India

7.NS Number System

• 7.NS.i Knowing our Numbers: Integers

  • 7.NS.i.1 Multiplication and division of integers (through patterns). Division by zero is meaningless

    • Integer multiplication and division rules (VII-C.6)
    • Multiply and divide integers (VII-C.7)
    • Complete multiplication and division sentences with integers (VII-C.8)

  • 7.NS.i.2 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.

    • Properties of addition and multiplication (VII-P.9)

  • 7.NS.i.3 Word problems including integers (all operations)

    • Add and subtract integers: word problems (VII-C.5)

• 7.NS.ii Fractions and rational numbers:

  • 7.NS.ii.1 Multiplication of fractions

    • Multiply fractions and whole numbers (VII-G.7)
    • Multiply fractions (VII-G.9)
    • Multiply mixed numbers (VII-G.10)

  • 7.NS.ii.2 Fraction as an operator

    • Multiply fractions and mixed numbers: word problems (VII-G.11)

  • 7.NS.ii.3 Reciprocal of a fraction

    • Multiplicative inverses (VII-A.3)

  • 7.NS.ii.4 Division of fractions

    • Divide fractions (VII-G.13)
    • Divide mixed numbers (VII-G.14)

  • 7.NS.ii.5 Word problems involving mixed fractions

    • Fractions: word problems with graphs and tables (VII-F.4)
    • Compare fractions: word problems (VII-F.7)
    • Add and subtract mixed numbers (VII-G.3)
    • Multiply fractions and mixed numbers: word problems (VII-G.11)
    • Divide fractions and mixed numbers: word problems (VII-G.15)
    • Add, subtract, multiply and divide fractions and mixed numbers: word problems (VII-G.17)

  • 7.NS.ii.6 Introduction to rational numbers (with representation on number line)

    • Equivalent fractions (VII-F.2)
    • Write fractions in lowest terms (VII-F.3)
    • Lowest common denominator (VII-F.5)
    • Compare and order fractions (VII-F.6)
    • Convert between mixed numbers and improper fractions (VII-F.8)
    • Compare mixed numbers and improper fractions (VII-F.9)
    • Identify rational numbers (VII-H.1)
    • Compare rational numbers (VII-H.3)
    • Put rational numbers in order (VII-H.4)

  • 7.NS.ii.7 Operations on rational numbers (all operations)

    • Add and subtract rational numbers (VII-H.5)
    • Multiply and divide rational numbers (VII-H.7)

  • 7.NS.ii.8 Representation of rational number as a decimal.

    • Convert between decimals and fractions or mixed numbers (VII-H.2)

  • 7.NS.ii.9 Word problems on rational numbers (all operations)

    • Add, subtract, multiply and divide fractions and mixed numbers: word problems (VII-G.17)

  • 7.NS.ii.10 Multiplication and division of decimal fractions

    • Multiply decimals (VII-E.3)
    • Multiply decimals and whole numbers: word problems (VII-E.4)
    • Divide decimals (VII-E.5)
    • Divide decimals by whole numbers: word problems (VII-E.6)

  • 7.NS.ii.11 Conversion of units (length & mass)

    • Compare and convert metric units (VII-N.2)
    • Metric mixed units (VII-N.3)
    • Convert square and cubic units of length (VII-N.4)
    • Convert between cubic metres and litres (VII-N.5)

  • 7.NS.ii.12 Word problems (including all operations)

    • Add and subtract decimals: word problems (VII-E.2)
    • Multiply decimals and whole numbers: word problems (VII-E.4)
    • Divide decimals by whole numbers: word problems (VII-E.6)
    • Add, subtract, multiply and divide decimals: word problems (VII-E.8)
    • Multiply fractions and mixed numbers: word problems (VII-G.11)
    • Divide fractions and mixed numbers: word problems (VII-G.15)
    • Add, subtract, multiply and divide fractions and mixed numbers: word problems (VII-G.17)

• 7.NS.iii Powers:

  • 7.NS.iii.1 Exponents only natural numbers.

    • Understanding exponents (VII-I.1)
    • Evaluate exponents (VII-I.2)
    • Solve equations with variable exponents (VII-I.3)

  • 7.NS.iii.2 Laws of exponents (through observing patterns to arrive at generalisation.)

