NCERT Math Curriculum Survey

Last updated 26/08/2020

6th Standard

1. Knowing our Numbers

Decimal number system, dealing with large numbers, estimation and approximations, chained operations.

Potential Tasks

  • (In-text) Arranging objects in increasing/decreasing orders

2. Whole Numbers

How whole numbers work. Properties of association and distribution over mathematical operations.

Potential Tasks

  • (Weak) Number Line representation & operations
  • (In-text) Distributivity of multiplication over addition: Breaking apart grids, and combining them again to show distributive properties.
  • (In-text) Patterns of whole numbers: arranging ‘n’ objects into regular shapes.

3. Playing with Numbers

Multiples, Divisors, Factors. Primes and Composites. Divisibility tests. HCF & LCM.

Potential Tasks

  • (In-text) Factors and Multiples as arrangements of objects
  • (In-text)(Collab) Two-person game involving number cards and the concept of multiples and factors, with the aim to have the highest total of cards at the end
  • (Weak) Trying out the Sieve of Eratosthenes: Identifying Prime Numbers
  • (Weak) Factor Trees
  • (In-text) HCF & LCM based word problems involving physical quantities: volumes, distances, steps, repetitions

4. Basic Geometrical Ideas

Points, Lines and their types, Rays, Curves, Polygons, Angles, Triangles, Quadrilaterals, Circles

Potential Tasks

  • (In-text) Identifying geometries in real life
  • (In-text) Creating geometries out of primitive objects (folding papers to explore intersecting and parallel lines, making shapes out of matchsticks)
  • (In-text) Position of objects (inside, on, outside)

5. Understanding Elementary Shapes

Measuring & Identifying Lines, Angles, 2D & 3D Shapes

Potential Tasks

  • (In-text) Measuring & identifying by sight and scales (lines, angles, shapes)
  • (In-text) Orientation using a compass, while understanding angles
  • (In-text)(Collab) 2 student activities using their respective instrument boxes: creating shapes and measuring them
  • (In-text) Identifying faces, edges, and vertices

6. Integers (October 2020)

What Integers are, negative numbers, ordering, number line, operations

Potential Tasks

  • (In-text)(Collab) Sharing and borrowing objects to meet requirements
  • (In-text)(Collab) Dice based board game involving addition of integers
  • (In-text)(Collab) Relative motion based on steps and integers
  • (In-text) Ordering of Integers: Wells and Water Depth
  • (Weak) Integer Number Line

7. Fractions

What fractions are, how to express them, proper, improper & mixed fractions, fractional comparisons and operations

Potential Tasks

  • (In-text)(Collab) Sharing fractions of real objects
  • (In-text) Shading fractions of grids
  • (Weak) Fractional Number Line
  • (In-text) Differently breaking up objects to demonstrate equivalent fractions, to compare fractions, or to perform fractional operations

8. Decimals

What decimals are, converting fractions to decimals, number line, operations, measurements

Potential Tasks

  • (Weak) Decimal Number Line
  • (In-text) Measuring items (costs, lengths & weights) using a decimal scales and grids

9. Data Handling

Data/Information, Tally marks, pictographs, bar graphs

Potential Tasks

  • (Weak) Bar Graph visualisations

10. Mensuration

Perimeter, Area

Potential Tasks

  • (In-text) Measuring the perimeter of objects
  • (In-text) Measuring 2D area by shading

11. Algebra

Variables, Equations, Solving Equations

Potential Tasks

  • (In-text)(Collab) Patterns as Equations (matchstick arrangements)
  • (In-text) Spatial word-problems relating to algebra

12. Ratio and Proportion

Comparing quantities through ratios, and identifying and working with proportions

Potential Tasks

  • (In-text) Comparing objects and quantities through ratios

13. Symmetry

Types of symmetry, reflections

Potential Tasks

  • (In-text) Ink-blot devils, paper snowflakes, rangoli patterns
  • (In-text) Kaleidoscope
  • (In-text) Identifying reflections and symmetry around us

14. Practical Geometry

Constructing shapes using stuff from an instrument box

Potential Tasks

  • (In-text) Using instruments to construct geometrical figures
  • (In-text) Paper folding to build intuition for construction steps

Brain Teasers

Quite a few collab + spatial problems in the brain teaser section

7th Standard

1. Integers

Number line, properties of integer operations

Potential Tasks

  • (In-text)(Weak) A 2-player boardgame involving dice
  • (Spatial) Alternate arrangements or routes (distributivity)

2. Fractions and Decimals

More detailed operations and rules

Potential Tasks

  • (In-text)(Weak) Multiplaction/divisions of fractions as ‘parts’ of an object
  • (In-text)(Weak) Grid-based operations on decimals

3. Data Handling

Tables, Mean, Range, Mode, Median, using bar graphs, chance and probability

Potential Tasks

  • Mean, median, mode of objects
  • Playing with scales of bar graphs
  • Real objects + probability? Blended AR

4. Simple Equations

Solving equations, real-life equations

Potential Tasks

  • (In-text) Physical puzzles as equations (marbles, runs, fruits)

5. Lines and Angles

Types of angles (acute obtuse reflex complementary supplementary adjacent) and lines (intersecting, transversal, parallel)

