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Understanding Primary Math

Home
Why we Learn Math in School?
Why Math is Best Suited to Develop Thinking Skills
The Reality of Math Education in Indian Schools
How I Relearnt Primary School Math
Documenting My Understanding of Primary Math
The Primary Math Project
Understanding Primary Math – For Effective Teaching
Structure of the Book (A)
Math and Our Brain
Math Prior to Schooling
Early Days of Math in School
Perceptual Numbers
Strengthening Perceptual Numbers
Pre-Number Concepts 1
Pre-Number Concepts 2
Pre-Number Concepts 3
Spatial Skills
What is a Number?
Numbers and Magnitudes
Development of Number Sense 1
Development of Number Sense 2(A)
Activity Based Learning
Learning Numbers - Framework for Activities(A)
Advantages of ABL
Single Digit Numbers
Representing Numbers 1-9
Representation of Single Digit Numbers – By Matching(A)
Representing Numbers 1-9 using real life examples (A)
Finger Representation 1
Importance of Fingers in Math
Knowledge for Class 1
Cardinal & Ordinal Numbers
Simple Counting 1
Simple Counting 2
Complex Counting
Aggregating Systems
Place Value Systems
Difficulties with the Place Value Concept
What is Zero?
Zero as a Number
Impact of Zero
Place Value System - 1
Place Value System - 2
Understanding Place Value (A)
Visualizing Place Value 1
Visualizing Place Value 2
Advantages of the Place Value System 1
Advantages of the Place Value System 2
Non-Standard Representations
Non-Decimal Place Value Systems
Test for Understanding Place Value
Representing Numbers 0-99
Number Representation - 2-digit numbers(A)
Finger Representation 2
Representing Numbers 0 – 999
Word Representation of Numbers
Comprehending Very Large Numbers
Number Names – Indian Tradition
Digit, Numeral & Number
Properties of Numbers 1
Properties of Numbers 2
Properties of Number Sets
Relations Between Numbers
Triangle & Square Numbers
Number Theory
Prime Numbers
Fundamental Theorem of Arithmetic
Why is Zero an even number?
Operations involving 0
Arithmetic Operation Metaphors
Summary of Operation Metaphors
Addition Metaphors 1
Addition Metaphors 2
Subtraction Metaphors 1
Subtraction Metaphors 2
More Addition & Subtraction Metaphors
Addition & Subtraction Vocabulary(A)
Division Metaphors 1
Division Metaphors 2
Origins of Multiplication
Multiplication Metaphors 1
Multiplication Metaphors 2
Multiplication Metaphors 3
Teaching Operation Metaphors 1
Teaching Operation Metaphors 2
Neglect of Metaphors
Exponents
Scientific Notation
Abacus Vs Algorithm
Arithmetic Operations
Addition
Subtraction
Addition Fluency 1
Addition Fluency 2
Addition Fluency 3
Subtraction Fluency
Multiplication 1
Multiplication 2
Multiplication Tables
Constructing the Multiplication Table
One Page Multiplication Table(A)
Patterns in the Multiplication Table
Remembering Multiplication Facts
Multiplication – Other Methods
Multiplication with Fingers
Logic of Finger Multiplication
Division 1
Division 2
Division by 1-Digit Number(A)
Division by 2-Digit Number 1(A)
Division by 2-Digit Number 2(A)
Multiplication table for 2-digit number(A)
Divisibility Rules
What is Number Sense?
