Grade 4 (Topics)

1. 1 Learning Numeration
   • 1.1 Numeration in Thousands
   • 1.2 Numeration in Millions
   • 1.3 Place Values
   • 1.4 Comparing and Ordering Numbers
   • 1.5 Rounding
   • 1.6 Introducing Decimals Using Money
   • 1.7 Purchasing and Making Change
   • 1.8 Problem Solving
2. 2 Addition and Subtraction Part I
   • 2.1 Mental Addition and Subtraction
   • 2.2 Estimating Sums and Differences
   • 2.3 Addition and Subtraction of Whole Numbers
   • 2.4 Addition and Subtraction across Zeroes
   • 2.5 Addition and Subtraction Patterns over Increasing Place Values
3. 3 Addition and Subtraction Part II
   • 3.1A Finding the Missing Digits
   • 3.1B Finding the Missing Digits
   • 3.2 Problem Solving with Missing or Extra Information
   • 3.3 Mixed Problem Solving
   • 3.4 Problem Solving Using Pictures and Equations
4. 4 Multiplication Part I
   • 4.1 Multiplication Concept
   • 4.2 Number Patterns for Multiplication
   • 4.3 Multiplication Facts to 9
   • 4.4 Properties of Multiplication
   • 4.5 Multiplication Using 2, 3, and 4 as Factors
5. 5 Multiplication Part II
   • 5.1 Multiplication Using 5, 6, and 7 as Factors
   • 5.2 Multiplication Using 8 and 9 as Factors
   • 5.3 Multiplication Using 10, 11, and 12 as Factors
   • 5.4 Multiplication in Horizontal and Vertical Form
   • 5.5 Multiplication by the Same Number
   • 5.6 Problem Solving Using Pictures and Equations
6. 6 Division
   • 6.1 Division Concept
   • 6.2 Connecting Multiplication with Division
   • 6.3 Division Facts to 9
   • 6.4 Special Division Problems
   • 6.5 Problem Solving Using Pictures and Equations
7. 7 Multiplying by 1-Digit Numbers Part I
   • 7.1A Multiple
   • 7.1B Find the Multiples of Given Numbers
   • 7.2A Multiplication Using Multiples of 10 and 100
   • 7.2B Multiplication Using Multiples of 10 and 100
   • 7.3 Multiplication Using Mental Math
   • 7.4A Estimate the Product
   • 7.4B Estimate the product of word problem
   • 7.5 Problem Solving as Using Reasoning
8. 8 Multiplying by 1-Digit Numbers Part II
   • 8.1 Expanded Forms in Multiplication
   • 8.2 Multiply 2-Digit Numbers by 1-Digit Number without Regrouping
   • 8.3 Multiply 2-Digit Numbers by 1-Digit Number with Regrouping
   • 8.4 Multiplication of 3-Digit Numbers by 1-Digit Number with Regrouping
   • 8.5 Problem Solving Using Pictures and Equations
9. 9 Algebra Part I
   • 9.1 Introducing Variables and Expressions
   • 9.2 Writing Variable Expressions
   • 9.3 Geometric Growth Pattern
   • 9.4 Addition and Subtraction
   • 9.5 Multiplication and Division
10. 10 Algebra Part II
    • 10.1 Evaluate Variable Expressions
    • 10.2 Understanding Like and Unlike Terms
    • 10.3 Addition and Subtraction of Like Terms
    • 10.4 Simplify the Expressions Using the Order of Operations
    • 10.5 Problem Solving Using Object and Reason
11. 11 Multiplication Strategies
    • 11.1 Multiplication Facts to 12
    • 11.2 Use Mental Math for Large Number Multiplications
    • 11.3A Estimating Products
    • 11.3B Estimating Products
    • 11.4 Arrays and Expanded Form
    • 11.5 2-Digit Numbers Multiplication
    • 11.6 3-Digit and 2-Digit Number Multiplication
12. 12 Multiplication by 2-Digit Numbers
    • 12.1 Multiplication with Numbers Ending at Zero
    • 12.2 Multiplying Three 1-Digit Numbers
    • 12.3 Multiplication Patterns over Increasing Place Values
    • 12.4 Special Multiplication Problems
    • 12.5 Equalities and Inequalities in Multiplication Sentences
    • 12.6 Multistep Multiplication Problems
13. 13 Dividing by 1-Digit Numbers Part I
    • 13.1 Mental Math Using Division
    • 13.2 Estimate Quotients
    • 13.3 Find Remainders
    • 13.4 Division Models and Symbols
    • 13.5 Divide 2- and 3-Digit Numbers by 1-Digit Numbers
    • 13.6 Divide 2- and 3-Digit Numbers by 2-Digit Numbers
    • 13.7 Divide Larger Numbers by Multiples of 10
14. 14 Dividing by 1-Digit Numbers Part II
    • 14.1 Identifying Missing Numbers in Division Equations
    • 14.2 Divide Numbers Ending at Zeroes
    • 14.3 Equalities and Inequalities in Division Sentences
    • 14.4 Factors
    • 14.5 Recognize Prime and Composite Numbers
    • 14.6 Problem Solving
    • 14.7A Mixed Operations: Multiplication and Division
    • 14.7B Mixed Operations: Multiplication and Division
15. 15 Geometry Part I
    • 15.1 Points, Lines, and Planes
    • 15.2A Rays, Line Segments, and Angles
    • 15.2B Rays, Line Segments, and Angles
    • 15.3A Measuring Angles
    • 15.3B Measuring Angles
