Comprehensive Singapore Math Curriculum Map (Ages 3-12)

 Comprehensive Singapore Math Curriculum Map (Ages 3-12)

INTRODUCTION TO SINGAPORE MATH

Singapore Math is distinguished by its concrete-pictorial-abstract (CPA) approach, which ensures deep conceptual understanding before moving to abstract mathematics. This curriculum map provides a comprehensive guide for educators and homeschool parents, detailing the progression of mathematical concepts from ages 3-12, with specific manipulatives, methodologies, and mastery benchmarks.

EARLY YEARS (AGES 3-5)

AGE 3-4 (NURSERY/PRE-K)

NUMBER SENSE FOUNDATIONS

Key Concepts:

• Counting sequence 1-10
• One-to-one correspondence
• Number recognition
• Sorting and classification
• Basic shapes recognition
• Simple patterns

Manipulatives and Materials:

• Counting bears/cubes
• Sorting trays and objects
• Number cards with dots
• Magnetic numbers
• Shape blocks
• Pattern blocks

Concrete Stage Activities:

1. Counting Objects:

   • Teacher demonstration: Count objects one by one, touching each while saying the number
   • Student activity: Count various sets of objects up to 5, then 10
   • Frequency: Daily, 5-10 minutes
   • Mastery indicator: Accurately counts objects to 10 with one-to-one correspondence

2. Sorting Activities:

   • Teacher demonstration: Sort objects by one attribute (color, size, shape)
   • Student activity: Sort collections by given attributes
   • Frequency: 3 times weekly, 10 minutes
   • Mastery indicator: Sorts objects correctly by a single attribute

3. Shape Exploration:

   • Teacher demonstration: Introduce basic shapes with 3D objects
   • Student activity: Find examples of shapes in the environment
   • Frequency: 2 times weekly, 10 minutes
   • Mastery indicator: Names and identifies circle, square, triangle, rectangle

Pictorial Stage Activities:

1. Number Cards with Pictures:

   • Teacher demonstration: Match quantity pictures with numbers
   • Student activity: Match cards showing different quantities of the same object
   • Frequency: 3 times weekly, 10 minutes
   • Mastery indicator: Connects quantities 1-10 with correct numerals

2. Pattern Card Matching:

   • Teacher demonstration: Show simple AB patterns with pictures
   • Student activity: Continue or copy simple picture patterns
   • Frequency: 2 times weekly, 10 minutes
   • Mastery indicator: Continues an AB pattern correctly

End-of-Year Competencies:

• Counts verbally to 20
• Recognizes numerals 1-10
• Counts up to 10 objects accurately
• Sorts objects by one attribute
• Creates and continues simple patterns
• Recognizes and names basic shapes

AGE 4-5 (KINDERGARTEN 1)

EXTENDED NUMBER SENSE

Key Concepts:

• Counting sequence 1-20
• Comparing quantities (more/less/same)
• Beginning addition/subtraction concepts
• Simple measurement comparisons
• Pattern creation
• Positional language

Manipulatives and Materials:

• Ten frames
• Connecting cubes
• Balance scales
• Measurement tools (non-standard)
• Pattern blocks
• Position cards

Concrete Stage Activities:

1. Ten Frames:

   • Teacher demonstration: Place counters on ten frames to show numbers
   • Student activity: Represent numbers using ten frames and counters
   • Frequency: 3 times weekly, 15 minutes
   • Mastery indicator: Quickly represents numbers to 10 on ten frames

2. Comparison Activities:

   • Teacher demonstration: Compare two sets using terms "more," "less," "same"
   • Student activity: Create sets with more/less/same objects
   • Frequency: 2 times weekly, 15 minutes
   • Mastery indicator: Accurately compares quantities up to 10

3. Beginning Addition Scenarios:

   • Teacher demonstration: Model combining sets with manipulatives
   • Student activity: Create "adding stories" with objects
   • Frequency: 2 times weekly, 15 minutes
   • Mastery indicator: Combines small sets and counts total

Pictorial Stage Activities:

1. Comparison Cards:

   • Teacher demonstration: Compare picture cards showing different quantities
   • Student activity: Arrange picture cards by quantity
   • Frequency: 2 times weekly, 15 minutes
   • Mastery indicator: Orders pictures by quantity correctly

