at next session: a mix of low to high

+Thanks…… are your students this excited by rich tasks?

+

Day 3

+Outcomes Day 2 & 3:

Analyze student work with the Standards for Mathematical Practice and content standards.

Analyze, adapt, and implement a task with the integrity of the Common Core State Standards.

+Welcome Back Activity

Success, challenge, barrier, breakthrough

Reflect on your experiences focusing on the Standards for Mathematical Practices in your classroom.

Use separate post-it notes to capture your successes, challenges, barriers, and/or breakthroughs

Post on appropriate poster

Read post-it notes on all posters and select one that resonates with you.

Quick share of selected post-its.

+

Homework Review

+Looking at Tasks Used

Trade the task you used with another person.

Do a task analysis of each other’s tasks using the following components:

Cluster/standard DOK Standards for Mathematical Practices Is it a rich task?

Discuss findings with each other.

+Looking at student work

With your same partner/group, complete the following “Looking at Student Work” protocol.

Sort one person’s classroom set of papers into high, medium, and low piles (according to student’s understanding of the mathematical content) and come to agreement on which papers belong in which piles. Record your criteria for high, medium, & low.

Repeat with the other group member’s set of papers.

+BREAK TIME!!!

15 minutes….Go

+Critiquing the Reasoning of Others in Action

+Video Task

5 minutes to work on independently

Work in table groups to discuss thinking

Analyze task using task analysis worksheet (from Day 1 – add to bottom of sheet)

Discuss whole group

Watch video

+Looking into a high school classroomInside Mathematics Public Lesso

n: Quadratic Functions

• What makes this activity evidence of critiquing the reasoning of others? Modeling?

• What observable conditions supported critiquing the reasoning of others? Modeling?

• What observable conditions constrained critiquing the reasoning of others? Modeling?

+

Publishers Criteria Shifts

+Key Shifts to look for….

Focus:

Coherence:

Rigor:Underline one sentence from each of these sections that helps you “make sense” of these shifts.

+Wrap up Activity

Evaluations

Thank You!