    • 15.4A Identifying Polygons
    • 15.4B Identifying Polygons
    • 15.5 Recognizing Shapes and Angles
16. 16 Geometry Part II
    • 16.1 Count and Compare Sides, Edges, Faces, and Vertices
    • 16.2A Types of Triangles
    • 16.2B Types of Triangles
    • 16.3A Classify Quadrilaterals
    • 16.3B Classify Quadrilaterals
    • 16.4 Circles and Parts of a Circle
    • 16.5 Calculate Radius, Diameter, and Circumference
17. 17 Fractions
    • 17.1A Parts of Sets
    • 17.1B Parts of Sets
    • 17.2 Relate Fractions and Division
    • 17.3 Fraction of a Number
    • 17.4 Estimating Fractions
    • 17.5 Evaluate Equivalent and Non-Equivalent Fractions
    • 17.6 Simplify the Fractions
    • 17.7 Proper and Improper Fractions
    • 17.8A Ordering and Comparing Fractions
    • 17.8B Ordering and Comparing Fractions
    • 17.9 Problem Solving
18. 18 Fraction Operation
    • 18.1 Adding Fractions with Like Denominators
    • 18.2A Subtracting Fractions with Like Denominators
    • 18.2B Subtracting Fractions with Like Denominators
    • 18.3 Adding Fractions with Unlike Denominators
    • 18..4 Subtracting Fractions with Unlike Denominators
    • 18.5 Adding More Fractions with Like/Unlike Denominators
    • 18.6 Converting Fractions to Mixed Numbers
    • 18.7 Convert Mixed Numbers to Fractions
    • 18.8 Find the Missing Numerator and Denominator
    • 18.9 Problem Solving Using Pictures and Equations
19. 19 Decimals
    • 19.1A Decimal Concepts
    • 19.1B Decimal Concepts
    • 19.2 Compare and Order Decimal Numbers
    • 19.3 Fractions and Decimals Conversion
    • 19.4 Rounding Decimal Numbers
    • 19.5 Compare Pairs of Numbers in Decimal or Fraction Form
    • 19.6 Using Number Lines to Understand Fractions and Decimals
    • 19.7 Fractions, Mixed Numbers, and Decimals on a Number Line
20. 20 Decimal Number Operation
    • 20.1 Addition
    • 20.2 Subtraction
    • 20.3A Estimating Sums and Differences
    • 20.3B Estimating Sums and Differences
    • 20.4A Addition and Subtraction Using Decimal Numbers
    • 20.4B Addition and Subtraction Using Decimal Numbers
    • 20.5 Addition or Subtraction of 3 or More Decimal Numbers
    • 20.6A Multiply a Decimal Number by a Whole Number
    • 20.6B Multiply a Decimal Number by a Whole Number
    • 20.7 Divide a Decimal Number by a Whole Number
    • 20.8 Inequalities with Addition and Subtraction
    • 20.9 Problem Solving
21. 21 Measurement Part I
    • 21.1 Area Concept
    • 21.2 Measure Area of Squares and Rectangles
    • 21.3 Area of Irregular Shapes
    • 21.4 Area of Parallelograms
    • 21.5 Area of Triangles
    • 21.6 Perimeter
    • 21.7 Use of Area and Perimeter to Determine Cost
22. 22 Measurement Part II
    • 22.1 Length in Customary Units
    • 22.2 Capacity in Customary Units
    • 22.3 Weight in Customary Units
    • 22.4 Convert Customary Units
    • 22.5 Length in Metric Units
    • 22.6 Capacity in Metric Units
    • 22.7 Weight in Metric Units
    • 22.8 Changing Metric Units
23. 23 Solid and Measurement
    • 23.1A Identify Solid Figures
    • 23.1B Identify Solid Figures
    • 23.3 Find Volume
    • 23.5 Time and Elapsed Time
    • 23.6 Calendar
    • 23.7 Temperature
24. 24 Graph
    • 24.1 Read a Table
    • 24.2 Make Frequency Table
    • 24.3 Understanding Bar Graphs
    • 24.4A Locate a Point on a Coordinate Plane
    • 24.4B Locate a Point on a Coordinate Plane
    • 24.4C Locate a Point on a Coordinate Plane
    • 24.6 Find the Mean and the Median
    • 24.7 Find the Mode and the Range
    • 24.8 Read and Create Stem-and-Leaf Plots
    • 24.9 Read and Create Circle Graphs
25. 25 Equation and Function
    • 25.1 Algebra: Equal or Not Equal
    • 25.2 Algebra: Solving Addition and Subtraction Equations
    • 25.3 Algebra: Solving Multiplication and Division Equations
    • 25.5A Understanding Function Tables
    • 25.5B Understanding Function Tables
    • 25.6A Develop Linear Functions
    • 25.6B Develop Linear Functions
    • 25..7 Graph Linear Functions
26. 26 Transformation, Congruence, and Symmetry
    • 26.1 Translation Image of Figures
    • 26.2 Reflection
    • 26.3 Rotation of Figures
    • 26.4 Congruent Figures
    • 26.5 Similar Figures
    • 26.6 Line Symmetry of Figures
    • 26.7 Rotational Symmetry of Figures
27. 27 Probability
    • 27.1 Experiments and Outcomes
    • 27.2 Combination of Outcomes
    • 27.4 Probability Expressions
    • 27.5 Probability of an Event
    • 27.6 Problem Solving: Use Reasoning