2. Simple Pictorial Addition:

   • Teacher demonstration: Show pictures of objects combining
   • Student activity: Draw simple addition scenarios
   • Frequency: 2 times weekly, 15 minutes
   • Mastery indicator: Represents addition stories with pictures

End-of-Year Competencies:

• Counts verbally to 30
• Recognizes and writes numerals 1-20
• Counts up to 20 objects accurately
• Compares sets using appropriate language
• Demonstrates understanding of addition as combining
• Creates patterns with 2-3 elements
• Uses positional vocabulary correctly

AGE 5-6 (KINDERGARTEN 2)

NUMBER OPERATIONS FOUNDATION

Key Concepts:

• Numbers to 100
• Addition and subtraction within 10
• Simple word problems
• Measurement with non-standard units
• Time concepts (days, hours)
• 2D and 3D shapes
• Data collection and simple graphs

Manipulatives and Materials:

• Number bonds materials
• Part-whole mats
• Unifix cubes
• Base-10 blocks (introduction)
• Non-standard measuring tools
• Shape blocks and solids
• Pictographs materials

Concrete Stage Activities:

1. Number Bonds:

   • Teacher demonstration: Show parts-whole relationships with manipulatives
   • Student activity: Create different number bonds for numbers to 10
   • Frequency: 3 times weekly, 20 minutes
   • Mastery indicator: Finds all number bonds for numbers to 10

2. Base-10 Introduction:

   • Teacher demonstration: Group objects by tens and ones
   • Student activity: Represent two-digit numbers with grouped objects
   • Frequency: 2 times weekly, 20 minutes
   • Mastery indicator: Represents numbers to 20 with tens and ones

3. Addition and Subtraction with Manipulatives:

   • Teacher demonstration: Model addition/subtraction stories with objects
   • Student activity: Solve simple word problems using manipulatives
   • Frequency: Daily, 20 minutes
   • Mastery indicator: Solves addition/subtraction problems within 10

Pictorial Stage Activities:

1. Number Bond Diagrams:

   • Teacher demonstration: Draw number bond diagrams for numbers
   • Student activity: Complete number bond worksheets
   • Frequency: 3 times weekly, 15 minutes
   • Mastery indicator: Correctly completes number bond diagrams

2. Bar Model Introduction:

   • Teacher demonstration: Draw simple bar models for part-whole relationships
   • Student activity: Match bar models to number bonds
   • Frequency: 2 times weekly, 15 minutes
   • Mastery indicator: Understands basic bar model representation

Abstract Stage Activities:

1. Number Sentences:
   • Teacher demonstration: Write number sentences for addition/subtraction
   • Student activity: Create number sentences for simple scenarios
   • Frequency: 3 times weekly, 15 minutes
   • Mastery indicator: Writes correct number sentences for addition/subtraction within 10

End-of-Year Competencies:

• Counts to 100
• Recognizes numbers to 100
• Writes numbers to 20
• Creates all number bonds to 10
• Adds and subtracts within 10 fluently
• Represents simple word problems with objects
• Measures using non-standard units
• Identifies 2D and 3D shapes
• Creates and interprets simple pictographs

PRIMARY YEARS (GRADES 1-3)

GRADE 1 (AGE 6-7)

NUMBER AND OPERATIONS TO 100

Key Concepts:

• Numbers to 100
• Addition and subtraction within 100
• Place value (tens and ones)
• Mental math strategies
• Multiplication as repeated addition
• Division as sharing
• Money (coins and bills)
• Measurement (length, weight)
• Time (hour and half-hour)

Manipulatives and Materials:

• Base-10 blocks
• Place value charts
• Number bond cards
• Bar model templates
• Play money
• Measurement tools
• Clock manipulatives

Concrete Stage Activities:

1. Place Value with Base-10 Blocks:

   • Teacher demonstration: Represent two-digit numbers with blocks
   • Student activity: Model numbers with tens and ones blocks
   • Frequency: 3 times weekly, 20 minutes
   • Mastery indicator: Accurately represents two-digit numbers

2. Addition with Regrouping:

   • Teacher demonstration: Show regrouping with base-10 blocks
   • Student activity: Practice addition requiring regrouping with blocks
   • Frequency: 3 times weekly, 20 minutes
   • Mastery indicator: Explains and demonstrates regrouping

