Guide for implementing the
CDE professional
development module on the
Standards for Mathematical
Practice.
California Common Core State Standards: Professional Learning Modules
Notes to consider
The Module overview
frames what is expected
from this PD. Also, the
Thinking about thinking is
a good tool for reflective
learning.
Table of Contents
o
Welcome
o
Module Overview

Thinking about Thinking

Background of the CCSS for Mathematics
o
Pre-Assessment

o
For those that have not
completed the CCSS CISC
Modules 1, 2 & 3 through
SCOE, this unit is not
optional. For all others,
this unit is a good review
of the standards for math
practice and could be
optional.
What Do You Know?
Unit 1: Teaching and Learning the Standards for Mathematical Practice

1.0 Observing Students
 (3 Classroom Videos: Gr 2, 6, 8; with 3 journal questions about the
videos)

1.1 Two types of Mathematics Standards

1.1.1 The Standards for Mathematical Content


Approx time to complete
45 – 60 minutes

1.1.2 The Standards for Mathematical Practice

Doing and Using Mathematics

The Eight SMP

For All Learners, All the Time

Common Core SMP
1.2 Interaction of Practice Standards and Content Standards
 (Jason Zimba Video, 1:13 & 2 review journal questions about SMPs
and one reflective journal question)

1.2.1 Bringing Structure

1.2.2 Connecting Content and Practice: Points of Intersection



1.3.1 Language Learning and Mathematics

1.3.2 Students with Disabilities

1.3.3 Supporting English Learners (3:50 video on CCSSM & ELLs)

1.3.4 21st Century Skills
1.4 Looking Ahead

o
Grain Size (One reflective journal question)
1.3 Meeting the Needs of All Students


Balance and Depth of Understanding
1.4.1 Taking the Next Step
Unit 1 References
Unit 2: Overarching Habits of Mind: MP1 and MP6

2.0 Unpacking MP1 and MP6 (2 reflective journal questions)
Unit 2 focuses on
deepening your
understanding of the
various aspect of the
standards for
mathematical practice:
1. Make sense of
problems and persevere
in solving them.
6. Attend to precision

2.1 Sense Making and Mindsets (math activity and 4 journal questions)

2.1.1 Teacher Mindsets


2.1.2 Engaging Students

Questions that Engage (2:27 video of teacher facilitating using
questioning strategies; 3 reflective journal questions and one video question)

Posing Questions and Responding to Students (activity to get teachers
discussing questing that promote SMP 1)


2.1.3 Mindsets
2.2 Student Self-Efficacy and Perseverance (MP1)


Multiple grade level
videos and content are
used throughout the unit.

2.2.1 The “Hook” to Persevere
2.2.2 Task Summary and Reflection (2 reflective journal questions about the
previous activity that looks at tasks that make connections versus procedural
tasks)
2.3 Attending to Precision (MP6)

2.3.1 Focusing on Mathematical Statements (3 activity-based journal
questions)

Approx time to complete
60 – 90 minutes
Making Sense of Problems (one reading summary journal question)

2.3.2 Analyses of Teachers’ Statements
2.3.3 An Example of Students Attending to Precision (3 videos of students
taking about math; 3 journal questions)
2.4 Summary and Reflection (2 reflective journal questions)
Unit 3 examines MP2 and
MP3, Reasoning and
Explaining; specifically
how to reason abstractly
and quantitatively,
construct viable
arguments, and critique
the reasoning of others.
This unit will focus on
how students learn to:
o
Unit 3: Reasoning and Explaining (MP2 and MP3)

3.0 Unpacking MP2 and MP3 (2 reflective journal questions)

3.0.1 Introduction to a 5th-grade classroom: The case for these practices
(2:11 video of student interpretation of SMP3 and follow up journal question)


3.0.2 Connections Across the Standards
3.1 Beginning to Reason: Definitions and Conjectures

3.1.1 Student Definitions and Explanations (activity centered on clear and
logical explanations at multiple grade levels; three activity questions and one
reflective journal question.)

3.1.2 Developing a Community of Reasoners


Construct viable
arguments
Respond to the reasoning
of others

Increase the viability of
their arguments
Unit 3 highlights a 5th-
3.1.3 Introduction to Conjectures

Lesson Designed to Introduce Viable Arguments (sample 5th grade
lesson and student video response 0:19)

Selecting a Significant Task to Initiate Conjectures (another student
video response to 5th grade task 2:09; two journal questions about video)


Meeting the Needs of Diverse Learners (one reflective question)
Next Phase of Lesson Forming Conjectures
3.1.4 Achieving Consensus through a Community of Reasoners (two
reflective journal questions)

3.2 Explaining and Justifying

Taxonomy of Questions in Mathematical Discourse

3.2.1 Levels of Explanations: Level 1 (Student Video 0:32)

3.2.2 Levels of Explanation: Bridging Level 1 and 2 (Student Video 1:02)

3.2.3 Levels of Explanation: Level 2 (Student Video 2:00)

3.2.4 Levels of Explanation: Level 3 (Student Video 0:43 and two journal
response questions)
grade classroom as the
students learn to use the
reasoning and explaining
practices. Although the
focus is on one grade
level, teachers of all
grade levels can transfer
the concepts learned to
their instructional
practices.


