## Topics with syllabus and resources

Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.

Estimation of outcome of number operations.

Numbers in Indian and International Systems and their comparison

Place value - recapitulation and extension

- Natural numbers
- Whole numbers

- Need for negative numbers.
- Connection of negative numbers in daily life.
- Representation of negative numbers on number line.
- Ordering of negative numbers, Integers.
- Identification of integers on the number line,
- Operation of addition and subtraction of integers,
- Addition and subtraction of integers on the number line
- Comparison of integers,
- ordering of integers.

- Concepts :
- Need for Negative Numbers
- Connection of Negative Numbers in Daily Life
- Representation of Negative Numbers on Number Line
- Ordering of Negative Numbers, Integers.
- Identification of Integers on the Number Line,
- Operation of Addition and Subtraction of Integers
- Addition and Subtraction of Integers on the Number Line
- Comparison of Integers
- Concept for Ordering of Integers
- Concept for Negative Numbers and Integers

- Number line.
- Seeing patterns, identifying and formulating rules for operations on numbers.

- HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM × HCF = product of two numbers

- Simplification of brackets.
- Multiples and factors,
- divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility)
- Even/odd and prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as products of prime factors.

- Idea of sets.
- Representation of sets.
- Types of sets: Finite/infinite and empty.
- Cardinality of a set

Difference between fraction and ratio.

Concept of Ratio.

Unitary method (with only direct variation implied).

- Revision of what a fraction is.
- Fraction as a part of whole.
- Representation of fractions (pictorially and on number line).
- Fraction as a division.
- Proper, improper & mixed fractions.
- Equivalent fractions
- Comparison of fractions
- Operations on fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions).

- Concepts :
- Concept for Fractions
- Concept of Fraction as a Part of Whole
- Representation of Fractions (Pictorially and on Number Line).
- Concept for Fraction as a Division.
- Proper, Improper and Mixed Fractions.
- Concept for Equivalent Fractions
- Comparison of Fractions
- Operations on Fractions (Avoid Large and Complicated Unnecessary Tasks). (Moving Towards Abstraction in Fractions).

- Review of the idea of a decimal fraction.
- Place value in the context of decimal fraction.
- Inter conversion of fractions and decimal fractions (avoid recurring decimals at this stage).
- Word problems involving addition and subtraction of decimals (two operations together on money, mass, length and temperature).

Idea of percent as fraction with 100 as denominator

Idea of speed and simple daily life problems related to speed, time and distance

Introduction to constants, variable and unknown through patterns and through appropriate word problems and generalisations (For example 1+3=22, 1+3+5=32,

1+3+5+7=42 , sum of first n odd numbers = n2.).

Terminology associated with algebra- like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms

Introduction to unknowns through examples with simple contexts (single operations)

- Concepts :
- Concept of Substitution

Framing algebraic expressions.

Evaluation of algebraic expressions by substituting a value for the variable.

Introduction to linear equation in one variable.

Basic geometrical ideas (2 -D): Introduction to geometry. Its linkage with and reflection in everyday experiences.

Line, line segment, ray.

Open and closed figures.

Interior and exterior of closed figures.

Curvilinear and linear boundaries

Angle — Vertex, arm, interior and exterior.

- Concepts :
- Concepts of Fundamental (Geometry)
- Concept for Basic Geometrical Ideas (2 -d)
- Concept for Linkage with and Reflection in Everyday Experiences.
- Concept for Line, Line Segment, Ray.
- Concept for Open and Closed Figures.
- Concept for Interior and Exterior of Closed Figures.
- Curvilinear and Linear Boundaries
- Angle — Vertex, Arm, Interior and Exterior.

Measure of angles

Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle.

Measure of Line segment

Pair of lines – Intersecting and perpendicular lines, Parallel lines.

Triangle — vertices, sides, angles, interior and exterior, altitude and median.

Classification of triangles (on the basis of sides, and of angles).

Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.

Simple polygons (introduction) (Upto octagons regulars as well as non-regular).

Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.

Symmetry: (reflection)

Observation and identification of 2-D symmetrical objects for reflection symmetry.

Operation of reflection (taking mirror images) of simple 2-D objects

Recognising reflection symmetry (identifying axes).

- Concepts :
- Concept of Revision Exercise Symmetry (Including Constructions on Symmetry)
- Symmetry: (Reflection)
- Concept of Observation and Identification of 2-d Symmetrical Objects for Reflection Symmetry.
- Operation of Reflection (Taking Mirror Images) of Simple 2-d Objects
- Recognising Reflection Symmetry (Identifying Axes).

Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular and square), pyramid (triangular and square), Identification and

locating in the surroundings.

Elements of 3-D figures. (Faces, Edges and vertices).

Nets for cube, cuboids, cylinders, cones and tetrahedrons.

- Concepts :
- Concept of Recognition of Solids
- Identification of 3-d Shapes: Cubes, Cuboids, Cylinder, Sphere, Cone, Prism (Triangular and Square), Pyramid (Triangular and Square)
- Identification and Locating in the Surroundings.
- Elements of 3-d Figures. (Faces, Edges and Vertices).
- Nets for Cube, Cuboids, Cylinders, Cones and Tetrahedrons.

- Concept of perimeter and introduction to area
- Introduction and general understanding of perimeter using many shapes.
- Shapes of different kinds with the same perimeter.
- Concept of area, Area of a rectangle and a square
- Conversion of units (Mass, time, money, and capacity) from to smaller to larger and vice-versa
- Counter examples to different misconcepts related to perimeter and area.
- Perimeter of a rectangle – and its special case – a square.
- Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.

- Concepts :
- Concept of Perimeter and Area of Plane Figures
- Introduction and General Understanding of Perimeter Using Many Shapes.
- Shapes of Different Kinds with the Same Perimeter.
- Concept of Area, Area of a Rectangle and a Square
- Conversion of Units (Mass, Time, Money, and Capacity) from to Smaller to Larger and Vice-versa
- Counter Examples to Different Misconcepts Related to Perimeter and Area.
- Perimeter of a Rectangle – and Its Special Case – a Square.
- Deducing the Formula of the Perimeter for a Rectangle and Then a Square Through Pattern and Generalisation.

Collection of data to examine a hypothesis

Collection and organisation of data - examples of organising it in tally bars and a table.

Pictograph- Need for scaling in pictographs interpretation & construction of pictograph

Mean and median of data not having more than ten observations

- Concepts :
- Concepts of Mean and Median