3. Subtraction with Regrouping:

   • Teacher demonstration: Model "trading" a ten for ten ones
   • Student activity: Practice subtraction requiring regrouping
   • Frequency: 3 times weekly, 20 minutes
   • Mastery indicator: Accurately performs subtraction with regrouping

Pictorial Stage Activities:

1. Bar Models for Word Problems:

   • Teacher demonstration: Draw part-whole and comparison bar models
   • Student activity: Create bar models for simple word problems
   • Frequency: 3 times weekly, 25 minutes
   • Mastery indicator: Correctly represents problems with bar models

2. Place Value Drawings:

   • Teacher demonstration: Draw tens as lines and ones as dots
   • Student activity: Represent numbers with place value drawings
   • Frequency: 2 times weekly, 20 minutes
   • Mastery indicator: Creates accurate pictorial representations

Abstract Stage Activities:

1. Mental Math Strategies:

   • Teacher demonstration: Model adding/subtracting by place value
   • Student activity: Practice mental calculation strategies
   • Frequency: Daily, 15 minutes
   • Mastery indicator: Uses place value for mental calculations

2. Number Sentences for Word Problems:

   • Teacher demonstration: Translate word problems to equations
   • Student activity: Write equations for various problem types
   • Frequency: 3 times weekly, 25 minutes
   • Mastery indicator: Creates correct equations for problems

End-of-Year Competencies:

• Understands place value to 100
• Adds and subtracts within 100, with and without regrouping
• Solves one-step word problems with bar models
• Demonstrates beginning understanding of multiplication
• Tells time to the half-hour
• Measures length and weight with standard units
• Recognizes and uses coins and bills

GRADE 2 (AGE 7-8)

OPERATIONS TO 1000 AND FOUNDATIONS OF MULTIPLICATION/DIVISION

Key Concepts:

• Numbers to 1000
• Addition and subtraction within 1000
• Place value (hundreds, tens, ones)
• Multiplication tables (2, 3, 4, 5, 10)
• Division with remainders
• Fractions (halves, thirds, fourths)
• Money (making change)
• Measurement (meter, centimeter, kilogram)
• Time (5-minute intervals)
• Picture graphs and bar graphs

Manipulatives and Materials:

• Base-10 blocks (expanded use)
• Place value charts
• Multiplication arrays
• Equal sharing materials
• Fraction circles/bars
• Measurement tools
• Money manipulatives
• Graph templates

Concrete Stage Activities:

1. Place Value with Three-Digit Numbers:

   • Teacher demonstration: Represent three-digit numbers with blocks
   • Student activity: Model numbers with hundreds, tens, and ones
   • Frequency: 2 times weekly, 20 minutes
   • Mastery indicator: Accurately represents three-digit numbers

2. Multiplication with Arrays:

   • Teacher demonstration: Show multiplication as arrays
   • Student activity: Create arrays for multiplication facts
   • Frequency: 3 times weekly, 25 minutes
   • Mastery indicator: Builds arrays for multiplication facts

3. Division as Equal Sharing:

   • Teacher demonstration: Model division with manipulatives
   • Student activity: Share objects equally among groups
   • Frequency: 3 times weekly, 25 minutes
   • Mastery indicator: Demonstrates division with objects

4. Fraction Models:

   • Teacher demonstration: Show fractions with area models
   • Student activity: Create models showing halves, thirds, fourths
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Accurately represents simple fractions

Pictorial Stage Activities:

1. Bar Models for Multi-Step Problems:

   • Teacher demonstration: Draw models for two-step problems
   • Student activity: Create bar models for various problem types
   • Frequency: 3 times weekly, 25 minutes
   • Mastery indicator: Uses bar models effectively for problem-solving

2. Multiplication Drawings:

   • Teacher demonstration: Draw repeated groups for multiplication
   • Student activity: Represent multiplication scenarios with pictures
   • Frequency: 2 times weekly, 20 minutes
   • Mastery indicator: Creates pictorial multiplication representations

Abstract Stage Activities:

1. Mental Math with Three-Digit Numbers:

   • Teacher demonstration: Model breaking numbers by place value
   • Student activity: Practice calculation strategies
   • Frequency: Daily, 15 minutes
   • Mastery indicator: Uses effective mental calculation strategies

