Chapter : 1 Number System
Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc
Place value (recapitulation and extension.,
Operations on large numbers
Word problems on number operations involving large numbers
Estimation of outcome of number operations.
Introduction to a sense of the largeness (up to 8 digits) and approximation of large numbers
Numbers in Indian and International Systems and their comparison.
Natural numbers and Whole numbers
Properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity)
Seeing patterns, identifying and formulating rules for operations on numbers
Negative Numbers and Integers
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
Idea of sets
Representation of sets
Types of sets: Finite/infinite and empty
Cardinality of a set
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
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).
Playing with 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
HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM × HCF = product of two numbers.
Chapter : 2 Ratio and Proportion
Difference between fraction and ratio
Concept of Ratio
Proportion as equality of two ratios
Unitary method (with only direct variation implied)
Word problems on ratio and proportions
Idea of percent as fraction with 100 as denominator
Idea of speed and simple daily life problems related to speed, time and distance.
Chapter : 3 Algebra
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.)
Generate such patterns with more examples and generalisation
Introduction to unknowns through examples with simple contexts (single operations)
Terminology associated with algebra- like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms
Framing algebraic expressions
Evaluation of algebraic expressions by substituting a value for the variable
Introduction to linear equation in one variable
Chapter : 4 Geometry
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
- Triangle — vertices, sides, angles, interior and exterior, altitude and median
- Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral
- Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior
Understanding Elementary Shapes (2-D and 3-D):
- Measure of Line segment
- Measure of angles
- Pair of lines – Intersecting and perpendicular lines, Parallel lines
- Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle
- Classification of triangles (on the basis of sides, and of angles)
- Types of quadrilaterals – Trapezium, parallelogram, rectangle, square, rhombus.
- Simple polygons (introduction) (Upto octagons regulars as well as non-regular).
- 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
Constructions (using Straight edge Scale, protractor, compasses)
Chapter : 5 Mensuration
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 misconceptions 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.
3D Figures - Cubes and Cuboids
Introduction to Volume
Chapter : 6 Data Handling
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
Construction of bar graphs for given data interpreting bar graphs
Mean and median of data not having more than ten observations