1. + Day 2

2. + 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. Done early: Update your Classroom Culture reflections

3. + Reflection What is your current reality around classroom culture? What can you do to enhance your current reality?

4. + Outcomes Day 2: Overall Outcomes on Agenda……Remember the Whole Child! Analyze student work with the Standards for Mathematical Practice and content standards. Deepen understanding of the progression of learning and coherence around the CCSS-M Conceptual Category Functions Understand the SBAC Assessment Claim 4 for Mathematics. Analyze and adapt tasks with the integrity of the Common Core State Standards.

5. + Homework Review

6. + 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.

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8. + Homework Strategy Sharing 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 next time. How did using the Proficiency matrix work? Are there changes you’d like to make?

9. + Standards of Student Practice in Mathematics Proficiency Matrix

10. + Digging Deeper: Constructing Viable Arguments & Critiquing Reasoning of Others and Modeling with Mathematics In table groups Each person reads one side of the Mathematical Practices (#3 & #4) compilation handouts. Highlight three new ideas found in your assigned reading Share in your group. Use these the ideas and what you learned using the matrix with students to “enhance” the Proficiency matrix on the blank matrix

11. + Applying your learning From previous homework: you found/created or adapted to make a rich task. Have you turned in your item for the Intel CCSS-M Item bank – digital is preferred, hard copy is better than not at all!!!!!

12. + BREAK TIME!!! 15 minutes….Go

13. + Functions Progression Cont. Move back into your brainstorm groups from last session

14. + Functions Assign one Domain to each table group 1. 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”

15. + 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

16. + Grade 8 Functions Clusters Major: Define, evaluate and compare functions Supporting: Use functions to model relationships between quantities

17. + Functions: Connections What 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

18. + Functions: Connections What connections are there between the Functions domains/clusters and the other high school conceptual categories? Look for connections to other high school conceptual categories in the CCSS document—where are the other items from your list? Suggestion: Divide and conquer….. Notate on your list the cluster(s)/standard(s) where these related items are located in the CCSS

19. + 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 8 th grade Connections to other high school conceptual categories Presentation: Select one person to talk about each of the above bullets for @ 2 minutes each

20. + Rich Tasks

21. 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

22. + 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.

23. + Is this a rich task?

24. 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?

25. + Old Way of Doing Business MSP PE 7.1.E and CCSS 7.EE.4 Katarina bought n apples. She gave half of the apples to Jens. Then she put some of the apples in sack lunches. After that, she had 1 apple remaining. The equation shown represents this situation. n/2 – 3 = 1 Solve the equation for n to determine the number of apples Katarina bought. Write your answer on the line. How many apples did Katarina buy? _____________________ apples

26. + New Ways of Doing Business SBAC 7.EE.4 David wants to buy 2 pineapples and some bananas. The price of 1 pineapple is $2.99. The price of bananas is $0.67 per pound. David wants to spend less than $10.00. Write an inequality that represents the number of pounds of bananas, b, David can buy. On the number line below, draw a graph that represents the number of pounds of bananas David can buy.

27. + New Ways of Doing Business SBAC 7.EE.1 & 7.EE.2 For numbers 1a–1e, select Yes or No to indicate whether each of these expressions is equivalent to 2(2x + 1). 1a. 4x + 2  Yes  No 1b. 2(1 + 2x)  Yes  No 1c. 2(2x) + 1  Yes  No 1d. 2x + 1 + 2x + 1  Yes  No 1e. x + x + x + x + 1 + 1  Yes  No

28. + New Ways of Doing Business SBAC 7.EE.1 In the following equation, a and b are both integers. a(3x – 8) = b – 18x What is the value of a? What is the value of b?

29. + Applying your learning From previous homework: you found/created or adapted to make a rich task. Find/create or adapt a task to make another rich task Have you turned in your item for the Intel CCSS-M Item bank – digital is preferred, hard copy is better than not at all!!!!!

30. + …… are your students this excited by rich tasks?

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32. + SBAC Claim 4

33. + Let’s do some Math Work on the Salary Task Be sure to read the entire problem before getting started Be prepared for us to call time, even if you are not yet finished. Using your task analysis worksheet, determine the DOK level(s), CCSS content standard, SMP (Standards for Mathematical Practice)

34. + SBAC Assessment Claims for Mathematics “Students can demonstrate progress toward college and career readiness in mathematics.” “Students can demonstrate college and career readiness in mathematics.” “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” Overall Claim (Gr. 3-8) Overall Claim (High School) Claim 1 Concepts and Procedures Claim 2 Problem Solving Claim 3 Communicating Reasoning Claim 4 Modeling and Data Analysis

35. + 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.

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38. You have information in this location on your handout – check to see how well you determined the DOK, SMP, and content standards.

39. + Share out - 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?

40. + Instructional Actions

41. + 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

42. + 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.

43. + 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 Write up on the Intel task sheet. Find someone at another table to share your task with.

44. + Critiquing the Reasoning of Others in Action

45. + 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

46. + Looking into a high school classroom Inside Mathematics Public Lesson: 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?

47. + Publishers Criteria Shifts

48. + Key Shifts to look for…. Focus: Coherence: Rigor: At your table, choose folks to read one of each of these sections. Underline one sentence from your section that helps you “make sense” of this shift. Share at your table.

49. + Reflection What is your current reality around classroom culture? What can you do to enhance your current reality?

50. + Wrap up Activity Evaluations Handouts, ppts, and items written are located on: www.psesd-math.wikispaces.com Thank You!