2. Multi-Step Problem Solving:

   • Teacher demonstration: Show approach to two-step problems
   • Student activity: Solve problems requiring multiple operations
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Solves two-step word problems correctly

End-of-Year Competencies:

• Understands place value to 1000
• Adds and subtracts within 1000 fluently
• Knows multiplication facts for 2, 3, 4, 5, 10
• Divides using facts from multiplication tables
• Recognizes and represents simple fractions
• Solves two-step word problems using bar models
• Tells time to 5-minute intervals
• Creates and interprets simple graphs
• Makes change with money

GRADE 3 (AGE 8-9)

MULTIPLICATION, DIVISION, AND FRACTIONS

Key Concepts:

• Numbers to 10,000
• Addition and subtraction within 10,000
• Multiplication tables (completed 0-10)
• Division with and without remainders
• Fractions (equivalent, comparison)
• Measurement (mass, volume, length)
• Time (minute)
• Area and perimeter
• Bar graphs and line plots

Manipulatives and Materials:

• Place value charts and materials
• Multiplication grid
• Division boards
• Fraction strips and circles
• Area and perimeter materials
• Measurement tools
• Graph paper

Concrete Stage Activities:

1. Multi-Digit Multiplication:

   • Teacher demonstration: Model multiplication with base-10 materials
   • Student activity: Calculate products using manipulatives
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Accurately multiplies 2-digit by 1-digit numbers

2. Long Division Process:

   • Teacher demonstration: Show division process with manipulatives
   • Student activity: Perform division with concrete materials
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Demonstrates division algorithm with materials

3. Fraction Comparison:

   • Teacher demonstration: Show comparing fractions with same denominator
   • Student activity: Use fraction strips to compare fractions
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Accurately compares fractions with models

4. Area and Perimeter Models:

   • Teacher demonstration: Show area and perimeter with unit squares
   • Student activity: Calculate area and perimeter of shapes
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Finds area and perimeter accurately

Pictorial Stage Activities:

1. Bar Models for Multiplication/Division:

   • Teacher demonstration: Draw models for multiplication/division
   • Student activity: Create bar models for various problem types
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Uses bar models for multiplication/division problems

2. Fraction Diagrams:

   • Teacher demonstration: Draw fraction representations
   • Student activity: Create pictorial models of fractions
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Represents fractions accurately in diagrams

Abstract Stage Activities:

1. Multi-Digit Computation:

   • Teacher demonstration: Show standard algorithms
   • Student activity: Practice computation with efficient methods
   • Frequency: Daily, 20 minutes
   • Mastery indicator: Uses algorithms correctly and efficiently

2. Complex Problem Solving:

   • Teacher demonstration: Model multi-step problem approach
   • Student activity: Solve challenging word problems
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Systematically solves complex problems

End-of-Year Competencies:

• Understands place value to 10,000
• Adds and subtracts within 10,000 fluently
• Knows all multiplication facts to 10×10
• Multiplies 2-digit by 1-digit numbers
• Divides 2-digit by 1-digit numbers with and without remainders
• Compares and orders fractions with like denominators
• Finds area and perimeter of rectilinear figures
• Solves multi-step word problems
• Measures with standard units
• Creates and interprets scaled graphs

INTERMEDIATE YEARS (GRADES 4-6)

GRADE 4 (AGE 9-10)

FRACTIONS, DECIMALS, AND MULTI-DIGIT OPERATIONS

Key Concepts:

• Numbers to 100,000
• Multi-digit multiplication and division
• Fractions (addition, subtraction with like denominators)
• Decimals (tenths, hundredths)
• Angles and geometric properties
• Area and perimeter
• Time (elapsed time)
• Data analysis

Manipulatives and Materials:

• Place value blocks and charts
• Area models for multiplication
• Fraction circles and bars
• Decimal grid materials
• Protractors and angle models
• Graph paper
• Time materials

Concrete Stage Activities:

1. Multi-Digit Multiplication:

   • Teacher demonstration: Use area model for multiplication
   • Student activity: Calculate products using area model
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Accurately multiplies multi-digit numbers

2. Fraction Addition Models:

   • Teacher demonstration: Show adding fractions with like denominators
   • Student activity: Use fraction pieces to add fractions
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Demonstrates fraction addition with models

