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# 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.