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Grade 6
Algebraic Expressions
Variables and Constants

Grade 6

1. Large Numbers (7-Digit to 9-Digits)

1.1. Representation of Large Numbers

1.1.1. Write Large Numbers by Separating the Periods

1.1.2. Write Numerals as Number Names

1.1.3. Write Number Names as Numerals

1.1.4. Relation Between Different Periods

1.1.5. Numbers in Expanded Form

1.2. Successor and Predecessor

1.2.1. Successor of a Number

1.2.2. Predecessor of a Number

1.3. n Digit Numbers

1.4. Place of a Digit

1.5. Compare Large Numbers

1.6. Operations on Large Numbers

1.6.1. Addition of Large Numbers

1.6.2. Subtraction of Large Numbers

1.6.3. Multiplication of large numbers

1.6.4. Division of Large Numbers

1.6.5. Word Problem on Operations on Large Numbers

1.6.5.1. Word Problem on Addition of Large Numbers

1.6.5.2. Word Problem on Subtraction of Large Numbers

1.6.5.3. Word Problem on Multiplication of Large Numbers

1.6.5.4. Word Problem on Division of Large Numbers

1.7. Rounding Numbers

1.7.1. Rounding off numbers

1.7.1.1. Rounding off to the nearest ten

1.7.1.2. Rounding off to the nearest hundred

1.7.1.3. Rounding off to the nearest thousand

1.7.2. Estimating Sum

1.7.3. Estimating Difference

1.7.4. Estimating Products

1.7.5. Estimating Quotients

2. Roman Numerals (up to 1000)

2.1. Introduction to Roman Numerals

2.2. Write Roman Numerals for Hindu-Arabic Numerals

2.3. Meaningless Roman Numerals

2.4. Compare Roman Numerals

2.6. Word Problems on Basic Arithmetic Using Roman Numerals

3. Whole Numbers

3.1. Introduction to Natural Numbers and Whole Numbers

3.2. Operations on Whole Numbers

3.2.1. Addition and Subtraction of Whole Numbers

3.2.1.1. Addition of Whole Numbers

3.2.1.2. Properties of Addition on Whole Numbers

3.2.1.3. Solving Magic Square

3.2.2. Subtraction of Whole Numbers

3.2.2.1. Properties of Subtraction on Whole Numbers

3.2.2.2. Multiplication and Division of Whole Numbers

3.2.2.2.1. Multiplication of Whole Numbers

3.2.2.2.2. Properties of Multiplication of Whole Numbers

3.2.2.2.3. Division of Whole Numbers

3.2.2.2.4. Properties of Division of Whole Numbers

3.2.2.3. Word Problems on Whole Numbers

4. Integers

4.1. Introduction to Integers

4.2. Representation of Integers on a Number Line

4.3. Successor and Predecessor of an Integer

4.4. Comparing Integers

4.5. Absolute Value of an Integer

4.6. Operations on Integers

4.6.1. Addition and Subtraction of Integers

4.6.1.1. Addition of Integers

4.6.1.2. Addition of Integers on the Number Line

4.6.1.3. Properties of Addition of Integers

4.6.2. Subtraction of Integers

4.6.2.1. Subtraction of Integers on the Number Line

4.6.2.2. Properties of Subtraction of Integers

4.6.2.3. Multiplication and Division of Integers

4.6.2.3.1. Multiplication of Integers

4.6.2.3.2. Properties of Multiplication of Integers

4.6.2.3.3. Division of Integers

4.6.2.3.4. Properties of Division of Integers

4.6.2.4. Mixed Operations on Integers

4.6.2.5. Word Problems on Integers

5. Factors and Multiples

5.1. Factors and Multiples of a Number

5.1.1. Finding Factors of a Number

5.2. Finding Multiples of a Number

5.2.1. Word Problems on Factors and Multiples

5.2.2. Properties of Factors and Multiples

5.3. Types of Numbers

5.3.1. Odd and Even Numbers

5.3.1.1. Even numbers

5.3.1.2. Odd numbers

5.3.1.3. Properties of Odd and Even numbers

5.3.2. Prime and Composite Numbers

5.3.2.1. Understanding Prime and Composite Numbers