    • 7.NS.iii.2.i a to the m power x aⁿ= a to the m+n power

      • Multiplication with exponents (VIII-F.8)

    • 7.NS.iii.2.ii (a to the m power)ⁿ = a to the mn power

      • Power rule (VIII-F.11)

    • 7.NS.iii.2.iii a to the m power/aⁿ = a to the m–n power, where m–n ∈?

      • Division with exponents (VIII-F.9)
      • Multiplication and division with exponents (VIII-F.10)
      • Evaluate expressions using properties of exponents (VIII-F.12)

7.A Algebra

• 7.A.A Algebraic Expressions

  • 7.A.A.1 Generate algebraic expressions (simple) involving one or two variables

    • Write variable expressions for arithmetic sequences (VII-O.7)
    • Write variable expressions (VII-P.1)
    • Write variable expressions: word problems (VII-P.2)

  • 7.A.A.2 Identifying constants, coefficient, powers

    • Identify terms and coefficients (VII-P.7)

  • 7.A.A.3 Like and unlike terms, degree of expressions e.g., x²y etc. (exponent ≤ 3, number of variables)

    • Add and subtract like terms (VII-P.13)

  • 7.A.A.4 Addition, subtraction of algebraic expressions (coefficients should be integers).

    • Add and subtract like terms (VII-P.13)

  • 7.A.A.5 Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)

    • Solve equations using properties (VII-P.11)
    • Write an equation from words (VII-Q.2)
    • Write and solve equations that represent diagrams (VII-Q.4)
    • Solve one-step equations (VII-Q.5)
    • Solve two-step equations (VII-Q.6)
    • Solve equations: word problems (VII-Q.7)
    • Solve equations involving like terms (VII-Q.8)
    • Solve equations: complete the solution (VII-Q.9)

7.RP Ratio and Proportion

• 7.RP.1 Ratio and proportion (revision)

  • Understanding ratios (VII-J.1)
  • Identify equivalent ratios (VII-J.2)
  • Write an equivalent ratio (VII-J.3)
  • Equivalent ratios: word problems (VII-J.4)
  • Compare ratios: word problems (VII-J.6)
  • Do the ratios form a proportion? (VII-J.8)
  • Do the ratios form a proportion: word problems (VII-J.9)
  • Solve proportions (VII-J.10)
  • Solve proportions: word problems (VII-J.11)
  • Estimate population size using proportions (VII-J.12)

• 7.RP.2 Unitary method continued, consolidation, general expression.

  • Unit rates (VII-J.5)
  • Unit prices (VII-L.3)
  • Unit prices: find the total price (VII-L.4)

• 7.RP.3 Percentage - an introduction.

  • What percentage is illustrated? (VII-K.1)

• 7.RP.4 Understanding percentage as a fraction with denominator 100

  • Estimate percents of numbers (VII-K.4)
  • Solve percent equations (VII-K.7)
  • Solve percent equations: word problems (VII-K.8)

• 7.RP.5 Converting fractions and decimals into percentage and vice-versa.

  • Convert between percents, fractions and decimals (VII-K.2)
  • Compare percents to fractions and decimals (VII-K.3)

• 7.RP.6 Application to profit and loss (single transaction only)

  • Percents of numbers and money amounts (VII-K.5)
  • Percents of numbers: word problems (VII-K.6)
  • Price lists (VII-L.2)
  • Percent of a number, discount and more (VII-L.5)
  • Find the percent: discount and mark-up (VII-L.6)
  • Sale prices: find the original price (VII-L.7)
  • Multi-step problems with percents (VII-L.8)

• 7.RP.7 Application to simple interest (time period in complete years).