3. Decimal Models:

   • Teacher demonstration: Represent decimals with base-10 blocks
   • Student activity: Model decimal numbers with materials
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Accurately represents decimal values

Pictorial Stage Activities:

1. Area Model Drawings:

   • Teacher demonstration: Draw area models for multiplication
   • Student activity: Use area model drawings for calculation
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Creates accurate area models

2. Fraction and Decimal Number Lines:

   • Teacher demonstration: Plot fractions/decimals on number lines
   • Student activity: Create and use fraction/decimal number lines
   • Frequency: 2 times weekly, 25 minutes
   • Mastery indicator: Correctly places values on number lines

3. Bar Models for Complex Problems:

   • Teacher demonstration: Draw models for complex problems
   • Student activity: Create bar models for multi-step problems
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Uses bar models effectively for complex problems

Abstract Stage Activities:

1. Standard Algorithms:

   • Teacher demonstration: Show standard algorithms for all operations
   • Student activity: Practice efficient computation methods
   • Frequency: Daily, 20 minutes
   • Mastery indicator: Uses algorithms correctly and efficiently

2. Fraction and Decimal Computation:

   • Teacher demonstration: Show procedures for fraction/decimal calculations
   • Student activity: Calculate with fractions and decimals
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Computes accurately with fractions/decimals

End-of-Year Competencies:

• Multiplies multi-digit numbers
• Divides with two-digit divisors
• Adds and subtracts fractions with like denominators
• Understands decimal notation to hundredths
• Compares and orders decimals
• Measures and draws angles
• Solves complex multi-step word problems
• Analyzes and interprets data from graphs
• Calculates elapsed time

GRADE 5 (AGE 10-11)

FRACTION AND DECIMAL OPERATIONS, RATIOS

Key Concepts:

• Numbers to 1,000,000
• Operations with fractions (unlike denominators)
• Operations with decimals
• Ratio concepts
• Percentage introduction
• Volume of rectangular prisms
• Classifying two-dimensional figures
• Line plots with fractions

Manipulatives and Materials:

• Fraction manipulatives
• Decimal grid materials
• Ratio tables and materials
• Percentage models
• Volume cubes
• Geometry models
• Graphing materials

Concrete Stage Activities:

1. Fraction Operations with Unlike Denominators:

   • Teacher demonstration: Show finding common denominators
   • Student activity: Use fraction pieces to add/subtract fractions
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Demonstrates operations with unlike denominators

2. Decimal Operations:

   • Teacher demonstration: Model decimal operations with materials
   • Student activity: Calculate with decimal models
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Performs decimal operations accurately

3. Ratio Relationships:

   • Teacher demonstration: Show ratios with concrete objects
   • Student activity: Create physical ratio models
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Demonstrates understanding of ratios

4. Volume Models:

   • Teacher demonstration: Build rectangular prisms with unit cubes
   • Student activity: Find volume by counting cubes
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Calculates volume accurately

Pictorial Stage Activities:

1. Fraction Operation Diagrams:

   • Teacher demonstration: Draw visual models for fraction operations
   • Student activity: Create diagrams for fraction problems
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Creates accurate models for fraction operations

2. Ratio Tables and Double Number Lines:

   • Teacher demonstration: Show ratio relationships with tables/lines
   • Student activity: Complete ratio tables for scenarios
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Uses ratio tables effectively

3. Percent Models:

   • Teacher demonstration: Draw models showing percentage
   • Student activity: Create visual representations of percentages
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Accurately represents percentages visually

Abstract Stage Activities:

1. Fraction and Decimal Algorithms:

   • Teacher demonstration: Show efficient procedures
   • Student activity: Practice computation with fractions/decimals
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Computes accurately with fractions/decimals

2. Ratio and Percentage Problems:

   • Teacher demonstration: Model solving ratio/percentage problems
   • Student activity: Solve various types of ratio/percentage problems
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Solves ratio and percentage problems correctly

End-of-Year Competencies:

• Adds and subtracts fractions with unlike denominators
• Multiplies and divides fractions
• Performs all operations with decimals
• Understands and applies ratio concepts
• Converts between fractions, decimals, and percentages
• Calculates volume of rectangular prisms
• Classifies two-dimensional figures by properties
• Solves problems involving fractions, decimals, and percentages
• Creates and interprets line plots with fraction data

