# NCERT Math syllabus: Grade 1 to 5

(ncert.nic.in)

Make sure to read the "General Points for Textbook Writers" in the linked doc because that explains the philosophy of why this syllabus is designed this way and how it should be executed. For example, they've taken a thumb rule o 140 classes o 30-40 minutes each per year. They also say that sequencing of concepts should not be linear, but spiral. They also emphasise the need for students to articulate their reason which is an important aspect of meta-cognition which is known to be crucial for effective learning.

# Grade 1

## Geometry (10 hrs.)

**SHAPES & SPATIAL UNDERSTANDING**

• Develops and uses vocabulary of spatial relationship(Top, Bottom, On, Under, Inside, Outside, Above, Below, Near, Far, Before, After)

**SOLIDS AROUND US**

• Collects objects from the surroundings having different sizes and shapes like pebbles, boxes, balls, cones, pipes etc.

• Sorts, Classifies and describes the objects on the basis of shapes, and other observable properties.

• Observes and describes the way shapes affect movements like rolling and sliding.

• Sorts 2-D shapes such as flat objects made of card etc.

## Numbers (46 hrs.)

**DEVELOPING A SENSE OF NUMBERNESS, COUNTING AND OPERATIONS OF NUMBERS 1 - 9 AND ZERO**

• Observes object and makes collections of objects.

• Arranges the collection of objects in order by – Matching and – One to one correspondence

• Counts the number of objects in a collection.

• Makes collection of objects corresponding to a specificnumber.

• Recognises and speaks numbers from 1 to 9.

• Uses numbers from 1 to 9 in counting and comparison. (Real objects and repeated events like clapping to be used for counting)

• Reads and writes numerals from 1 to 9.

• Adds and subtracts using real objects and pictures.

• Adds and subtracts the numbers using symbols ‘+’and ‘-’.

• Approaches zero through the subtraction pattern (suchas 3 – 1 = 2, 3 – 2 = 1, 3 – 3 = 0).

**NUMBERS FROM (10 - 20)**

• Forms Number sequence from 10 to 20.

• Counts objects using these numbers.

• Groups objects into a group of 10s and single objects.

• Develops the vocabulary of group of ‘tens’ and ‘ones’.

• Shows the group of tens and ones by drawing.

• Counts the number of tens and ones in a given number.

• Writes the numerals for eleven to nineteen.

• Writes numerals for ten and twenty.

• Compares numbers upto 20.

**ADDITION AND SUBTRACTION (UPTO 20)**

• Adds and subtracts numbers upto 20.

**NUMBERS FROM 21 - 99**

• Writes numerals for Twenty-one to Ninety nine.·Groups objects into tens and ones.

• Draws representation for groups of ten and ones.

• Groups a number orally into tens and ones

**MENTAL ARITHMETIC**

• Adds two single digit numbers mentally.

## Money (3 hrs.)

• Identifies common currency notes and coins.

• Puts together small amounts of money.

## Measurement (13 hrs.)

**LENGTH**

• Distinguishes between near, far, thin, thick, longer/taller,shorter, high, low.

• Seriates objects by comparing their length

• Measures short lengths in terms of non-uniform units(in the context of games e.g. ‘Gilli Danda’ and ‘marble-games’).

• Estimates distance and length, and verifies using non-uniform units (e.g. hand span etc.)

**WEIGHT**

• Compares between heavy and light objects.

**TIME**

• Distinguishes between events occurring in time using terms -earlier and later.

• Gets the qualitative feel of long & short duration, of school days v/s holidays.

• Narrates the sequence of events in a day.

## Data Handling (6 hrs.)

• Collects, represents and interprets simple data such as measuring the arm length or circumference of the head using a paper strip

## Patterns (10 hrs. )

• Describes sequences of simple patterns found in shapes in the surroundings and in numbers, e.g. stamping activity using fingers and thumb.

• Completes a given sequence of simple patterns found in shapes in the surroundings and in numbers.

# Grade 2

## Geometry (13 hrs.)

**SHAPES & SPATIAL UNDERSTANDING**
3-D and 2-D Shapes

• Observes objects in the environment and gets aqualitative feel for their geometrical attributes.• Identifies the basic 3-D shapes such as cuboid, cylinder,cone, sphere by their names.

