1. Number System

• 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)
• 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 (lengths & mass)
  • Word problems (including all operations)
• Powers
  • Exponents only natural numbers.
  • Laws of exponents (through observing patterns to arrive at generalization.)

2. Algebra

• Algebraic Expressions
  • Review of elementary concepts in Algebra.
  • Identifying constants, coefficient, powers
  • Like and unlike terms, degree of expressions e.g. x y 2 etc. (exponent ≤ 3 number of variables ≤ 2)
  • Addition, subtraction of algebraic expressions (coefficients should be integers).
  • Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)
  • Multiplication of algebraic exp.(co-efficient should be integers)

3. Ratio and Proportion

• Ratio and proportion (revision)
• Unitary method continued consolidation, general expression.

4. Percentage

• An introduction w.r.t life situation.
• Understanding percentage as a fraction with denominator 100
• Converting fractions and decimals into percentage and vice-versa.
• Application to profit & loss (single transaction only)
• Application to simple interest (time period in complete years)

5. Geometry

• 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)
• 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 D > it’s third side
  • Pythagoras Theorem (Verification only)
• Symmetry
  • Recalling symmetry
  • Idea of rotational symmetry, observations of rotational symmetry of 2D objects. (90º,120º, 180º)
  • Operation of rotation through 90º &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
• Representing 3D in 2D
  • Cuboids, cylinders, cones and tetrahedrons.
  • Drawing 3D figures in 2D showing hidden faces.
  • Identification & counting of vertices edges, faces, nets (for cubes cuboids, & cylinders, cones) using pictures.
  • Matching pictures with objects (Identifying names)
  • Representing the space around approximately through visual estimation.
• Congruence
  • Congruence through superposition (examples-coins, biscuits, bangles, stamps, etc.)
  • Extend congruence to simple geometrical shapes e.g. triangles, circles.
• Construction (Using scale, protractor, compass)
  • Perpendicular bisector.
  • Angle bisector- making angles of 30º, 45º, 90º etc. (using compasses)
  • Angle equal to a given angle (using compass)
  • Drawing a line perpendicular to a given line from a point a) on the line b) outside the line
  • Construction of a line parallel to a given line from a point outside it.(Simple proof as remark with the reasoning of alternate angles)

6. Mensuration

• Revision of perimeter, Idea of p, 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.

7. Data handling

• Collection and organisation of data – choosing the data to collect for a hypothesis testing.
• Mean, median and mode of ungrouped data understanding what they represent.
• Constructing bar graphs
• 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. Preparing the bar graph.
• Comparing the observation with that for a coin. Observing strings of throws, notion of Randomness of ungrouped data.