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

2. 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.

3. 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.

4. 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?

5. 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

6. 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:]

7. 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)

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.

9. 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?

10. 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

11. 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

12. Wrap Up Assignments Please leave notebooks if you wish
Carefully read student thinking interview assignment. Select student with your CT and 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

13. 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

14. 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)