Overview Introduction to base ten blocks Practice modeling subtraction Share practice from mini-problems Problem planning groups Grade level groups Wrap up

Base-10 Blocks Names of the materials - (Little) cubes - Longs (or rods) - Flats - Big cubes No assigned values; we can choose the unit. Important for work with decimals.

Modeling the Standard Subtraction Algorithm The “modeler”: Select a multi-digit subtraction problem with regrouping. Tell your group whether you will be using a take-away or comparison interpretation of subtraction. Model the subtraction -- talk through each step and carefully map between the materials and the written form. The “critics”: Use the modeling checklist to make notes about the performance. Provide comments and suggestions based on your observations. If your group finishes early, each person should try a new problem using the other interpretation of subtraction.

Analyzing Common Student Errors How might a student have gotten each incorrect answer? What might each error tell you about a student’s understanding of place value? What questions would you want to ask each student to probe his or her thinking?

Problem Planning Groups What happened in your discussions? What went well? What didn’t go as well? What were some productive moves you used and/or challenges you faced with regard to the following: Creating a productive environment in which students were able to share and listen to each other Supporting all students to engage with the problem and achieve your instructional goal Keeping the work focused on important aspects of the mathematics

Problem Planning Groups #1: Karla(2), Lindsay(2), Meaghan(1), Diana(1), Aimee(3), Justine(2), Lani(2) [#2:] #3: Wendy(5), Julie(3), Melanie(5) (or #4), Jessica S(2) #4: Jessica T(2), Graham(4), O’lou(7/8), Michele(4), LesLeigh(6/7), Kristy(1), Brian(7), Rob M (5, 7/8) #5: Alyson(7), Rob S, Dawn(1), Dave(7/8), Gordon(5), Chrystal(3/4), Lee(4), Lori(3/4) [#6:]

Grade Level Groups Meaghan(1), Diana(1), Dawn(1), Kristy(1) 2a. Karla(2), Lindsay(2), Justine(2) 2b. Lani(2), Jessica S(2) Jessica T(2) 3/4. Aimee(3), Julie(3), Chrystal(3/4), Lori(3/4) Michele(4), Graham(4), Lee(4) Wendy(5), Melanie(5) (or #4), Rob S(5) 5+. Gordon(5), Rob M (5, 7/8) LesLeigh(6/7) 7+. Brian(7), Alyson(7), O’lou(7/8), Dave(7/8)

Grade Level Groups: Directions for Sharing Practice Provide a context for your audio segment by briefly sharing relevant background information. Explain your reasons for choosing this segment and what you hope to learn from your group’s interactions. Play your audio segment, and answer any clarification questions about what happened in the segment. Use your completed question track form to highlight some of the questions you used during the segment, the purposes you had for those questions, and your impressions of student responses to the questions. Share improvements you made to any of the questions in the segment and your rationale behind those improvements. Invite group members make comments and provide feedback based upon your question purposes, student responses, discussion planning considerations, or the course principles.

Learning From and Improving Practice How could you improve or add to the techniques you use in discussions? Record at least one thing you will try during the lesson you will teach near the end of the term. Why is this something you want to improve or try? How does it relate to purposes of questioning, discussion planning considerations, or the course principles?

Why did we do this today? Completing a “cycle of practice” Developing your skills at leading a discussion Learning from practice and committing to improvements based on what you learn Learning to talk about your own practice and provide feedback to others

Initial Cycle of Learning About Practice Enacting improved practice Determining productive direction for future practice Considering and preparing for practice Enacting practice Consolidating learnings from practice Exposure to practice

Wrap Up Assignments Please leave notebooks if you wish Carefully read student thinking interview assignment. Select student with your CT and email this info before next class. Write a reflection about what you have learned and plan to try from your work on the mini-problem Readings Please leave notebooks if you wish

The Course Matrix: Principled Practice Guiding Principles Domains of Practice Attending to the integrity of the mathematics Committing to the learning and achievement of all students Establishing and managing a productive learning environment Learning from and systematically improving practice Eliciting, interpreting, and assessing students’ ideas Modeling and representing mathematical ideas Leading a whole class discussion Designing,enact-ing, analyzing, improving lessons

Initial Cycle of Learning About Practice (TGuide version) Enacting improved practice (engaging purposefully in a more complete/nuanced teaching practice and/or in a setting that more closely embodies an authentic teaching context while collecting artifacts to support professional learning and improvement) Determining productive direction for future practice (planning improved course(s) of action for use in subsequent teaching) Enacting practice (engaging purposefully in a setting that embodies key dimensions of authentic teaching contexts & collecting artifacts to support learning from practice) Consolidating learnings from practice (collaborative and self-reflection on practice utilizing experience, purpose, considerations, and principles) Considering and preparing for practice (building background knowledge about purposes, considerations, and principles, as well as specific options for practice; planning core elements of practice in a supported context) Exposure to practice (hearing about, remembering, or noticing practices in a domain of teaching)