How to learn Class 7: Mathematics

NCERT syllabus (National Council of Educational Research and Training): Mathematics, Class 7

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1. Number System · Knowing our Numbers

Fractions on a number line: Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line

Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

Unit Conversions: Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate

Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
Collecting Like Terms: Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence
Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
Percentages (age 12+): Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest

Understanding angles (age 11+): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems
Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections
Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

Angles in triangles (age 12+): Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

Types of angles (age 8+): Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown values

Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability