Academic year:

## Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Number System | - |

200 | Commercial Arithmetic | - |

300 | Algebra | - |

400 | Geometry | - |

500 | Data Handling (Statistics) | - |

Total | - |

## Syllabus

100 Number System

101 Integers

- Concept of Integers
- Multiplication and Division of Integers
- Properties of Operations on Integers
- Concept for Commutativity, Associativity, Existence of Identity
- Inverse and Distributivity
- Problem Solving Using Operations on Integers
- Statement Problems on Integers Using All Fundamental Operations.

- Multiplication and division of integers
- Properties of operations on integers: Commutativity, associativity, existence of identity and inverse and distributivity
- Problem solving using operations on integers
- Solution of word problems involving integers (all operations)

102 Rational Numbers

- Concept of Rational Numbers
- Word Problems on Rational Numbers (All Operations)
- Decimal Representation of Rational Numbers
- Concept for Problem Solving Using Operations on Rational Numbers
- Concept of Decimal Numbers

- Introduction to rational numbers (withrepresentation on numberline)
- Word problems onrational numbers (alloperations)
- Decimal representation of rational numbers
- Problem solving using operations on rational numbers and decimal fractions

103 Fractions (Including Problems)

- Fraction as an operator
- Reciprocal of a fraction

104 Decimal Fractions (Decimals)

- Concept of Decimal Numbers
- Concept for Multiplication
- Division of Decimal Numbers
- Decimal Division through models.

- Multiplication and

division of decimal

fractions

105 Exponents (Including Laws of Exponents)

- Concept of Exponents
- Concept for Exponents Only Natural Numbers.
- Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.)
- Concept for Application of Laws of Exponents in Simple Daily Life Problems

- Exponents only natural numbers.
- Laws of exponents (through observing patterns to arrive at generalisation.)
- Application of laws of exponents in simple daily life problems.

200 Commercial Arithmetic

201 Ratio and Proportion (Including Sharing in a Ratio)

- Ratio and proportion (revision)

202 Unitary Method (Including Time and Work)

- Concept of Unitary Method (Including Time and Work)
- Unitary Method Continued, Consolidation, General Expression for Unitary Method .
- Relation Between Speed, Time and Distance

- Unitary method continued, consolidation, general expression for unitary method .
- Speed, distance, time

203 Percent and Percentage

- Concept of Percent and Percentage
- Concept for Understanding Percentage as a Fraction with Denominator 100
- Converting Fractional Numbers to Percentage
- Converting Decimals to Percentage

- Percentage- an introduction.
- Understanding percentage as a fraction with denominator 100
- Converting fractions and decimals into percentage and vice-versa.

204 Profit, Loss and Discount

- Application to profit and loss (single transaction only)

205 Simple Interest

- Concept of Principal, Interest, Amount, and Simple Interest
- Simple Interest for one year
- Simple Interest for multiple years

- Concept for Application to Simple Interest (Time Period in Complete Years).

- Application to simple interest (time period in complete years).

300 Algebra

301 Fundamental Concepts (Including Fundamental Operations)

- Fundamental Concepts
- Terms, Factors and Coefficients of Expression
- Algebraic Expressions
- Variable
- Constant
- Algebraic Expressions
- Value of Expression
- Number line and an expression

- Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only.

- Terms related to algebra like constants, variable, terms, coefficient of terms, like and unlike terms, etc.
- Generate algebraic expressions.
- Performs operations (addition and subtraction) on algebraic expressions with integral coefficients only.

302 Simple Linear Equations (Including Word Problems)

- Simple Linear Equations in One Variable
- Concept for Inequalities
- The sign > means, "is greater than" i.e.; if 'a' is greater than 'b', we write : a > b.
- The sign < means, "is less than" i.e.; if 'a' is less than 'b', we write : a < b.

- Concept for Solution of Simple Inequalities in One Variable

- Simple linear equations in one variable (in contextual problems) with two operations.
- Inequalities and solution of simple inequalities in one variable

303 Set Concepts (Some Simple Divisions by Vedic Method)

- Concept of Set Concepts
- Concept for Revision Idea of Sets
- Concept for Universal Sets
- Concept for Cardinal Property of Sets

- Revision idea of sets
- Equal, equivalent, universal sets
- Cardinal property of sets

400 Geometry

401 Lines and Angles (Including Construction of Angles)

- Introduction to Lines and Angles
- Concept for Pairs of Angles
- Concept for Properties of Parallel Lines with Transversal
- Interior angle theorem
- Corresponding angles and alternate angles theorem

- Construction of a Line Parallel to a Given Line from a Point Outside It .

Understanding shapes:-

- Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite).
- Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles).
- Construction of a line parallel to a given line from a point outside it .

402 Triangles

- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Concept for Angle Sum Property
- Concept for Exterior Angle Property
- Concept for Construction of Simple Triangles.

Properties of triangles:-

- Angle sum property
- Exterior angle property
- Construction of simple triangles.

403 Pythagoras Theorem

- Pythagoras Theorem (Verification only)

404 Symmetry (Including Reflection and Rotation)

- Concept of Symmetry
- Concept of Reflection Symmetry
- Concept for Idea of Rotational Symmetry, Observations of Rotational Symmetry of 2-d Objects. (900, 1200, 1800)

Symmetry:-

- Recalling reflection symmetry
- Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (900, 1200, 1800)

405 Recognition of Solids (Representing 3-d in 2-d)

- Concept of Recognition of Solids
- Faces, Edges and Vertices
- Concept for Mapping the Space Around Approximately Through Visual Estimation.

Representing 3-D in 2-D :-

- Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
- Mapping the space around approximately through visual estimation.

406 Congruency: Congruent Triangles

- Congruence of Triangles
- Concept for Congruence Through Superimposition
- Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
- Criteria for Congruence of Triangles

Congruence :-

- Congruence through superimposition
- Extend congruence to simple geometrical shapes e.g. triangles, circles.
- Criteria of congruence

407 Mensuration

- Mensuration
- Concept of Perimeter
- Circumference of a Circle
- Concept of Area
- Concept of Measurement Using a Basic Unit Area of a Square, Rectangle, Triangle, Parallelogram and Circle, Rings and Combined Figures.

- Revision of perimeter and Idea of Circumference of Circle
- Area
- Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, rings and combined figures.

500 Data Handling (Statistics)

501 Data Handling

- Concept of Data Handling
- Data Handling
- Data
- Types of Data

- Concept for Collection and Organisation of Data – Choosing the Data to Collect for a Hypothesis Testing
- Concept of Median
- Concept of Mode
- Concept for Constructing
- Interpretation of Bar Graphs

- Collection and organisation of data – choosing the data to collect for a hypothesis testing
- Mean, median and mode of ungrouped data – understanding what they represent
- Constructing and interpreting bar graphs

502 Probability

- Basic Ideas of Probability
- Concept for Feel of Probability Using Data Through Experiments.
- Concept for Notion of Chance
- Concept for Tabulating and Counting Occurrences
- Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness.

Feel of probability using data through experiments. Notion of chance in events like tossing coins, dice etc. Tabulating and counting occurrences of 1 through 6 in a number of throws. Comparing the observation with that for a coin. Observing strings of throws, notion of randomness.

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