Potential Tasks

  • (In-text) Identify line types and angles
  • (In-text) Parallel line + transversal angles in real objects

6. The Triangle and its Properties

Medians, Altitude, properties of angles, types of triangles, pythagoras theorem

Potential Tasks

  • (Weak) Initial intuition of medians and altitude
  • (Weak) 2D tasks to prove theorems and properties

7. Congruence of Triangles

Congruence properties

Potential Tasks

  • (In-text) Overlapping objects to test congruence
  • (Weak) Discussing triangles and congruence
  • (In-text) Enrichment Activity: cutout comparisons for congruence

8. Comparing Quantities

Ratios, types of ratios, unitary method, percentage, estimation, profit and loss, simple interest

Potential Tasks

  • Measuring ratios, combining proportions of real objects

9. Rational Numbers (October 2020)

What they are, why they’re needed, how to represent them as decimals, number line, operations

Potential Tasks

  • Word problems involving real quantities/movements

10. Practical Geometry

Construction of lines, angles, and triangles under various constraints and criteria

Potential Tasks

  • (In-text) Building intuition through paper folding

11. Perimeter and Area

Rectangles, Triangles, Parallelograms, Circles, Formulae, Conversion of Units

Potential Tasks

  • (In-text) Perimeters and areas in cut-outs and real objects
  • Real world word problems and applications
  • Conversion of units as dis-assembling and reassembling objects

12. Algebraic Expressions

Terms, Coefficients, Polynomials, Operations, Finding the value, formulae

Potential Tasks

  • (In-text) Patterns as expressions/equations

13. Exponents and Powers

What they are, laws, operations, decimals as exponents, large numbers in standard form

Potential Tasks

  • Visualising exponential increase and comparisons

14. Symmetry

Symmetry in polygons, line & rotational symmetry

Potential Tasks

  • (In-text) Folding exercises
  • Reflections
  • Visualising symmetry

15. Visualising Solid Shapes

Plane figures and solid shapes, faces, edges and vertices, nets, drawing 3D solids as 2D illustrations, isometric sketches, sections, shadows

Potential Tasks

  • (In-text) Identifying shapes, faces, edges
  • (In-text) Nets
  • (In-text) Projecting solids onto flat surfaces
  • (In-text) Visualising Projections
  • (In-text) Sections of solids
  • (In-text) Projections as shadows
  • (In-text) Projections as rotations

8th Standard

1. Rational Numbers

Properties of rational numbers, number line operations

Potential Tasks

  • (Weak) Number line visualisations

2. Linear Equations in One Variable

Solving equations, applications of linear equations

Potential Tasks

  • None as such

3. Understanding Quadrilaterals

Polygons and their classification (sides, convex/concave, regular/irregular), properties of sides and angles,

Potential Tasks

  • (In-text) Paper folding and cutting to get various kinds of polygons
  • (In-text) Tracing paper to help understand angle relations
  • (In-text) Working with real geometrical equipment

4. Practical Geometry

Constructing quadrilaterals with different types of known information

Potential Tasks

  • (In-text) Assembling geometries using sticks, understanding constraints

5. Data Handling

Frequency distributions, histogram, pie charts, chance and probability, likelihood,

Potential Tasks

  • (In-text) Visualising charts and graphs
  • Understanding results in probability
  • Probability activities using class data (birthdates, heights)

6. Squares and Square Roots

Properties of squares, square roots, methods and formulae

Potential Tasks

  • (In-text) Visualising patterns formed by square numbers

7. Cubes and Cube Roots

Properties and formulae for cubes & cube roots

Potential Tasks

  • (In-text) Visualising patterns formed by cube numbers

8. Comparing Quantities (October 2020)

Increase/Decrease in percentages, discounts, profit & loss, taxes, interest (simple/compound)

Potential Tasks

  • (Weak) Visualising word problems, compounding interest

9. Algebraic Expressions and Identities

Operations on expressions, terms and coefficients, identities

Potential Tasks

  • (In-text) Variable Number Lines

10. Visualising Solid Shapes

Views of shapes, mapping, faces edges vertices

Potential Tasks

  • (In-text) Identifying shapes in real life
  • (In-text) Understanding shape views and projections (matching projections)
  • (In-text) Mapping Spaces, measuring distances
  • (In-text) Faces edges vertices

11. Mensuration

Formulae for areas, surface areas, volume & capacity

Potential Tasks

  • (In-text) Graph sheet cutting to understand area formulae
  • (In-text) Intuition for surface areas (unwrapping objects)
  • Word problems involving volumes and rates

12. Exponents and Powers

Negative exponents, Laws, expressing small numbers, comparing large and small numbers

Potential Tasks

  • None as such

13. Direct and Inverse Proportions

What these are, and how they work in real life

Potential Tasks

  • (In-text) Direct Proportion Physical Intuition: shadows, volumes
  • (In-text) Inverse Proportion Physical Intuition: rates, counters, work

14. Factorisation

Finding factors of expressions

Potential Tasks

  • None as such

15. Introduction to Graphs

Bar graphs, Pie charts, histograms, line graphs, coordinates, applications to algebraic expressions

Potential Tasks

  • Visualising graphs
  • (In-text) Understanding coordinate systems

16. Playing with Numbers

Games and puzzles, letters for digits, tests of divisibility

Potential Tasks

  • None as such