Thinking Mathematics for Early Grades
K-2
FACILITATOR MANUAL
Module
1
The Ten Principles of Thinking
Mathematics and Common Core
Mathematical Practices
Approximately 3 or 3.5 hours
Activities
CCSSM
Opening Introductions
1. Triangle Tables
TDE Framework
(4) Reflecting on Teaching
MP 1 Making sense
MP 2 Reasoning
MP 9 Model mathematically
(1) Content & Pedagogy
(2) Culture and Learning
(3) Communications
(3) Engagement
(4) Flexibility,
Responsiveness
2.
The Ten Principles
3.
TM Principles and
Evaluation
Framework
4.
Introduction to
Common Core
Mathematics
Standards
A. General
Background
B. CC Introduction
C. Standards for
mathematical
Practice
Knowing the CCSS for mathematics
5.
Mathematical
Practices in Real
Classrooms
MP 1 -8 Connecting expected
practices and classrooms
(1 ) Knowledge of content &
pedagogy
(1) Setting instructional
outcomes
6.
Intersection of
Principles and
Practices
Understanding development of
ideas
(1) Designing coherent
instruction
7.
The Progressions
(1) Instructional Objectives
(1) Designing coherent
instruction
Module
2
PATTERNS AND RELATIONSHIPS
IN MATHEMATICS
Activities
CCSSM
1. Auditory, Physical,
Visual, Spatial Patterns
2. Hundred Board
Activities
MP7. Structure
NBT 1-2 Place value
3. Word Arithmetic
MP 7. Look for and make use of structure
MP 1. Make sense of problems; look for
entry points
MP 2. Reason abstractly and quantitatively
4. Relationships and
Properties of
Operations
MP7. Structure
OA K-2. Meaning of operations
NBT 1-2
5. Wrap Up - Connections
TDE Framework
(1) Knowledge of
content and
structure of
discipline
(1) Knowledge of
content and
structure of
discipline
(1) Knowledge of
content and
structure of
discipline
MODULE
3
Developmental Path from Counting to
Addition & Subtraction
Activities
1. Counting and Cardinality
A. First Steps: Counting &
Cardinality
B. Gelman and Gallistel’s Five
Principles of Counting
C. Numbers and Quantities
2. Constructing the Base-Ten
Number System and Place Value
A. Building the Infrastructure
B. Place value
C. PV and flexible thinking
D. Counting Beyond K
3. Number and operation in base
ten
A. Ten frames and computing
B. Decomposition as a Hallmark
of Number Sense
C. Decomposition to Knowing
10
D. Solving small problems
E. Early Experiences with
Decomposition
F. Continuum of
representations
4. Number and Operations in Base
Ten Place value, models, word
problems
A. From Knowing 10 to Making
Tens
B. Acquiring Basic Facts in a
Thinking Curriculum
C. Making Multiples of 10 with
multidigit addends
CCSSM
TDE Framework
CC K
(1) Knowledge of content and
structure of discipline
(2) Using assessment in
instruction
NBT K-2
MP 1 Making sense
MP 2 Reasoning
Sequencing learning
Supporting diverse ways of
thinking
MP 7 Looking for and
making use of structure
MP 1 Making sense
CC K
OA K-2




OA Gr. 1-2
NBT K-2
MP 2 Reasoning
MP 5 Strategic use of
tools
Supporting diverse ways of
thinking
Providing practice
Sequencing learning
Knowing difficult pts.
Providing tools
D. Games for Thinking Flexibly
E. Reflection
5. Wrap Up – Connections
Module
4
Principles, Practices, and Lessons
Activities
CCSSM
TDE Framework
1. Viewing a Lesson
Gr. 1 OA
Gr. 2 NBT
(1) Pedagogy
(1) Coherent
Instruction
(4) Reflecting on
Teaching
2. Linking the Ten
Principles to a Lesson
MP 1 Make Sense
MP 2 Reason
MP 4 Model
MP 5 Use tools strategically
(3)Engaging students in
learning
(3)Flexibility &
Responsiveness.
(3)Questioning &
Discussion
(2)Respect & rapport
3. Identifying
mathematical practices
in the lesson
MP 1 Make sense
MP 2 Reason
MP3 Construct viable
arguments
MP 8 Regulatory in repeated
reasoning
MP 4 Modeling
(4) Reflecting on
Teaching
(4) Growing and
Developing
Professionally
Module
5
Situational Context & Problem Classification
Activities
1. Discussion: Tapping Experience
CCSSM
MP 1 Making Sense
2. 2. Word Problems Research
NBT
3.
Problem Classification
TDE Framework
(2) Knowledge of students;
identifying difficulties-using
assessment in instruction
(1) Knowledge of resources
(1) Content and pedagogy
(1) Knowledge of content and
pedagogy
OA 1, 2 Represent and
solve problems
(1) Knowing stumbling blocks—
knowledge of students
4. What’s Difficult for kids (re: how
they are written)
(3) Engaging students in learning
5. Targeted Problem Creation
6. Approaching Word Problems
7. Reflections
MD 2 Relate addition and
subtraction to
length
MP 1 Making Sense
MP 4 Model
MP 5 Use tools
strategically
(1) Content & pedagogy--Building
understanding of problems
(2) Questioning & discussion
Module
6
Multiple Strategies
Activities
CCSSM
1. What is Going On?
MP 7. Look for and make use of
structure.
