# 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*