Overview of this Afternoon from 1PM to 3:45 PM Intro and Norms CCSSMP Doing Mathematics Processing Mathematics Making Connections.

Overview of this Afternoonfrom 1PM to 3:45 PM

• Intro and Norms

• CCSSMP

• Doing Mathematics

• Processing Mathematics

• Making Connections

Lenses to Consider During our Sessions

Learner Lens Teacher/Leader Lens

Working Together

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.

Learning Needs Discussion

In table groups of no more than 4, share your experiences.

oWhat experiences did you share in common?

oWhat experiences were different?

Community Agreements

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.

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.”

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.

Mathematical Practice

1. 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?

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?

3. Construct viable arguments and critique the reasoning of others.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics

Which ropes are ‘Thin’? Which ropes are ‘Medium’?Which ropes ‘Thick’?

Explain your reasoning.

5. Use appropriate tools strategically

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

Novice – short items focused on skills and routines

Apprentice – medium performance tasks with scaffolding

Expert – long tasks with high cognitive load and/or complexity

Types of Tasks

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. Perhaps the first point, which is widely accepted, is that teaching must be active, or rather active learning. George Polya

Overview

PART and WHOLE

Work through the Levels beginning with A, then B, C, D then E.

PROBLEM OF THE MONTH

What do

you

think?

Can youexplain that to me?

  Let’s work together! 

Part and WholePart and WholePart and WholePart 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.

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.

Part and Whole Part and Whole Part and Whole 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?

Part and WholePart and WholeGallery WalkGallery Walk

Part and WholePart and WholeGallery WalkGallery 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

PART and WHOLE

Work through the Levels beginning with A, then B, C, D then E.

PROBLEM OF THE MONTH

What do

you

think?

Can youexplain that to me?

  Let’s work together! 

Part and WholePart and WholePart and WholePart 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.

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.

Part and Whole Part and Whole Part and Whole 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?

Part and WholePart and WholeGallery WalkGallery Walk

Part and WholePart and WholeGallery WalkGallery 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