Overview of this Afternoon from 1PM to 3:45 PM Intro and Norms CCSSMP Doing Mathematics Processing Mathematics Making Connections HI, I am Sally and with Shannah and Lori, we will be working with you this afternoon. Since we have just come together for the first time, it is important that we spend a little time to set some norms to support our work together. We will also have the opportunity to do and process a very rich mathematical task together. In our work with you we will be giving you individual time as well as group time. So when you see us us this signal…hand and arm raised…please finish your last thought and pull together as a collective group. Also, we will be making connections between the math that we do and what we hard this morning with an emphasis on the CCSSMP. 1

Lenses to Consider During our Sessions You will have materials available to you to use in your classrooms and you will have the opportunity to explore some these materials as a learner. Be thinking about how you might use some of things you learn in the classroom as well as how they might benefit your interaction with other teachers, site leaders and administrators. Learner Lens Teacher/Leader Lens 2

Working Together This may be a new experience for many of you- to do math together and to write prototypes of formative assessment tasks. Thus, we want to make our time together as productive and stress free as possible.

Building Relationships to Learn Think about a time when you worked in a group on an activity. List 5 or more things that made it successful. Think of a time when you struggled to work in a group on an activity. List 5 or more things that made it difficult. So being aware of each other as individuals with our own experiences and values when it comes to group work and collaboration, we want to give you this opportunity to have individual think time around these two bullets and then an opportunity to share and discuss with others. We will give you 5 minutes to think about and record your ideas on this paper.

Learning Needs Discussion In table groups of no more than 4, share your experiences. What experiences did you share in common? What experiences were different? Now is the opportunity to share and to learn from and about each other. We will give you 5 minutes here to do this. Please remember, when you see this hand signal, we would like you to finish your thoughts and come together whole group. We heard some wonderful things as we walked around the room: Would anyone like to share some thoughts regarding either bullet?

Community Agreements And so, it is important that, as a group, we have in place some community agreements regarding the protocols for our work together.

Community Agreements What agreements (norms) do we need for a community of math learning that supports risk-taking, sharing ideas, conjectures, and insights?

Community Agreements No one is as smart as all of us are together. Take a few minutes to read the proposed Community Agreements. There are different types of norms. One set is the “social” set…the intrapersonal interactions between and among individuals, small groups and an entire community. These norms help us as teachers to provide a structure for discourse and for classroom management expectations. So, in order for us to set the stage for our learning community we would like to look at some social norms that typically come up in our groups. Here is a list of typical responses to the question, “What do you consider important mathematical social and community norms?” Over the course of learning mathematics this week we want to be reflective not only of student learning considerations but also of ourselves as adult learners. We need to be comfortable in our learning groups, yet challenged to deepen our mathematical knowledge. We may choose to work within the same group or not, but whichever the grouping, we want to be reflective of how we work in a group (what do you need and what do others need?). Because norms are constantly works in progress, we will revisit our agreements throughout the week.

Please check in with your group members to decide if you would be able to support and honor these community agreements as the structure or protocol for our work together. HAND SIGNAL Please, individually, give a thumbs up with okay, sideway thumbs if not sure, and thumb down if no. Please note that we have a parking lot poster when any individual or group may voice their thoughts regarding these community agreements which we will bring to the whole group to discuss.

A Parking Lot

Community Agreements are… “helpful because it helped me to realize that when I try to help someone I might not actually be helping them.” “helpful because having them helps us students figure a way to work with each other and understand each other.” “great because people had time to think and cooperate in groups.” “awesome because it reminded me of how to treat other people.” “helpful because it was easier for me to work.”

Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

persevere in solving them. Make sense of problems and persevere in solving them.

2. Reason Abstractly and Quantitatively Where are a+b, b-a and a-b? What can you say about where a/b is? a b

Construct viable arguments and critique the reasoning of others. Valerie shares some of the 12 candies. She gives Cindy 1 candy for every 3 candies she eats herself. How many does she give Cindy? Getting students to evaluate strategies. Decide when to use them. Develop internal criteria for evaluating solutions.

Construct viable arguments and critique the reasoning of others. Getting students to evaluate strategies. Decide when to use them. Develop internal criteria for evaluating solutions.

4. Model with mathematics

5. Use appropriate tools strategically Which ropes are ‘Thin’? Which ropes are ‘Medium’? Which ropes ‘Thick’? Explain your reasoning.

6. Attend to Precision Imagine that you have just discovered this ancient floor tiling pattern in Syria.   You telephone New York to tell them about this exciting discovery. Describe the pattern as accurately as you can, so that someone else can draw it without seeing it. Describe the shapes as completely as you can.  ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

7. Look for and make use of structure Sidewalk Patterns

8. Look for and express regularity in repeated reasoning

CCSSM Assessments

Types of Tasks Novice – short items focused on skills and routines Apprentice – medium performance tasks with scaffolding Expert – long tasks with high cognitive load and/or complexity

Mathematics, you see, is not a spectator sport Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean doing mathematics? In the first place it means to be able to solve mathematical problems. George Polya, (1887 - 1985) Father of Problem Solving; “How to Solve It”, 1945

Let me tell you what my idea of teaching is Let me tell you what my idea of teaching is. Perhaps the first point, which is widely accepted, is that teaching must be active, or rather active learning. George Polya

Overview

PROBLEM OF THE MONTH PART and WHOLE What do you think? Can you explain that to me?   Let’s work together!  PART and WHOLE Work through the Levels beginning with A, then B, C, D then E. Show all slides for an overview first then return HERE. 27

Part and Whole During this quiet think time, please read all levels of the Problem of the Month. As you read… • Think of clarifying questions you may have for your group • Think of possible strategies you might like to try Then… • Ask your clarifying questions of your group and share your ideas on possible strategies • Begin working on Level A first.