5.3.2.2. Composite Numbers

5.3.2.3. Prime Numbers

5.3.2.4. Properties of Composite and Prime Numbers

5.3.3. Twin Primes

5.3.4. Prime Triplet

5.3.5. Co-Primes

5.3.6. Perfect Numbers

5.3.7. Tests of Divisibility

5.3.7.1. Test Divisibility by 2

5.3.7.2. Test Divisibility by 3

5.3.7.3. Test Divisibility by 4

5.3.7.4. Test Divisibility by 5

5.3.7.5. Test Divisibility by 6

5.3.7.6. Test Divisibility by 7

5.3.7.7. Test Divisibility by 8

5.3.7.8. Test Divisibility by 9

5.3.7.9. Test Divisibility by 10

5.3.7.10. Test Divisibility by 11

5.3.8. Prime Factorization of a Number

5.3.9. HCF and LCM

5.3.9.1. HCF (Highest Common Factor)

5.4. LCM (Lowest Common Multiple)

5.4.1. Properties of LCM and HCF

5.4.2. Word problems on HCF and LCM

6. Fractions

6.1. Fraction and Fractional numbers

6.2. Fractions on a Number Line

6.3. Fraction as a Part of a Collection

6.4. Fractional Part of a Collection

6.5. Identifying Like and Unlike Fractions

6.6. Unit Fraction

6.7. Proper, Improper and Mixed Fractions

6.7.1. Understand the Meaning of Proper, Improper and Mixed Fractions

6.7.2. Convert Improper Fractions to Mixed Fractions

6.7.3. Convert Mixed Fractions to Improper Fractions

6.8. Equivalent Fractions

6.9. Simplest Form of a Fraction

6.10. Comparing Fractions

6.10.1. Comparing Like Fractions

6.10.2. Comparing Fractions with Same Numerator

6.10.3. Comparing Unlike Fractions

6.11. Operations on Fractions

6.11.1. Addition of Fractions

6.11.1.1. Addition of Like Fractions

6.11.1.2. Addition of Unlike Fractions

6.11.1.3. Addition of Mixed Fractions

6.11.1.4. Word Problems on Addition of Fractions

6.11.2. Subtraction of Fractions

6.11.2.1. Subtraction of Like Fractions

6.11.2.2. Subtraction of Unlike Fractions

6.11.2.3. Subtraction of Mixed Fractions

6.11.2.4. Word Problems on Subtraction of Fractions

6.11.3. Addition and Subtraction of Fractions

6.11.3.1. Simplify Expressions Involving Addition and Subtraction

6.11.3.2. Word Problems on Addition and Subtraction of Fractions

7. Decimals

7.1. Introduction on Decimals

7.2. Reading a Decimal Number

7.3. Place Value Chart

7.4. Expanded Form of Decimal Numbers

7.5. Like and Unlike Decimals

7.6. Equivalent Decimals

7.7. Comparing Decimals

7.8. Ordering Decimals

7.9. Relate Decimals and Fractions

7.9.1. Convert Decimals to Fractions

7.9.1.1. Convert Decimals to Proper Fractions

7.9.1.2. Convert Decimals to Improper Fractions

7.9.1.3. Convert Decimals to Mixed Fractions

7.9.2. Convert Fractions to Decimals

7.9.2.1. Convert Fractions with Denominators as Powers of 10 to Decimals

7.9.2.2. Convert Any Fractions to Decimals

7.9.4. Conversion of Metric Units using Decimals

7.10. Addition and Subtraction of Decimals

7.10.1. Addition of Decimals

7.10.2. Subtraction of Decimals

7.10.3. Mixed Operations on Decimals: Addition and Subtraction

7.10.4. Word Problems on Addition and Subtraction of Decimals

8. Simplification

8.1. Numerical Expressions Without Brackets (DMAS)

8.2. Numerical Expressions With Brackets (BODMAS)

9. Ratio and Proportion

9.1. Ratio

9.1.1. Terms of a Ratio

9.1.2. Equivalent Ratio

9.1.3. Ratio in the Simplest Form

9.1.4. Ratio of Two Quantities by Converting Them in Same Units

9.1.5. Comparison of Ratios

9.1.6. Word Problems on Ratio

9.2. Proportion

9.2.1. Terms of a Proportion

9.2.2. The Condition for the Given Numbers/Ratios to be in Proportion

