 # Class 7 Mathematics Karnataka Board Syllabus

### 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.  Study Materials for Class 7   