Number Sense
Number Sense is Critical
Development of Number Sense
Teaching Number Sense
The Number Line 1
Strengthening Number Sense 1
Strengthening Number Sense 2
Operational Fluency
Number & Math Talks
Problem Strings
Number Patterns with 36 Tokens(A)
Computing 18 X 5(A)
Language & Mathematics 1
Language & Mathematics 2
Language & Mathematics 3
Words with Multiple Meanings(A)
Math as a Language 1
Math as a Language 2(A)
Math Words in Daily Language
Math Notations & Symbols
A list of Symbol Names
Multiple Meanings of the = & - Signs
Language & Word Problems
Purpose of Word Problems
Understanding Word Problems 1
Understanding Word Problems 2
Solving Word Problems 1
Teaching Word Problems
Constructing Word Problems
Components of a Math Story(A)
Solving Word Problems 2
Word Problems on Number Properties
Problems With Multiple Answers
Numberless Word Problems
Understanding Fractions
Difficulties with Fractions
Fractions as Numbers 1
Fractions as Numbers 2
Fractions - Two Perspectives
Representing Fractions 1
Representing Fractions 2
Representing Fractions 3
Types of Fractions
Equivalent Fractions
Whole & Part
Properties & Relations of Fractions
Addition of Fractions 1
Addition of Fractions 2
Addition of Fractions 2 Addition of Fractions 3
Number Sense in Fractions
Fraction Multiplication
Fraction Division
Rational Numbers
Word Problems in Fractions 1
Word Problems in Fractions 2
Understanding Decimal Fractions 1
Understanding Decimal Fractions 2
Representing Decimal Fractions
Converting to Decimal Fractions 1
Converting to Decimal Fractions 2
Converting from Decimal Fractions
Operations on Decimal Fractions 1
Operations on Decimal Fractions 2
Decimals in Daily Life
Irrational Numbers
Inculcating Reasoning Skills
Additive & Multiplicative Thinking
Additive Thinking
Multiplicative Thinking 1
Multiplicative Thinking 2
Proportional Thinking
Problems to Think About
Ratio Table
Problems with Multiple Answers
Ratios
Ratios in Daily Life
Ratios & Fractions
Math of Proportions
Understanding Integers 1
Understanding Integers 2
Representation of Integers
Integer Experiences in Daily Life
Integer Operations - 1
Integer Operations - 2
integer Multiplication 1 (A)
Integer Addition (A)
Integer Subtraction (A)
Integer Multiplication 2 (A)
Integers in the Classroom - 1
Integers in the Classroom - 2
Integer Additions With Bottle Tops (A)
Axioms of Arithmetic 1
Axioms of Arithmetic 2
Fundamental Laws of Arithmetic
Axiom of Closure
Order of Operations
Properties & Relations of Operations
Development of Numbers 1
Development of Numbers 2
Development of Numbers 3
The Number Line 2
Development of Numbers 4
Classification of Numbers 1(A)
Classification of Numbers 2(A)
What is Geometry
Geometry Curriculum Framework(A)
Space We Live In
Solids
Plane Geometry
Lines & Points
Multiple Lines & Shapes 1
Paper Folding Activities(A)
Multiple Lines & Shapes 2
Understanding Angles 1
Understanding Angles 2
Angles – Critical Thinking(A)
More About Angles
Angle Types & Measures 1
Angle Types & Measures 2
Special Pairs of Angles 1
Special Pairs of Angles 2
Parallel Lines
Operations with Angles
Triangles - Basic Concepts
Types of Triangles
Types of Triangles(A)
Triangles – Four Centres
Triangles – Congruency & Similarity
Triangle Concepts Summary(A)
Properties of Triangles - Activity
Pythagoras Theorem
Pythagoras Theorem – A Visual Proof(A)
Quadrilaterals
Types of Quadrilaterals(A)
Parallelogram Family
Other Polygons
Curved Figures
Symmetry of Plane Figures
Circles 1
Circles 2
Conic Sections
Finding Approximate Value of π
Geometric Solids
Understanding Measurement
Story of Measurement 1
Measurement of Time
Story of Measurement 2
International System of Measurements
The SI System
Measurement – The Future
Perimeter
Area
Activities on Perimeter & Area(A)
Volume & Surface Area
Math and Other School Subjects
Math & Physical Sciences
Math & Social Sciences
Math & Geography
Math & Astronomy
Math & Biological Sciences
Math & Performing Arts
Math & Visual Arts
Math & Sports
Math & Computer Science
Statistics
Presenting Data
Interpreting Data
Expenses & Income
Understanding Business
Understanding Percentage
Sale Purchase, Profit & Loss
Work, Labor & Wages
Banking Operations
Algebraic Thinking
Variables & Constants
Language of Algebra
Algebraic Expressions 1
Algebraic Expressions 2
Visualizing Algebraic Expressions 1
Visualizing Algebraic Patterns(A)
Visualizing Algebraic Expressions 2
Simple Equations
Solving Simple Equations
Coordinate Geometry
Types of Thinking
What is Mathematical Thinking?
