1. Use the next 10 minutes to share.... Goal…
Sharing Number String
Use the next 10 minutes to share....
Goal…
What strategies or properties did you want students to think about?
Outcome…
Did you have similar experiences?
What adjustments did you make?
Next step…
Identify your next area of focus with Number Talks.
Need student copies of the Exploratory Challenge (pages 4-5 in the student edition)

2. ASW: Focusing on Student Thinking
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
December 3, 2015

3. PRR: NCTM Articles on Fractions
Gr 1 – 3 Making Fractions Meaningful
Gr 4 – 7 Unpacking Referent Units in Fractions
Discuss one of these ideas:
Share one connection you made to the work last summer.
Share one idea that might be incorporated into your work with students.

4. Learning Intentions & Success Criteria
We are learning to use what we know about learning trajectories to identify thinking trends in student work.
Success Criteria:
We will use our understanding of learning trajectories to plan instructional responses to move students along their learning path.

5. Tapping into Our OGAP Work
“…growing understanding of the “learning trajectories” or common pathways of development in these areas have the potential to provide teachers with…
a clear articulation of learning goals
how students’ thinking should develop
learning activities that are likely to move students along the path towards achieving those goals
(Heritage, 2008; Sztajn, Confrey, Wilson, & Edginton, 2012).

6. Frameworks We’ve Used: Fraction Strategies & OGAP Trajectories
Developing Fraction Ideas
Equal sharing problems and Children’s Strategies for Solving Them.
Fraction Standard Progression (Gr 3 – 5)
Proportional Reasoning
OGAP Learning Trajectory
Read the progressions p. Ratios, Rates Proportional Relationships 2-3
Make this handout.
Read 2 paragraphs starting at bottom of page 2 and complete the top paragraph on page 3.

7. Fine Tuning Our Sort: Frameworks & Standards
Pull out student work: 6F, 6G, 6M Use OGAP Framework to identify the stage of student thinking. Read 6.RP.3 – Where is this student in meeting the standard?

8. Fine Tuning Our Sort: Frameworks & Standards
6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Turn and Talk…
What instructional experiences will these students need to move forward in their proportional thinking?

9. Fine Tuning Our Sort: Frameworks & Standards

10. Fine Tuning Our Sort: Frameworks & Standards
6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

11. Now It’s Your Turn

12. Fine Tuning Your SWA
Focus on one grade level task.
Come to consensus on the standard(s) connected to the task and work expectations needed to meet the standard.
Complete your SWA form (if not done).

13. Recalibrating what it means to Meets Expectations
Individually recheck your student work.
Select one piece of student work that fits the criteria.
Share characteristics of the work that “Meets expectations.”
One last task.
Use the student work you just discussed to identify a
continuum of thinking.
What instructional suggestions might you make for these students?

14. Teasing out “Approaching and Developing”
Start with work in the “Approaching” pile.
Step #1 - Individually
Select a few papers from your approaching pile. Use the work to identify common misconceptions and common understandings.
Use a post-it to briefly describe the misconception or understanding.
Be prepared to share with your group.
Step #2 – Your grade level table group
Make a continuum of student thinking from Developing to Approaching.

15. Planning Next Steps What common misconceptions did you notice?
Step #3: As a table group develop a plan:
What common misconceptions did you notice?
What experiences will students’ need in order to move them along their learning trajectory?
Complete the instructional suggestions columns on the final page of the SWA form.
Use the next 10 minutes of class to individually complete the reflection on bottom: Include suggestions your table group discussed about ideas to incorporate in your work with students.
Add to your homework folder.
Benchmarking understanding -

16. Learning Intentions & Success Criteria
We are learning to use what we know about learning trajectories to identify thinking trends in student work.
Success Criteria:
We will use our understanding of learning trajectories to plan instructional responses to move students along their learning path.

17. SWA Homework
Between January 4 – 7th re-give your grade level tasks to your students. Bring both sets of work samples to class on January 7th. (No need to sort ahead of time.) Make sure not to do any instruction before the task. This will help to keep the experiences similar to September.

18. Disclaimer Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.
This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.