CBSE Class VI Mathematics

Mathematics in class 6 is an extremely important and scoring topic. The students are expected to strictly follow the curriculum Which has been circulated by NCERT and follow the books which have been published As for the syllabus issued by CBSE. When the child will go through various chapters which are being taught in class 6 mathematics then it is expected that the child will be able to perform the following activities with the help of their teachers and parents. Teachers  should look into the following activities and keep on testing class 6 mathematics students to make sure that the understanding of the students is such that they're able to clearly understand the concepts and will be in a position to apply the concepts in various situations as well as also help to improve the problem solving and mathematical analytical skills of class six students.

- Encounter situations having numbers up to 8 digits, e.g., cost of property, total population of different towns, etc.

- Compare numbers through situations like cost of two houses, number of spectators, money transactions, etc.

- Classify numbers on the basis of their properties like even, odd, etc.

- Observe patterns that lead to divisibility by 2,3,4,5,6,8,10 and 11.

- Create number patterns through which HCF and LCM can be discussed

- Explore daily life situations to involve the use of HCF and LCM

- Create and discuss daily life situations involving the use of negative numbers

- Observe situations that require the representation by fractions and decimals. Students are suggested to do Worksheets for class 6 Mathematics on a regular basis to make sure they are fully prepared for the exams.

- Use different contexts in mathematics to appreciate the necessity of representing unknowns by variables (alphabet)

- Explore and generalise the need of using variables alphabets

- Describe situations involving the need for comparing quantities by taking ratio

- Discuss and solves word problems that use ratios and unitary method

- Explore various shapes through concrete models and pictures of different geometrical shapes like triangles and quadrilaterals, etc and also for Sample Papers for Class 6 Mathematics

- Identify various geometrical figures and observe their characteristics in and outside the classroom  environment either individually or in groups

- Make different shapes with the help of available materials like sticks, paper cutting, etc.

- Observe various models and nets of 3-Dimensional (3-D) shapes like cuboid, cylinder, etc. and discuss about the elements of 3-D figures such as faces, edges and vertices and also refer to NCERT Solutions for Class 6 Mathematics.

- Share the concept of angles through some examples like opening the door, opening the pencil box, etc. Students can be asked to give more such examples from the surroundings

- Classify angles based on the amount of rotation.

Class 6 mathematics syllabus, examination structure and important topics. The syllabus for class 6 is mainly driven by the topics given in the mathematics books issued by NCERT books, most of the schools are also recommending books of other publishers which have additional worksheets, which the students can practice to score better in class tests and school level examinations. Details of important topics is given below:

Number System (60 hrs)

(i). Knowing our Numbers:

Consolidating the sense of number ness up to 5 digits, Size, estimation of numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of symbols =, >, < <,>and use of brackets, word problems on number operations involving large numbers up to a maximum of 5 digits in the answer after all operations. This would include conversions of units of length & mass (from the larger to the smaller units), estimation of outcome of number operations. Introduction to a sense of the largeness of, and initial familiarity with, large numbers up to 8 digits and approximation of large numbers)

(ii). Playing with Numbers:

Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, and 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 factorization, 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. All this is to be embedded in contexts that bring out the significance and provide motivation to the child for learning these ideas.

(iii). Whole numbers

Natural numbers, whole numbers, properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity), number line. Seeing patterns, identifying and formulating rules to be done by children. (As familiarity with algebra grows, the child can express the generic pattern.)

(iv).Negative Numbers and Integers

How negative numbers arise, models of negative numbers, connection to daily life, ordering of negative numbers, and representation of negative numbers on number line. Children to see patterns identify and formulate rules. What are integers, identification of integers on the number line, operation of addition and subtraction of integers, showing the operations on the number line (addition of negative integer reduces the value of the number) comparison of integers, ordering of integers.

(v). 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, addition and subtraction of 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)

Algebra (15 hrs.)

Introduction To Algebra

1. Introduction to variable through patterns and through appropriate word problems and generalizations (example 5 × 1 = 5 etc.)
2. Generate such patterns with more examples.
3. Introduction to unknowns through examples with simple contexts (single operations)

Ratio and Proportion (15 hrs.)

1. Concept of Ratio
2. Proportion as equality of two ratios
3. Unitary method (with only direct variation implied)
4. Word problems

Geometry (65 hrs.)

(i).Basic geometrical ideas (2 -D):

Introduction to geometry. Its linkage with and reflection in everyday experience.

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.

(i). Understanding Elementary

Shapes (2-D and 3-D):

1. Measure of Line segment
2. Measure of angles
3. Pair of lines – Intersecting and perpendicular lines – Parallel lines
4. Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle
5. Classification of triangles (on the basis of sides, and of angles)
6. Types of quadrilaterals – Trapezium, parallelogram, rectangle, square, rhombus.
7. Simple polygons (introduction) (Up to octagons regulars as well as non-regular).
8. Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular), pyramid (triangular and square) Identification and locating in the surroundings
9. Elements of 3-D figures. (Faces, Edges and vertices)
10. Nets for cube, cuboids, cylinders, cones and tetrahedrons.

(iii).Symmetry: (reflection)

1. Observation and identification of 2-D symmetrical objects for reflection symmetry
2. Operation of reflection (taking mirror images) of simple 2-D objects
3. Recognising reflection symmetry (identifying axes)

(iv).Constructions (using Straight edge Scale, protractor, compasses) • Drawing of a line segment

1. Construction of circle
2. Perpendicular bisector
3. Construction of angles (using protractor)
4. Angle 60°, 120° (Using Compasses)
5. Angle bisector- making angles of 30°, 45°, 90° etc. (using compasses)
6. Angle equal to a given angle (using compass)
7. Drawing a line perpendicular to a given line from a point a) on the line b) outside the line.

Mensuration (15 hrs.)

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 Counter examples to different misconnects 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 generalization.

Data handling (10 hrs.)

(i).What is data - choosing data to examine a hypothesis?

(ii). Collection and organization of data - examples of organizing it in tally bars and a table.

(iii). Pictograph- Need for scaling in pictographs interpretation & construction. (iv).Making bar graphs for given data interpreting bar graphs+.