• Traces the 2-D outlines of 3-D objects.

• Observes and identifies these 2-D shapes.

• Identifies 2-D shapes viz., rectangle, square, triangle,circle by their names.

• Describes intuitively the properties of these 2-D shapes.

• Identifies and makes straight lines by folding, straight edged objects, stretched strings and draws free handand with a ruler.

• Draws horizontal, vertical and slant lines (free hand).

• Distinguishes between straight and curved lines.

• Identifies objects by observing their shadows.

## Numbers (46 hrs.)

• Reads and writes numerals for numbers up to ninety-nine.

• Expands a number with respect to place values.

• Counts and regroups objects into tens and ones.

• Uses the concept of place value in the comparison ofnumbers.

• Counts in various ways:–Starting from any number.–Group counting etc.

• Arranges numbers upto hundred in ascending and descending order.

• Forms the greatest and the smallest two digit numbers with and without repetition of given digits.

• Indicates and identifies the position of an object in aline.

**ADDITION AND SUBTRACTION**

• Adds and subtracts two digit numbers by drawing representations of tens and ones without and with regrouping.

• Adds zero to a number and subtracts zero from anumber.

• Observes the commutative property of addition through patterns.

• Solves addition, subtraction problems presented through pictures and verbal description.

• Describes orally the situations that correspond to the given addition and subtraction facts.

• Estimates the result of addition and subtraction and compares the result with another given number.

**PREPARATION FOR MULTIPLICATION AND DIVISION**

• Discussion of situations involving repeated addition and situations involving equal sharing.

• Activities of making equal groups.

**MENTAL ARITHMETIC**

• Adds and subtracts single digit numbers mentally.

• Adds and subtracts multiples of ten mentally

## Money (3 hrs.)

• Identifies currency - notes and coins.

• Puts together amounts of money not exceedingRs 50/-.

• Adds and subtracts small amounts of money mentally.

• Transacts an amount using 3-4 notes.

## Measurement (13 hrs.)

**LENGTH**

• Measures lengths & distances along short & long paths using uniform (non-standard) units, extends to longer lengths.

**WEIGHT**

• Compares two or more objects by their weight.

• Appreciates the need for a simple balance.

• Compares weights of given objects using simple balance.

**CAPACITY (VOLUME)**

• Compares and orders containers in terms of internal volume(capacity).

• Orders given containers as per their capacities on the basis of perception & verifies by pouring out etc.

**TIME**

• Gets familiar with the days of the week and months of the year.

• Gets a feel for sequence of seasons (varying locally).

• Sequences the events occurring over longer periods in terms of dates/days.

## Data Handling (6 hrs.)

• Collects data through measurement.

• Represents the data followed by discussion (e.g. heightsof children).

• Collects and presents the data on birthdays.

• Draws inferences from the data at the appropriate level.

## Patterns (10 hrs.)

• Observes and extends patterns in sequence of shapes and numbers.

• Searches for patterns in different ways of splitting anumber.

• Creates block patterns by stamping thumbprints, leafprints, vegetable prints, etc.

• Creates patterns of regular shapes by stamping.

# Grade 3

## Geometry (16 hrs.)

**SHAPES & SPATIAL UNDERSTANDING**

• Creates shapes through paperfolding, paper cutting.

• Identifies 2-D shapes

• Describes the various 2-D shapes by counting their sides, corners and diagonals.

• Makes shapes on the dot-grid using straight lines and curves.

• Creates shapes using tangram pieces.

• Matches the properties of two 2-D shapes by observing their sides and corners (vertices).

• Tiles a given region using a tile of a given shape.

• Distinguishes between shapes that tile and that do not tile.

• Intuitive idea of a map. Reads simple maps (not necessarily scaled)

• Draws some 3D-objects.

## Numbers (42 hrs.)

**NUMBER SEQUENCE UP TO 1000**

• Reads and writes 3-digit numbers.

• Expands a number w.r.t. place values.

• Counts in different ways - starting from any number

• Compares numbers.

• Forms greatest and smallest numbers using given digits.