Euclid & Logical Thinking
Logic & Proof – 1
Logic & Proof – 2
Proofs by Sight
Euclid’s Fifth Postulate
Proof in Indian Mathematics
Computational Thinking
Criticality of Primary Math
Role of Writing in Math
Numbers in Pre-Primary
Numbers in Primary K-5
Math Through Activities
Studying History of Math
Mathemagic Centre
Math Bulletin Boards
Misconceptions in School Math 1
Misconceptions in School Math 2
Unstated Assumptions
The Problem With Math Textbooks
Math in the Primary School - A Honest Look
Primary Math Curriculum – A Relook
Primary Math Curriculum – Graphic Framework(A)
Recreational Math
Folk Mathematics
Math Explorations
Magic Squares
Math Puzzles
Math Games
Math Jokes
Math Cartoons
Math Poems
Number Patterns
Math Puns
Math Related Idioms & Proverbs
Math Projects
The Number π
Fibonacci Sequence & the Golden Ratio
Important Math Days
Fermat’s Last Theorem
Bridges of Konigsberg
Famous Conjectures
Math Quotations
Excerpts from Books on Math
Modular Arithmetic
Logarithms
Spherical Geometry
Volume Relations
Factorials
Infinity
Proofs Without Words
Four Colour Map Theorem
The Mobius Strip
Beauty & Math
Dyscalculia
Math Savants
Math Phobia
Concepts & Conventions
Transcendental Numbers
Imaginary & complex Numbers
Role of Jokes in Math
Words for Huge Numbers
Set Theory
Non-Numerical Math Activities
Random Numbers
A Time Line for Math
Movies Based in Math
Fields Medal
Indian Mathematical Tradition
Srinivasa Ramanujan
National Mathematics Day
Vedic mathematics
Math & Sciences - A Symbiotic Relation
Math & the Sciences as Twins
Math - the Toolkit of the Sciences
Rhetorical Math to Symbolic Math
Math - the Vehicle of the Sciences
Math - the Engine of the Sciences
Self-Propelled Math
What is Mathematics 1
What is Mathematics 2
Nature of School Math
Factual Knowledge
Conceptual Knowledge
Procedural Knowledge
Attitudes & Beliefs
Definitions of Math
Power and Limits of Math
Math - Discovered or Invented?
Transformation of Math - 1
Transformation of Math - 2
Transformation of Math - 3
Teaching Concepts
Teaching Facts & Information
Teaching Procedures
How Do You Teach Number Three?
Bibliography

Understanding Primary Math

Home
Why we Learn Math in School?
Why Math is Best Suited to Develop Thinking Skills
The Reality of Math Education in Indian Schools
How I Relearnt Primary School Math
Documenting My Understanding of Primary Math
The Primary Math Project
Understanding Primary Math – For Effective Teaching
Structure of the Book (A)
Math and Our Brain
Math Prior to Schooling
Early Days of Math in School
Perceptual Numbers
Strengthening Perceptual Numbers
Pre-Number Concepts 1
Pre-Number Concepts 2
Pre-Number Concepts 3
Spatial Skills
What is a Number?
Numbers and Magnitudes
Development of Number Sense 1
Development of Number Sense 2(A)
Activity Based Learning
Learning Numbers - Framework for Activities(A)
Advantages of ABL
Single Digit Numbers
Representing Numbers 1-9
Representation of Single Digit Numbers – By Matching(A)
Representing Numbers 1-9 using real life examples (A)
Finger Representation 1
Importance of Fingers in Math
Knowledge for Class 1
Cardinal & Ordinal Numbers
Simple Counting 1
Simple Counting 2
Complex Counting
Aggregating Systems
Place Value Systems
Difficulties with the Place Value Concept
What is Zero?
Zero as a Number
Impact of Zero
Place Value System - 1
Place Value System - 2
Understanding Place Value (A)
Visualizing Place Value 1
Visualizing Place Value 2
Advantages of the Place Value System 1
Advantages of the Place Value System 2
Non-Standard Representations
Non-Decimal Place Value Systems
Test for Understanding Place Value
Representing Numbers 0-99
Number Representation - 2-digit numbers(A)
Finger Representation 2
Representing Numbers 0 – 999
Word Representation of Numbers
Comprehending Very Large Numbers
Number Names – Indian Tradition
Digit, Numeral & Number
Properties of Numbers 1
Properties of Numbers 2
Properties of Number Sets
Relations Between Numbers
Triangle & Square Numbers
Number Theory
Prime Numbers
Fundamental Theorem of Arithmetic
Why is Zero an even number?
