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