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Study 7th STANDARD - Mathematics

Maths Course Structure - Class VII

Number System

(i) Knowing our Numbers:Integers

  • Multiplication and division of integers (through patterns). Division by zero is meaningless
  • Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns).
  These would include examples from whole numbers as well. Involve expressing commutative and associative properties in a general form. Construction of counterexamples, including some by children. Counter examples like subtraction is not commutative.
  • Word problems including integers (all operations)



(ii) Fractions and rational numbers

  • Multiplication of fractions
• Fraction as an operator
• Reciprocal of a fraction
• Division of fractions
• Word problems involving mixed fractions
• Introduction to rational numbers (with representation on number line)
• Operations on rational numbers (all operations)
• Representation of rational number as a decimal.
• Word problems on rational numbers (all operations)
• Multiplication and division of decimal fractions
• Conversion of units (length & mass)
• Word problems (including all operations)



(iii) Powers

  • Exponents only natural numbers.
• Laws of exponents (through observing patterns to arrive at generalisation.)
  (i) am an am+n
(ii) (am)n =amn
(iii) am/an = am-n, where m - n ∈ Ν



Algebra

ALGEBRAIC EXPRESSIONS

  • Generate algebraic expressions (simple) involving one or two variables
• Identifying constants, coefficient, powers
• Like and unlike terms, degree of expressions e.g., x2y etc. (exponent ≤ 3, number of variables )
• Addition, subtraction of algebraic expressions (coefficients should be integers).
• Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)



Ratio and Proportion

  • Ratio and proportion (revision)
• Unitary method continued, consolidation, general expression.
• Percentage- an introduction.
• Understanding percentage as a fraction with denominator 100
• Converting fractions and decimals into percentage and vice-versa.
• Application to profit and loss (single transaction only)
• Application to simple interest (time period in complete years).



Geometry

(i) Understanding shapes

  • Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)
  • Properties of parallel lines with transversal (alternate,corresponding, interior, exterior angles)



(ii) Properties of triangles

  • Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)
• Exterior angle property
• Sum of two sides of a it's third side
• Pythagoras Theorem (Verification only)



(iii) Symmetry

  • Recalling reflection symmetry
• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90o, 120o, 180o)
• Operation of rotation through 90o and 180o of simple figures.
• Examples of figures with both rotation and reflection symmetry (both operations)
• Examples of figures that have reflection and rotation symmetry and vice-versa



(iv) Representing 3-D in 2-D

  • Drawing 3-D figures in 2-D showing hidden faces.
• Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
• Matching pictures with objects (Identifying names)
• Mapping the space around approximately through visual estimation.



(v) Congruence

  • Congruence through superposition (examplesblades, stamps, etc.)
• Extend congruence to simple geometrical shapes e.g. triangles, circles.
• Criteria of congruence (by verification) SSS, SAS, ASA, RHS



(vi) Construction (Using scale, protractor, compass)

  • Construction of a line parallel to a given line from a point outside it.(Simple proof as remark with the reasoning of alternate angles)
• Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.



Mensuration

  • Revision of perimeter, Idea of , Circumference of Circle Area Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two concentric circles.



Data handling

  (i) Collection and organisation of data – choosing the data to collect for a hypothesis testing.
(ii) Mean, median and mode of ungrouped data – understanding what they represent.
(iii) Constructing bargraphs
(iv) 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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