Operations involving 0
Arithmetic Operation Metaphors
Summary of Operation Metaphors
Addition Metaphors 1
Addition Metaphors 2
Subtraction Metaphors 1
Subtraction Metaphors 2
More Addition & Subtraction Metaphors
Addition & Subtraction Vocabulary(A)
Division Metaphors 1
Division Metaphors 2
Origins of Multiplication
Multiplication Metaphors 1
Multiplication Metaphors 2
Multiplication Metaphors 3
Teaching Operation Metaphors 1
Teaching Operation Metaphors 2
Neglect of Metaphors
Exponents
Scientific Notation
Abacus Vs Algorithm
Arithmetic Operations
Addition
Subtraction
Addition Fluency 1
Addition Fluency 2
Addition Fluency 3
Subtraction Fluency
Multiplication 1
Multiplication 2
Multiplication Tables
Constructing the Multiplication Table
One Page Multiplication Table(A)
Patterns in the Multiplication Table
Remembering Multiplication Facts
Multiplication – Other Methods
Multiplication with Fingers
Logic of Finger Multiplication
Division 1
Division 2
Division by 1-Digit Number(A)
Division by 2-Digit Number 1(A)
Division by 2-Digit Number 2(A)
Multiplication table for 2-digit number(A)
Divisibility Rules
What is Number Sense?
Number Sense
Number Sense is Critical
Development of Number Sense
Teaching Number Sense
The Number Line 1
Strengthening Number Sense 1
Strengthening Number Sense 2
Operational Fluency
Number & Math Talks
Problem Strings
Number Patterns with 36 Tokens(A)
Computing 18 X 5(A)
Language & Mathematics 1
Language & Mathematics 2
Language & Mathematics 3
Words with Multiple Meanings(A)
Math as a Language 1
Math as a Language 2(A)
Math Words in Daily Language
Math Notations & Symbols
A list of Symbol Names
Multiple Meanings of the = & - Signs
Language & Word Problems
Purpose of Word Problems
Understanding Word Problems 1
Understanding Word Problems 2
Solving Word Problems 1
Teaching Word Problems
Constructing Word Problems
Components of a Math Story(A)
Solving Word Problems 2
Word Problems on Number Properties
Problems With Multiple Answers
Numberless Word Problems
Understanding Fractions
Difficulties with Fractions
Fractions as Numbers 1
Fractions as Numbers 2
Fractions - Two Perspectives
Representing Fractions 1
Representing Fractions 2
Representing Fractions 3
Types of Fractions
Equivalent Fractions
Whole & Part
Properties & Relations of Fractions
Addition of Fractions 1
Addition of Fractions 2
Addition of Fractions 2 Addition of Fractions 3
Number Sense in Fractions
Fraction Multiplication
Fraction Division
Rational Numbers
Word Problems in Fractions 1
Word Problems in Fractions 2
Understanding Decimal Fractions 1
Understanding Decimal Fractions 2
Representing Decimal Fractions
Converting to Decimal Fractions 1
Converting to Decimal Fractions 2
Converting from Decimal Fractions
Operations on Decimal Fractions 1
Operations on Decimal Fractions 2
Decimals in Daily Life
Irrational Numbers
Inculcating Reasoning Skills
Additive & Multiplicative Thinking
Additive Thinking
Multiplicative Thinking 1
Multiplicative Thinking 2
Proportional Thinking
Problems to Think About
Ratio Table
Problems with Multiple Answers
Ratios
Ratios in Daily Life
Ratios & Fractions
Math of Proportions
Understanding Integers 1
Understanding Integers 2
Representation of Integers
Integer Experiences in Daily Life
Integer Operations - 1
Integer Operations - 2
integer Multiplication 1 (A)
Integer Addition (A)
Integer Subtraction (A)
Integer Multiplication 2 (A)
Integers in the Classroom - 1
Integers in the Classroom - 2
Integer Additions With Bottle Tops (A)
Axioms of Arithmetic 1
Axioms of Arithmetic 2
Fundamental Laws of Arithmetic
Axiom of Closure
Order of Operations
Properties & Relations of Operations
Development of Numbers 1
Development of Numbers 2
Development of Numbers 3
The Number Line 2
Development of Numbers 4
Classification of Numbers 1(A)
Classification of Numbers 2(A)
What is Geometry
Geometry Curriculum Framework(A)
Space We Live In
Solids
Plane Geometry
Lines & Points
Multiple Lines & Shapes 1
Paper Folding Activities(A)