**ADDITION AND SUBTRACTION**

• Adds and subtracts numbers by writing them vertically in the following two cases:

– without regrouping.

– with regrouping.

• Uses the place value in standard algorithm of addition and subtraction.

• Solves addition and subtraction problems in different situations presented through pictures and stories.

• Frames problems for addition and subtraction facts.

•Estimates the sum of, and difference between, two given numbers.

**MULTIPLICATION**

• Explains the meaning ofmultiplication (as repeated addition).

• Identifies the sign of multiplication.

• Constructs the multiplication tablesof 2, 3, 4, 5 and 10

• Uses multiplication facts in situations.

• Multiplies two digit numbers using standard algorithm and Lattice multiplication algorithm.

**DIVISION**

• Explains the meaning of division from context of equal grouping and sharing.

• Relates division with multiplication.

• Completes division facts:

– by grouping

– by using multiplication tables.

**MENTAL ARITHMETIC**

• Adds and subtracts single digit numbers and two digit numbers mentally.

• Doubles two digit numbers mentally (result not exceeding two digits).

## Money (5 hrs.)

• Converts Rupee. to Paise using play money.

• Adds and subtracts amounts using column addition, and subtraction without regrouping.

• Makes rate charts and bills.

## Measurement (21 hrs.)

**LENGTH**

• Appreciates the need for a standard unit.

• Measures length using appropriate standard units of length by choosing between centimetres. and metres.

• Estimates the length of given object in standard units and verifies by measuring.

• Uses a ruler

• Relates centimetre. and metre.

**WEIGHT**

• Weighs objects using non-standard Units.

• Appreciates the conservation of weight.

**VOLUME**

• Measures and compares the capacity of different containers in terms of non-standard units.

• Appreciates the conservation of volume.

**TIME**

• Reads a calendar to find a particularday and date.

• Reads the time correct to the hour.

• Sequences the events chronologically

## Data Handling (6 hrs.)

• Records data using tally marks.

• Collects data and represents interms of pictograph choosing appropriate scale and unit for display through pictographs.

• Draws conclusions from the data by discussing with the teacher.

## Patterns (6 hrs.)

• Identifies simple symmetrical shapes and patterns.

• Makes patterns and designs from straight lines and other geometrical shapes.

• Identifies patterns in the numerals for odd and even numbers and in adding odd and even numbers.

• Partitions a number in differentways.

• Identifies patterns in his surroundings

• Identifies patterns in multiplication with, and dividing by 10s.

# Grade 4

## Geometry (16 hrs.)

**SHAPES & SPATIAL UNDERSTANDING**

• Draws a circle free hand and withcompass.

• Identifies centre, radius and diameter of a circle.

• Uses Tangrams to create different shapes.

• Tiles geometrical shapes: using oneor two shapes.

• Chooses a tile among a given number of tiles that can tile a given region both intuitively and experimentally.

• Explores intuitively the area and perimeter of simple shapes.

• Makes 4-faced, 5-faced and 6-faced cubes from given nets especially designed for the same.

• Explores intuitively the reflections through inkblots, paper cutting and paper folding.

• Reads and draws 3-D objects, making use of the familiarity withthe conventions used in this.

• Draws intuitively the plan, elevation and side view of simple objects.

## Numbers (40 hrs.)

**NUMBERS AND OPERATIONS**

• Writes multiplication facts.

• Writes tables upto 10 × 10.

• Multiplies two and three digit numbers using lattice algorithm and the standard (column) algorithm.

• Divides a given number by another number in various ways such as:

– by drawing dots.

– by grouping.

– by using multiplication facts.

– by repeated subtraction.

• Applies the four operations to life situations.

• Frames word problems.

• Estimates sums, differences and products of given numbers.

**MENTAL ARITHMETIC**

• Adds and subtracts multiples of 10 and 100, mentally.

• Completes multiplication facts by adding partial products, mentally (e.g. 7 × 6 = 5 × 6 + 2 × 6).

**FRACTIONAL NUMBERS**

• Identifies half, one fourth and three-fourths of a whole.