GRADE 6 (AGE 11-12)

RATIOS, PROPORTIONS, AND EARLY ALGEBRA

Key Concepts:

• Ratio and proportion
• Percentage (complex problems)
• Positive and negative integers
• Algebraic expressions and equations
• Area of triangles and quadrilaterals
• Volume and surface area
• Statistical measures
• Probability concepts

Manipulatives and Materials:

• Number line models
• Algebra tiles
• Proportion models
• 3D geometric models
• Statistical tools
• Probability materials

Concrete Stage Activities:

1. Integer Operations:

   • Teacher demonstration: Use two-color counters for integers
   • Student activity: Model integer operations with counters
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Demonstrates operations with integers

2. Algebraic Expressions with Manipulatives:

   • Teacher demonstration: Represent variables and terms with tiles
   • Student activity: Model expressions with algebra tiles
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Creates models of algebraic expressions

3. Proportion Relationships:

   • Teacher demonstration: Show proportional relationships with materials
   • Student activity: Use manipulatives to solve proportion problems
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Uses proportional reasoning effectively

Pictorial Stage Activities:

1. Integer Number Lines:

   • Teacher demonstration: Show operations on number lines
   • Student activity: Represent integer operations on number lines
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Correctly uses number lines for integer operations

2. Algebra Diagrams:

   • Teacher demonstration: Draw models for algebraic relationships
   • Student activity: Create diagrams for equations
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Creates accurate models for equations

3. Ratio and Proportion Diagrams:

   • Teacher demonstration: Draw models for complex ratio problems
   • Student activity: Create visual representations for proportion problems
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Uses visual models for proportional reasoning

Abstract Stage Activities:

1. Algebraic Equations:

   • Teacher demonstration: Show solving equations systematically
   • Student activity: Solve various one-variable equations
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Solves equations correctly

2. Complex Percentage Problems:

   • Teacher demonstration: Model multi-step percentage problems
   • Student activity: Solve real-world percentage scenarios
   • Frequency: 3 times weekly, 30 minutes
   • Mastery indicator: Solves percentage problems accurately

3. Statistical Analysis:

   • Teacher demonstration: Show calculating measures of central tendency
   • Student activity: Analyze data sets and draw conclusions
   • Frequency: 2 times weekly, 30 minutes
   • Mastery indicator: Calculates and interprets statistical measures

End-of-Year Competencies:

• Understands ratio and proportional relationships
• Solves complex percentage problems
• Performs operations with positive and negative integers
• Writes and evaluates algebraic expressions
• Solves one-step and two-step equations
• Calculates area of triangles and quadrilaterals
• Determines volume and surface area of 3D figures
• Calculates statistical measures (mean, median, mode, range)
• Understands and applies basic probability concepts

TEACHING STRATEGIES AND ASSESSMENT

ASSESSMENT TOOLS

Formative Assessments:

• Observation checklists
• Exit tickets
• Quick quizzes
• Student self-assessment
• Mathematical discussions
• Journal entries

Summative Assessments:

• Unit tests with concrete, pictorial, and abstract components
• Performance tasks
• Multi-step problem-solving assessments
• Project-based assessments
• Cumulative reviews

PROGRESSION MONITORING

For Each Concept Area:

1. Concrete Understanding Check:

   • Can the student demonstrate the concept with manipulatives?
   • Can the student explain their thinking while using materials?

2. Pictorial Representation Check:

   • Can the student draw appropriate models?
   • Can the student translate between concrete materials and drawings?

3. Abstract Application Check:

   • Can the student solve problems without manipulatives or pictures?
   • Can the student apply the concept in new contexts?

