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## 1. Number System (50 hrs)

### (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

## 2. Algebra (20 hrs)

### (i) 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)

### (ii) Ratio and Proportion (20 hrs)

•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).

## 3. Geometry (60 hrs)

### (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.

## 4. Mensuration (15 hrs)

• 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.

## 5. Data handling (15 hrs)

(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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