A. Identify Use of 10 Principles
MP 1. Make sense of problems.
B. Revisit Research on
Look for entry points.
Multiple Strategies
MP 2. Reason abstractly and
C. Solution Analysis
quantitatively.
D. Common Errors
OA 2
E. Intervention
NBT 2
2. Teaching Alternate Strategies
A. Negative Numbers
B. Compensation
3. Semi-abstract Models
(Drawings)
A. The continuum
TDE Framework
(4) Reflecting on Teaching
(1) Knowledge of Pedagogy
MP. 7 Structure
OA 1-2.
NBT 1-2
(1) Knowledge of Pedagogy
(1) Knowledge of content:
Structure of discipline
(2) Environment of Respect
MP. 5 Strategic use of tools
MP.2 Reasoning
MP.7 Structure.
NBT 1-2
(1) Pedagogy
(3) Questioning & discussion
(3) Techniques
MP.1 Make sense of problems
MP. 5 Strategic use of tools
MP.2 Reasoning
(3) Flexibility
B. Development steps (Bar/
Tape models)
C. Partner Practice
4. Strategies Carousel
5. Summation and Reflection
(4) Reflection; Professional
community
Module
7
Recording and Questioning
Activities
CCSSM
TDE Framework
1. Recording, Questioning,
Reasoning
MP 1. Make sense of problems.
Look for entry points.
MP 5. Use tools strategically
MP 4. Model mathematically
OA
NBT
(1) Knowledge of Pedagogy
(3) Communicating with
students
(3) Engaging Students in L’g.
(3) Flexibility & responsiveness
A. Tools top develop
mathematical thinking
B. Student Recording
C. Recording Progression
2. Whole Group Modeling
A. Addition
OA 1-2.
NBT 1-2
B. Subtraction: Missing
Addends
(1) Knowledge of Content &
Pedagogy
(2) Environment of Respect
(3) Engaging students in
learning
C. Recording Students’
Thoughts
3. Recording with Partners
MP 1 Making sense
NBT 1- 2 decomposition
(3) Instructional Technique
(3) Demonstrating flexibility &
responsiveness
MP Strategic use of tools
MP Reasoning
MP7. Structure.
NBT 1-2
(1) Pedagogy
(3) Questioning & discussion
(3) Instructional techniques
A. Student Readiness to
Record
B. Partner Practice
4. Front and Center for Dress
Rehearsal!
5. The Teacher and Classroom
Discourse
A. Classroom Discussion
Challenges
B. Questions That Prompt
Mathematical Thinking
6. Summation and Reflection
K OA. 4 (record)
2 NBT. 7
2 NBT.9 (explain)
(1) Knowledge of content &
pedagogy
(2) Questioning & discussion
techniques
(3) Communicating with
students
(1) Knowledge of resources
(1) Setting instructional
outcomes
(4) Reflection; Professional
community
Module
8
Seeding Multiplication and Fractions
Activities
CCSSM
1. Focused Reading of
Standards
2. Building a Sense of
Groups
a. Pairs all around
b. Circles and Stars
c. Equal groups as
arrays
3. Early Fraction
Experiences
a. Focus on the
standard
4. Wrap up
TDE Framework
(1) Instructional
outcomes
CCSS introduction - Focus and
coherence
MP 1 Making sense of problems
(1) Knowledge of content
and pedagogy
MP 8 Constructing a valid
argument
(1) Knowledge of content
and pedagogy
Module
9
Building Strong Math Lessons
Activities
1.
Big Ideas
2.
Lessons, Units &
Trajectories
3.
CCSSM
TDE Framework
Connecting the Operations & Algebra
and Number & Operations in Base Ten
Progressions to the Big Ideas in
mathematics
CCSSM Progressions identify points on
the way to achieving standards and
learning trajectories help sequence and
build the steps needed.
(1) Knowledge of content and
sequence
(1) Instructional outcomes
Research on Strong
Math Lessons
CCSS introduction -Focus and coherence
MP 1 Making sense of problems
MP 2 Reasoning
MP 3 Building arguments
4.
Cognitive Level of Math
Tasks
MP1 Making sense
MP 2 Reasoning
MP 4 Model with mathematics
5.
Wrap-Up
(1) Setting instructional
outcomes
(2) Environment of Respect &
Rapport
(3) Questioning & discussion
techniques
(3) Flexibility & responsiveness
(1) Knowledge of content &
pedagogy
(1) Knowledge of students
(3) Questioning & Discussion
(3) Engaging students in
Learning
(1) Knowledge of content &
pedagogy
(1) Setting instructional
outcomes
(1) Designing coherent
instruction
(1) Content and contentrelated pedagogy
(1) Instructional outcomes;
value, sequence, alignment
(1) Prerequisites