DIFFERENTIATION STRATEGIES

For Struggling Learners:

• Extended time with concrete materials
• Simplified problems with same concepts
• Additional guided practice
• Visual supports and cues
• Step-by-step task cards

For Advanced Learners:

• Skip to more complex applications
• Open-ended problem-solving tasks
• Challenge questions with multiple solution paths
• Independent investigations
• Peer teaching opportunities

KEY PRINCIPLES OF SINGAPORE MATH METHODOLOGY

CONCRETE-PICTORIAL-ABSTRACT APPROACH

The CPA approach is the cornerstone of Singapore Math, ensuring deep conceptual understanding:

1. Concrete Stage:

   • Students manipulate physical objects to model mathematical concepts
   • Builds direct experience with mathematics
   • Establishes conceptual foundation

2. Pictorial Stage:

   • Students draw or use visual representations of mathematical ideas
   • Bridges concrete understanding to abstract concepts
   • Includes number bonds, bar models, and other visual representations

3. Abstract Stage:

   • Students work with symbols and notation
   • Apply understanding to algorithms and formulas
   • Transfer knowledge to new contexts

MENTAL MATH STRATEGIES

Singapore Math emphasizes mental mathematics through:

1. Number Sense Development:

   • Understanding place value deeply
   • Flexible thinking about numbers
   • Recognition of number relationships

2. Decomposition and Recomposition:

   • Breaking numbers apart in helpful ways
   • Recombining to simplify calculations
   • Using known facts to derive unknown facts

3. Making 10 and Making 100:

   • Strategic regrouping to facilitate calculation
   • Using benchmark numbers efficiently
   • Applying number bonds fluently

MODEL METHOD (BAR MODELING)

The bar model method is a signature feature of Singapore Math:

1. Part-Whole Models:

   • Represent addition and subtraction relationships
   • Show components and totals visually
   • Progress from simple to complex

2. Comparison Models:

   • Show relationships between quantities
   • Visualize "more than" and "less than"
   • Make abstract relationships concrete

3. Multi-Step Problem Models:

   • Break complex problems into manageable parts
   • Track known and unknown quantities
   • Create visual equation representations

Completing the Singapore Math Curriculum Map

KEY PRINCIPLES OF SINGAPORE MATH METHODOLOGY (continued)

SPIRAL PROGRESSION (continued)

1. Concepts Revisited:

   • Each concept is revisited at regular intervals
   • Each revisit deepens understanding and complexity
   • Prior knowledge serves as foundation for new learning

2. Thoughtful Sequencing:

   • Topics build upon each other systematically
   • Skills are developed in logical progression
   • Connections between concepts are emphasized

3. Careful Pacing:

   • Sufficient time allowed for mastery of foundational concepts
   • Strategic introduction of new concepts when prerequisites are solid
   • Balance between depth and breadth of content

METACOGNITION AND PROBLEM SOLVING

Singapore Math develops strong problem-solving skills through:

1. Explicit Problem-Solving Strategies:

   • Read and understand the problem
   • Identify relevant information and question
   • Choose appropriate strategy and representation
   • Solve and check solution
   • Reflect on process and alternative methods

2. Heuristics Instruction:

   • Draw a diagram or model
   • Look for patterns
   • Work backwards
   • Use guess and check
   • Make a systematic list
   • Use logical reasoning

3. Mathematical Reasoning:

   • Emphasis on explaining mathematical thinking
   • Justifying solutions and approaches
   • Making connections between concepts
   • Analyzing errors and misconceptions

CLASSROOM IMPLEMENTATION

LESSON STRUCTURE

A typical Singapore Math lesson follows this structure:

1. Anchor Task (5-10 minutes):

   • Engaging problem that introduces the concept
   • Activates prior knowledge
   • Creates need for new learning

2. Guided Learning (15-20 minutes):

   • Teacher demonstration of concept using CPA approach
   • Guided practice with manipulatives or visual models
   • Questioning to elicit student thinking

3. Independent Practice (15-20 minutes):

   • Students practice with similar problems
   • Application to varied contexts
   • Gradual release of scaffolding

4. Reflection and Consolidation (5-10 minutes):

   • Students share strategies and thinking
   • Misconceptions addressed
   • Key learning points summarized

CLASSROOM ENVIRONMENT

An effective Singapore Math classroom requires:

1. Physical Setup:

   • Accessible math manipulatives and tools
   • Visual displays of models and strategies
   • Space for collaborative work
   • Math vocabulary word wall

2. Learning Culture:

   • Emphasis on process over answers
   • Valuing multiple solution methods
   • Productive struggle encouraged
   • Growth mindset for mathematics

3. Discourse Practices:

   • Math talk moves (revoicing, restating, reasoning)
   • Partner and small group discussions
   • Explanation and justification expected
   • Appropriate mathematical vocabulary used

