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Lesson : Negative Numbers and Integers

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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

Natural numbers

Whole numbers

Properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity)

Number line

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

Sets

Idea of sets

Representation of sets

Types of sets: Finite/infinite and empty

Cardinality of a set

Fractions

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)

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.

Understanding Elementary Shapes (2-D and 3-D):

Symmetry: (reflection)

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

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