3.2.5 Levels of Explanation: Include All Students
3.3 Identifying Flaws in Reasoning

3.3.1 Discourse (three journal response questions)

3.3.2 Language (Student Video 2:37)

3.3.3 Definition of “Rule” (Student video 0:45)

3.4 Making Arguments More Viable

3.4.1 Flower Arrangements (A math task and two follow up journal questions)


3.4.2 Students Revise and Share Work with Partner

Approx time to complete
90 – 120 minutes
3.4.3 Students Share with Class and Revise

3.4.4 Group Collaboration (two reflective journal questions)
3.4.5 Student-Generated Math Challenge (Student video describing viable
arguments 3:44)


This unit examines MP4
and MP5; the practices
relating to modeling with
mathematics and using
tools. You will deepen
your understanding of
the various aspects of
each standard as you
work through this unit.
CCSS Mathematical Practices: Reason abstractly and quantitatively
3.5 Summary

3.5.1 Community of Reasoners

3.5.2 Conclusions (one reflective journal question)
Unit 4: Modeling and Using Tools (MP4 and MP5)

4.0 Unpacking MP4 and MP5 (three reflective journal questions)

4.1 Introduction to Modeling with Mathematics (MP4)

4.1.1 Examples of Modeling with Mathematics (different grade-level spans
modeling examples with the same real-life focus)



Multiple grade level
videos and content are
used throughout the unit.
Approx time to complete
60 – 90 minutes
Brandon’s Solution (Steps 1–3) (Three follow up journal questions)


o
Student Solutions

4.2.1 Early Grades (Grades K-5 math modeling activities)

4.2.2 Middle Grades (Grades 6-8 math modeling activities)

4.2.3 High School (Grades 9-12 math modeling activities)

4.2.4 Students Making Sense of a Problem & MP5 (Classroom video 5:53
and one follow up question)*
4.2.5 Summary (three reflective journal questions)
4.3 Introduction to Using Appropriate Tools Strategically (MP5) (one 4.1.1 follow–
up journal question)




4.1.2 Summary and Reflection (two follow up and reflective questions)
4.2 Modeling with Mathematics at Different Grade Level Spans


Meeting the Needs of All Learners
4.3.1 Tools for Each Grade Level Span (a partial list of tools)
4.3.2 Differentiating Instruction Through the Use of Technology and Tools
(three classroom videos: elementary 6:08, Secondary 2:00 & 6:15)
4.3.3 Summary and Reflection (one reflective journal question)
4.4 Use of Tools at Different Grade Level Spans (example task and appropriate
tools)

4.4.1 Using Tools Strategically: Video Examples (two videos: elementary
example 04:32 & secondary (middle) 5:42; one follow-up journal question)


This unit examines MP7
and MP8, the practices
that relate to seeing
mathematical structure
and generalization. You
will deepen your
understanding of the
various aspects of each
standard as you work
through this unit.
o
4.5 Summary and Reflection (four follow-up and reflective questions)
Unit 5: Seeing Structure and Generalizing (MP7 and MP8)


5.0 Unpacking MP 7 and MP 8 (two reflective journal questions)
5.1 Structure, Repeated Reasoning, and Generalization (grade level span
example and two reflective journal questions)


5.1.1 Generalization (one follow-up journal question)
5.2 Making Sense of a Growing Pattern (math activity with 6 follow-up questions
and two grade 6 students’ work videos 3:06 & 9:16)

Multiple grade level
videos and content are
used throughout the unit.
5.2.1 Summary and Reflection (three follow-up and reflective journal
questions)

5.3 Geometry Examples of Structure and Generalization (grade level span
example; three follow-up and reflective journal questions)

5.4 Performance Tasks and Student Work (grade level span example task w
student work; 4 to 8 follow-up and reflective journal questions per grade span)



o
This short section
provides time to debrief
this whole module and
discuss next steps.
5.4.1 Making Connections
5.5 Summary and Reflection (two reflective journal questions)
Approx time to complete
60 – 90 minutes
5.5.1 Video Examples (links to multiple video of grade level span specific
classrooms highlighting MP7 & MP8; 2 to 3 follow-up and reflective journal
questions per grade span)
Unit 6: Summary and Next Steps

6.0 Summary

6.0.1 Looking Back (same videos from section 1.0 with two follow-up journal
questions after completing all units)


Approx time to complete
15 – 30 minutes
4.4.2 Summary (three follow-up and reflective questions)
6.0.2 Reflections on Units 2 through 5
6.1 Take Action: Planning the Next Steps (same self-reflections from Unit 1 to
measure growth of confidence and three reflection journal questions)

o
6.1.1 Closure
Post-Assessment (same assessment as module overview to measure growth of
knowledge)
o
Certificate of Completion
o
Glossary
o
Resources

English Language Development Resources

Special Education Resources

Professional Organizations
o
Acknowledgements
o
Module Evaluation