PARENT INVOLVEMENT

Supporting home-school connections through:

1. Family Resources:

   • Parent guide to Singapore Math approach
   • Home activity kits with manipulatives
   • Videos demonstrating strategies
   • Problem-solving games for family engagement

2. Communication Channels:

   • Regular updates on current mathematical topics
   • Guidance on appropriate support at home
   • Celebration of mathematical thinking
   • Resources for addressing misconceptions

CURRICULUM INTEGRATION AND EXTENSIONS

INTERDISCIPLINARY CONNECTIONS

Mathematics connected to other subject areas:

1. Science Integration:

   • Data collection and analysis
   • Measurement in experiments
   • Patterns and relationships in natural phenomena
   • Application of ratio and proportion concepts

2. Social Studies Connections:

   • Data interpretation from demographics
   • Scale in maps and models
   • Timeline construction and analysis
   • Financial literacy applications

3. Language Arts Links:

   • Mathematical vocabulary development
   • Reading and interpreting word problems
   • Writing mathematical explanations
   • Creating story problems

TECHNOLOGY INTEGRATION

Strategic use of technology to enhance learning:

1. Digital Manipulatives:

   • Virtual base-10 blocks and fraction tools
   • Dynamic geometry software
   • Number line and grid apps
   • Digital ten frames and number bonds

2. Practice Applications:

   • Adaptive practice platforms
   • Game-based learning applications
   • Video tutorials for concepts
   • Interactive problem-solving simulations

3. Creation Tools:

   • Digital bar model creators
   • Graph generators
   • Slide presentations of mathematical thinking
   • Collaborative problem-solving platforms

ENRICHMENT OPPORTUNITIES

Extending learning for all students:

1. Mathematical Investigations:

   • Open-ended problem-solving tasks
   • Pattern exploration projects
   • Real-world application challenges
   • Mathematical modeling activities

2. Math Competitions and Clubs:

   • Problem-solving teams
   • Math Olympiad preparation
   • Math game clubs
   • Peer tutoring opportunities

3. Community Connections:

   • Guest speakers from math-related professions
   • Field trips with mathematical focus
   • Service projects applying mathematics
   • Math fair presentations

PROFESSIONAL DEVELOPMENT

TEACHER TRAINING ESSENTIALS

Key areas for teacher development:

1. Content Knowledge Enhancement:

   • Deep understanding of mathematical concepts
   • Awareness of common misconceptions
   • Knowledge of concept progressions
   • Proficiency with multiple solution methods

2. Pedagogical Skill Development:

   • Effective use of CPA approach
   • Bar modeling techniques
   • Questioning strategies
   • Formative assessment practices

3. Curriculum Implementation:

   • Lesson planning using Singapore Math structure
   • Materials management and organization
   • Differentiation strategies
   • Assessment design and analysis

ONGOING SUPPORT STRUCTURES

Sustaining high-quality implementation:

1. Professional Learning Communities:

   • Regular collaborative planning time
   • Lesson study cycles
   • Student work analysis protocols
   • Peer observation and feedback

2. Coaching and Mentoring:

   • In-classroom demonstration lessons
   • Co-teaching opportunities
   • Just-in-time support for challenges
   • Video reflection on practice

3. Resource Development:

   • Creation of shared materials bank
   • Compilation of effective tasks and problems
   • Documentation of student misconceptions
   • Building of assessment item banks

CONCLUSION

The Singapore Math approach represents a carefully designed progression that builds deep mathematical understanding through concrete experiences, visual representations, and abstract applications. By following this curriculum map, educators can implement a coherent, systematic approach to mathematics instruction that develops strong number sense, problem-solving abilities, and mathematical confidence in students from ages 3-12.

The key to successful implementation lies in maintaining fidelity to the core principles while adapting to meet student needs. With proper training, resources, and support, teachers can guide students to develop not only mathematical proficiency but also positive attitudes toward mathematics as a meaningful, accessible, and enjoyable discipline.

This curriculum map serves as a comprehensive guide, but should be viewed as a living document to be refined and enhanced through ongoing professional reflection and student feedback. By embracing the Singapore Math approach, schools commit to mathematical excellence that prepares students for future success in mathematics and beyond.