  • Simple interest (VII-L.10)

7.G Geometry

• 7.G.i Understanding shapes:

  • 7.G.i.1 Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)

    • Name, measure and classify angles (VII-R.2)
    • Identify complementary, supplementary, vertical, adjacent and congruent angles (VII-R.13)
    • Find measures of complementary, supplementary, vertical and adjacent angles (VII-R.14)

  • 7.G.i.2 Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)

    • Transversal of parallel lines (VII-R.15)

• 7.G.ii Properties of triangles:

  • 7.G.ii.1 Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)

    • Triangle angle-sum property (VII-R.7)

  • 7.G.ii.2 Exterior angle property

    • Exterior angle property (VII-R.8)

  • 7.G.ii.3 Sum of two sides of a it's third side

  • 7.G.ii.4 Pythagoras Theorem (Verification only)

    • Converse of Pythagoras' theorem: is it a right triangle? (VII-U.4)

• 7.G.iii Symmetry

  • 7.G.iii.1 Recalling reflection symmetry

    • Symmetry (VII-R.18)

  • 7.G.iii.2 Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (900, 1200, 1800)

    • Rotational symmetry (VI-T.2)

  • 7.G.iii.3 Operation of rotation through 900 and 1800 of simple figures.

  • 7.G.iii.4 Examples of figures with both rotation and reflection symmetry (both operations)

  • 7.G.iii.5 Examples of figures that have reflection and rotation symmetry and vice-versa

• 7.G.iv Representing 3-D in 2-D:

  • 7.G.iv.1 Drawing 3-D figures in 2-D showing hidden faces.

    • Nets of three-dimensional figures (VII-V.2)

  • 7.G.iv.2 Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).

    • Count vertices, edges and faces (VI-V.2)

  • 7.G.iv.3 Matching pictures with objects (Identifying names)

    • Bases of three-dimensional figures (VII-V.1)

  • 7.G.iv.4 Mapping the space around approximately through visual estimation.

    • Front, side and top view (VII-V.3)

• 7.G.v Congruence

  • 7.G.v.1 Congruence through superposition (examples-blades, stamps, etc.)

  • 7.G.v.2 Extend congruence to simple geometrical shapes e.g. triangles, circles.

    • Side lengths and angle measures of congruent figures (VII-S.2)
    • Congruence statements and corresponding parts (VII-S.3)

  • 7.G.v.3 Criteria of congruence (by verification) SSS, SAS, ASA, RHS

    • Congruent triangles: SSS, SAS and ASA (VIII-P.4)

• 7.G.vi Construction (Using scale, protractor, compass)

  • 7.G.vi.1 Construction of a line parallel to a given line from a point outside it. (Simple proof as remark with the reasoning of alternate angles)

    • Construct parallel lines (VII-T.4)

  • 7.G.vi.2 Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.

7.MEN Mensuration

• 7.MEN.1 Revision of perimeter, Idea of, Circumference of Circle

  • Perimeter (VII-W.1)
  • Area and perimeter: word problems (VII-W.4)
  • Circles: calculate area, circumference, radius and diameter (VII-W.5)

• 7.MEN. Area

  • 7.MEN.1 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

    • Area of rectangles and parallelograms (VII-W.2)
    • Area of triangles (VII-W.3)
    • Circles: calculate area, circumference, radius and diameter (VII-W.5)
    • Semicircles: calculate area, perimeter, radius and diameter (VII-W.7)
    • Quarter circles: calculate area, perimeter and radius (VII-W.8)
    • Area of compound figures with triangles, semicircles and quarter circles (VII-W.9)
    • Area between two shapes (VII-W.10)

7.DH Data handling

• 7.DH.i Collection and organisation of data – choosing the data to collect for a hypothesis testing.

  • Interpret tables (VII-X.1)
  • Interpret line plots (VII-X.2)
  • Create line plots (VII-X.3)
  • Interpret stem-and-leaf plots (VII-X.4)
  • Interpret bar graphs (VII-X.6)
  • Create bar graphs (VII-X.7)
  • Interpret histograms (VII-X.8)
  • Create histograms (VII-X.9)
  • Create frequency charts (VII-X.10)
  • Interpret line graphs (VII-X.11)
  • Create line graphs (VII-X.12)

• 7.DH.ii Mean, median and mode of ungrouped data – understanding what they represent.

  • Calculate mean, median, mode and range (VII-Y.1)
  • Interpret charts to find mean, median, mode and range (VII-Y.2)

• 7.DH.iii Constructing bargraphs

  • Create bar graphs (VII-X.7)

• 7.DH.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.

  • Probability of simple events (VII-Z.1)
  • Experimental probability (VII-Z.3)
  • Make predictions (VII-Z.4)