9.2.3. Find the Unknown Variable When Four Numbers are in Proportion

9.2.4. Find the Unknown Variable When Three Numbers are in Proportion

10. Unitary Method

11. Algebraic Expressions

11.1. Operations on Literals and Numbers

11.2. Variables and Constants

11.3. Coefficients of an Algebraic Expression

11.4. Types of Algebraic Expressions

11.5. Finding the Value of an Algebraic Expression

11.6. Operations on Algebraic Expressions

11.6.1. Addition of Algebraic Expressions

11.6.2. Subtraction of Algebraic Expressions

11.6.3. Addition and Subtraction of Algebraic Expressions

11.7. Simplifying Algebraic Expression by Eliminating the Grouping Symbols

12. Linear Equations in One Variable

12.1. Understanding Linear Equation

12.2. Writing Statements as Equations

12.3. Writing Equations as Statements

12.4. Verify that the Given Solution is the Solution of the Linear Equation

12.5. Solving Linear Equations

12.6. Word Problems Based on Linear Equations

13. Mensuration

13.1. Area of a Figure Composed of Unit Squares

13.2. Perimeter of a Figure Composed of Unit Squares

13.3. Perimeter of a Triangle

13.4. Perimeter of Polygons

13.5. Area and Perimeter of a Rectangle

13.6. Area and Perimeter of a Square

13.7. Circumference of a Circle

14. Geometry

14.1. Understand the Basic Terms in Geometry (Point, Line, Line Segment, Ray, and Plane)

14.2. Count the Number of Line Segments

14.3. Types of Lines

14.3.1. Parallel Lines

14.3.2. Perpendicular Lines

14.4. Intersecting Lines

14.4.1. Identifying the Type of Line

14.4.2. Collinear and Non-Collinear Points

14.4.3. Angle

14.4.3.1. Introduction to Angles

14.4.3.2. Interior and Exterior of An Angle

14.4.3.3. Finding the Number of Angles in the Given Figure

14.4.3.4. Types of an Angles

14.4.3.5. Measuring an Angle by a Protractor

14.4.4. Triangles

14.4.4.1. Introduction to Triangles

14.4.4.2. Congruent Triangles

14.4.4.3. Interior and Exterior of a Triangle

14.4.4.4. Types of Triangles by the Lengths of Sides

14.4.4.5. Types of Triangles by Angles

14.4.4.6. Count the Number of Triangles

14.4.4.7. Angle Sum Property of a Triangle

14.4.5. Curve

14.4.5.1. Straight and Curved Lines

14.4.5.2. Open Curve

14.5. Closed Curve

14.5.1. Simple Closed Curve

14.5.2. Identifying Closed and Open Figures

14.5.3. Polygon

14.5.3.1. Understanding Polygons

14.5.3.2. Name the Polygon

14.5.4. Quadrilateral

14.5.4.1. Introduction to Quadrilaterals

14.5.4.2. Convex and Concave Quadrilaterals

14.5.4.3. Interior and Exterior of a Quadrilateral

14.5.4.4. Angle Sum Property of a Quadrilateral

14.5.4.5. Special Types of Quadrilateral

14.5.5. Circle

14.5.5.1. Interior and Exterior of a Circle

14.5.5.2. Terms related to a Circle

14.5.5.3. Relationship between Radius and Diameter of a Circle

14.5.5.4. Concentric Circles

15. Three Dimensional (3-D) Shapes

15.1. Identifying 3-D Shapes

15.2. Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, Sphere, Pyramid and Prism)

16. Linear Symmetry

16.1. Linear Symmetry Around Us

16.2. Linear Symmetry in Geometric Figures

16.3. Linear Symmetry in Alphabets

17. Data Handling

17.1. Introduction to Data Handling

17.2. Tabular Representation of Data

17.3. Pictographs

17.3.1. Introduction to Pictograph

17.3.2. Drawing Pictographs

17.3.3. Interpreting Pictographs

17.4. Bar graphs

17.4.1. Drawing Bar Graphs

17.4.2. Interpreting Bar Graphs

Grade 6 Germany School Math Variables and Constants

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