• Identifies the symbols: 1/2 , 1/4, 3/4

• Explains the meaning of 1/2, 1/4 and 3/4.

• Appreciates equivalence of 2/4 and 1/2; and of 2/2, 3/3, 4/4 and 1.

## Money (5 hrs.)

**MONEY**

•Converts Rupees to Paise.

• Adds and subtracts amounts using column addition and subtraction with regrouping.

• Uses operations to find totals,change, multiple costs and unitcost.

• Estimates roughly the totals and total cost.

## Measurement (21 hrs.)

**LENGTH**

• Relates metre with centimetre;

• Converts metre into centimetres and vice versa.

• Solves problems involving length and distances.

• Estimates length of an object and distance between two given locations.

**WEIGHT**

• Weighs objects using a balance andstandard units.

• Determines sums and differencesof weights.

• Estimates the weight of an objectand verifies using a balance.

**VOLUME**

• Measures volumes of given liquidusing containers marked withstandard units.

• Determines sums and differences of volumes.

• Estimates the volume of a liquid contained in a vessel and verifies by measuring.

**TIME**

• Computes the number of weeks in a year.

• Correlates the number of days in a year with the number of days in each month.

• Justifies the reason for the need of a leap year.

• Reads clock time to the nearest hours and minutes.

• Expresses time, using the terms,‘a.m.’ and ‘p.m.’

• Estimates the duration of familiar events.

• Finds approximate time elapsed by (to the nearest hour) forward counting.

• Computes the number of days between two dates.

## Data Handling (6 hrs.)

• Collects data and represents in the form of bar graphs;

• Draws Inferences by discussing with the teacher.

## Patterns (6 hrs.)

• Identifies patterns in multiplication and division: multiples of 9,

• Casts out nines from a given number to check if it is a multipleof nine.

• Multiplies and divides by 10s, 100s.

• Identifies geometrical patterns based on symmetry.

# Grade 5

## Geometry (16 hrs.)

**SHAPES & SPATIAL UNDERSTANDING**

• Gets the feel of perspective whiledrawing a 3-D object in 2-D.

• Gets the feel of an angle through observation and paper folding.

• Identifies right angles in the environment.

• Classifies angles into right, acute and obtuse angles.

• Represents right angle, acute angle and obtuse angle by drawing andtracing.

• Explores intuitively rotations and reflections of familiar 2-D shapes.

• Explores intuitively symmetry in familiar 3-D shapes.

• Makes the shapes of cubes,cylinders and cones using nets especially designed for this purpose.

## Numbers (40 hrs.)

**NUMBERS AND OPERATIONS**

• Finds place value in numbers beyond 1000.

• Appreciates the role of place value in addition, subtraction and multiplication algorithms.

• Uses informal and standard division algorithms.• Explains the meaning of factors and multiples.

**MENTAL ARITHMETIC**

• Estimates sums, differences, products and quotients and verifies using approximation.

**FRACTIONAL NUMBERS**

• Finds the fractional part of a collection.

• Compares fractions.

• Identifies equivalent fractions.

• Estimates the degree of closeness of a fraction to known fractions (1/2, 1/4, 3/4 etc.)

• Uses decimal fractions in the context of units of length and money.

• Expresses a given fraction in decimal notation and vice versa.

## Money (5 hrs.)

• Applies the four operations insolving problems involvingmoney.

## Measurement (26 hrs.)

**LENGTH**

• Determines area and perimeter of simple geometrical figures.

• Applies the four operations in solving problems involving length,weight and volume.

• Relates commonly used larger and smaller units of length, weight and volume and converts one to the other.

• Applies simple fractions to quantities.

• Converts fractional larger unit intocomplete smaller units.

• Appreciates volume of a solid body: intuitively and also by informal measurement.

• Uses addition and subtraction in finding time intervals in simple cases.

## Data Handling (6 hrs.)

• Collects two-dimensional quantitative data.

• Represents the data in the form of a table.

• Draws a bar graph or a pictograph to present a data.

## Patterns (6 hrs.)

• Identifies patterns in square numbers, triangular numbers.

• Relates sequences of odd numbers between consecutive square numbers.

• Makes border strip and tiling patterns.

difficulty

childlike