Multiple Lines & Shapes 2
Understanding Angles 1
Understanding Angles 2
Angles – Critical Thinking(A)
More About Angles
Angle Types & Measures 1
Angle Types & Measures 2
Special Pairs of Angles 1
Special Pairs of Angles 2
Parallel Lines
Operations with Angles
Triangles - Basic Concepts
Types of Triangles
Types of Triangles(A)
Triangles – Four Centres
Triangles – Congruency & Similarity
Triangle Concepts Summary(A)
Properties of Triangles - Activity
Pythagoras Theorem
Pythagoras Theorem – A Visual Proof(A)
Quadrilaterals
Types of Quadrilaterals(A)
Parallelogram Family
Other Polygons
Curved Figures
Symmetry of Plane Figures
Circles 1
Circles 2
Conic Sections
Finding Approximate Value of π
Geometric Solids
Understanding Measurement
Story of Measurement 1
Measurement of Time
Story of Measurement 2
International System of Measurements
The SI System
Measurement – The Future
Perimeter
Area
Activities on Perimeter & Area(A)
Volume & Surface Area
Math and Other School Subjects
Math & Physical Sciences
Math & Social Sciences
Math & Geography
Math & Astronomy
Math & Biological Sciences
Math & Performing Arts
Math & Visual Arts
Math & Sports
Math & Computer Science
Statistics
Presenting Data
Interpreting Data
Expenses & Income
Understanding Business
Understanding Percentage
Sale Purchase, Profit & Loss
Work, Labor & Wages
Banking Operations
Algebraic Thinking
Variables & Constants
Language of Algebra
Algebraic Expressions 1
Algebraic Expressions 2
Visualizing Algebraic Expressions 1
Visualizing Algebraic Patterns(A)
Visualizing Algebraic Expressions 2
Simple Equations
Solving Simple Equations
Coordinate Geometry
Types of Thinking
What is Mathematical Thinking?
Euclid & Logical Thinking
Logic & Proof – 1
Logic & Proof – 2
Proofs by Sight
Euclid’s Fifth Postulate
Proof in Indian Mathematics
Computational Thinking
Criticality of Primary Math
Role of Writing in Math
Numbers in Pre-Primary
Numbers in Primary K-5
Math Through Activities
Studying History of Math
Mathemagic Centre
Math Bulletin Boards
Misconceptions in School Math 1
Misconceptions in School Math 2
Unstated Assumptions
The Problem With Math Textbooks
Math in the Primary School - A Honest Look
Primary Math Curriculum – A Relook
Primary Math Curriculum – Graphic Framework(A)
Recreational Math
Folk Mathematics
Math Explorations
Magic Squares
Math Puzzles
Math Games
Math Jokes
Math Cartoons
Math Poems
Number Patterns
Math Puns
Math Related Idioms & Proverbs
Math Projects
The Number π
Fibonacci Sequence & the Golden Ratio
Important Math Days
Fermat’s Last Theorem
Bridges of Konigsberg
Famous Conjectures
Math Quotations
Excerpts from Books on Math
Modular Arithmetic
Logarithms
Spherical Geometry
Volume Relations
Factorials
Infinity
Proofs Without Words
Four Colour Map Theorem
The Mobius Strip
Beauty & Math
Dyscalculia
Math Savants
Math Phobia
Concepts & Conventions
Transcendental Numbers
Imaginary & complex Numbers
Role of Jokes in Math
Words for Huge Numbers
Set Theory
Non-Numerical Math Activities
Random Numbers
A Time Line for Math
Movies Based in Math
Fields Medal
Indian Mathematical Tradition
Srinivasa Ramanujan
National Mathematics Day
Vedic mathematics
Math & Sciences - A Symbiotic Relation
Math & the Sciences as Twins
Math - the Toolkit of the Sciences
Rhetorical Math to Symbolic Math
Math - the Vehicle of the Sciences
Math - the Engine of the Sciences
Self-Propelled Math
What is Mathematics 1
What is Mathematics 2
Nature of School Math
Factual Knowledge
Conceptual Knowledge
Procedural Knowledge
Attitudes & Beliefs
Definitions of Math
Power and Limits of Math
Math - Discovered or Invented?
Transformation of Math - 1
Transformation of Math - 2
Transformation of Math - 3
Teaching Concepts
Teaching Facts & Information
Teaching Procedures
How Do You Teach Number Three?
Bibliography
More

Development of Number Sense 2(A)

The website and book development is done by his proud grandson, Vedh Krishnan

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