Poster #1: You and Your Partner’s Findings on One of the Levels of the POM Select a Level of the POM to share in words, pictures, and numbers the complete mathematical findings you and your partner have discovered about this level. Feel free to choose any level. The focus of your poster should be on how your findings can be justified mathematically and how your findings make sense. 31

Poster #2: Create a Status Check Poster of your and your partner’s findings on a Level you are still exploring Select a Level of the POM you are still exploring. The focus of your poster should be on your processes so far and where the two of you think you want to go next and/or questions and wonderings the two of you have about this level. Remember to justify or explain your processes the two of you have used so far and why they make mathematical sense. 32

Part and Whole In your group or with your partner, discuss and add this information to the TWO posters that you created… Determine the BIG IDEAS in mathematics on each selected POM level. Select one or two CCSSMP that your group or partner felt was evidenced in your mathematical work on this POM. Anticipate grade level strategies at each POM level. Posters will be created on 11x16” ? Paper and complete an enlarged matrix on the wall.

NORMS FOR A GALLERY WALK All discussion and conversation in a gallery walk is: About what each of us can learn from each other Respectful of ALL work The FOCUS of a gallery walk is on the MATHEMATICS of the problem: What is the mathematics of the poster? Was the thought process the same as yours? If no, what is different? Is the representation the same as yours? If no, what is different? What questions might you pose to the “author[s]” to clarify your own understanding of the mathematics presented? What mathematics contributes to your own understanding? What did you find mathematically interesting? What did you find mathematically challenging? What mathematics presented would you like to engage in? We would like all participants to take paper and pencil with them on the gallery walk. Please take notes on different strategies and questions you may have about different posters – questions you may want to discuss with the different groups. No post its: too early in norms to use. May use a docent or may not; Atlanta we did and in TN we did not. There are pros and cons to both approaches. Be flexible and play it by ear. 34

Part and Whole Gallery Walk The focus of the gallery walk is on the MATHEMATICS of the problem and “Shopping” for tools to add to your Teacher and Learner Toolbox: • Look for the development or progression of KEY mathematical ideas through the levels of this POM. • What are the mathematical relationships among the different strategies across the POM levels? • How are strategies similar and different across the POM levels?

Gallery Walk Each group will display their poster. Group members will examine, explore, and review the other groups’ posters to fill out their Gallery Walk Observation Guide. There will be time for your group to re-assemble and discuss the information shared in the groups’ posters. Please mind gallery walk norms and be respectful of the work and information shared.

Engaging in the POM

PROBLEM OF THE MONTH PART and WHOLE What do you think? Can you explain that to me?   Let’s work together!  PART and WHOLE Work through the Levels beginning with A, then B, C, D then E. Show all slides for an overview first then return HERE. 38

Part and Whole During this quiet think time, please read all levels of the Problem of the Month. As you read… • Think of clarifying questions you may have for your group • Think of possible strategies you might like to try Then… • Ask your clarifying questions of your group and share your ideas on possible strategies • Begin working on Level A first. While participants are working, we will look for strategies being used to share with the whole group, looking for a variety as well as representation across levels A through E. We will ask participants to record strategies onto overhead transparencies.

Poster #1: You and Your Partner’s Findings on One of the Levels of the POM Select a Level of the POM to share in words, pictures, and numbers the complete mathematical findings you and your partner have discovered about this level. Feel free to choose any level. The focus of your poster should be on how your findings can be justified mathematically and how your findings make sense. Hopefully this will provide for a variety of different levels and not just Level D and Level E. 40

Poster #2: Create a Status Check Poster of your and your partner’s findings on a Level you are still exploring Select a Level of the POM you are still exploring. The focus of your poster should be on your processes so far and where the two of you think you want to go next and/or questions and wonderings the two of you have about this level. Remember to justify or explain your processes the two of you have used so far and why they make mathematical sense. This should allow groups to talk about getting stuck and to list their wonderings. 41

Part and Whole In your group or with your partner, discuss and add this information to the TWO posters that you created… Determine the BIG IDEAS in mathematics on each selected POM level. Select one or two CCSSMP that your group or partner felt was evidenced in your mathematical work on this POM. Anticipate grade level strategies at each POM level.

NORMS FOR A GALLERY WALK All discussion and conversation in a gallery walk is: About what each of us can learn from each other Respectful of ALL work The FOCUS of a gallery walk is on the MATHEMATICS of the problem: What is the mathematics of the poster? Was the thought process the same as yours? If no, what is different? Is the representation the same as yours? If no, what is different? What questions might you pose to the “author[s]” to clarify your own understanding of the mathematics presented? What mathematics contributes to your own understanding? What did you find mathematically interesting? What did you find mathematically challenging? What mathematics presented would you like to engage in? 43

Part and Whole Gallery Walk The focus of the gallery walk is on the MATHEMATICS of the problem and “Shopping” for tools to add to your Teacher and Learner Toolbox: • Look for the development or progression of KEY mathematical ideas through the levels of this POM. • What are the mathematical relationships among the different strategies across the POM levels? • How are strategies similar and different across the POM levels?

Gallery Walk Each group will display their poster. Group members will examine, explore, and review the other groups’ posters to fill out their Gallery Walk Observation Guide. There will be time for your group to re-assemble and discuss the information shared in the groups’ posters. Please mind gallery walk norms and be respectful of the work and information shared.

Discussing What You Saw and Learned in the Gallery Walk

Whole Group Share Out

Website for POMs and Performance Tasks noycefdn.org