# Tamil Nadu SSLC Board Class 10 Maths Latest Syllabus 2022-2023

Mathematics is a subject that many students find challenging. It is a subject that is purely based on concepts and calculations. Students need a lot of practice to grasp the concepts of Mathematics and score good marks in the subject. Therefore, Extramarks provides students with the Tamil Nadu Class 10 Maths Syllabus, so that students can prepare well and achieve success in their Class 10 board examinations.

Class 10 is the academic session in which students form the fundamentals of all the subjects. Also, they decide the subjects that they want to choose for further studies. Therefore, it is a very critical year for students. It is very essential to have clear and strong basics to score good marks in Mathematics, and the first step is to go through the Tamil Nadu Class 10 Maths Syllabus.

## TN Board SSLC Maths Syllabus for Class 10

Extramarks provides students with the Tamil Nadu Class 10 Maths Syllabus so that they can have complete and authentic study material to prepare for their board examinations. The Tamil Nadu Class 10 Maths Syllabus provided by the Extramarks website is complete, reliable, and updated to help students score good marks in the board examinations.

The Tamil Nadu Class 10 Maths Syllabus is as follows-

• Relations and Functions – Ordered Pair, Cartesian product, Relations
• Numbers and Sequences – Euclid’s Division Lemma and Algorithm, Fundamental

Theorem of Arithmetic, Sequences, Arithmetic Progression

• Algebra – Simultaneous Linear Equations in three variables, GCD and LCM of

Polynomials, Rational expressions, Square Root of Polynomials, Quadratic

Equations and Graph, etc.

• Geometry – Similarity, Thales Theorem and Angle Bisector Theorem, Pythagoras

Theorem, Circles and Tangents, Concurrency Theorems

• Coordinate Geometry – Area of a Triangle, Area of a Quadrilateral, Inclination of a Line,

Straight Line, General Form of a Straight Line

• Trigonometry – Trigonometric Identities, Heights, and Distances
• Mensuration – Surface Area, Volume, Volume, and Surface Area of Combined Solids with no change in volume
• Statistics and Probability – Algebra of Events, Probability

For a more detailed Tamil Nadu Class 10 Maths Syllabus, students can subscribe to the Extramarks website.

### Tamil Nadu SSLC Board (TN SSLC) Maths 2022-2023 Syllabus for Class 10

The Tamil Nadu Class 10 Maths Syllabus provided by Extramarks helps provide students with a preview of the chapters that are to be covered in the course of the curriculum.

It is very important for students to go through the syllabus before starting to study the subject. The Tamil Nadu Class 10 Maths Syllabus helps students in making a timetable that helps in keeping a proper record of all the topics. This helps them divide their time systematically so that they can focus on all the topics. The Tamil Nadu Class 10 Maths Syllabus also helps students get an idea about the weightage of the respective chapters. Along with the Tamil Nadu Syllabus, Extramarks also provides students with the Tamil Nadu Previous Year Question Paper and the Tamil Nadu Sample Question Paper so that they can have good study material and can properly revise the Class 10 Mathematics curriculum. As a student-focused portal, Extramarks focuses on providing the best possible educational experience for its users. It provides them with all the essential learning modules for the board examinations so that they can score good marks in their examinations.

## STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING -CHENNAI – 06 TNCF – 2017 – DRAFT SYLLABUS – MATHEMATICS

### STANDARD 1 -10

 TOPIC CLASS 1 CLASS 2 CLASS 3 CLASS 4 CLASS 5 GEOME TRY Introduction to spatial orientation ·        To build a sense of spatial orientation. ·        To understand spatial relationship. ·        To understand the meaning of and use appropriate spatial vocabulary Eg. Top, Bottom, On, Under, Inside, Outside, Above, Below, Near, Far, Before, After, Front – Rear , More -Less, Thin – Fat and Big – Small     Introduction to shapes in real objects and its attributes ·        To correlate concrete things to their shapes ·        To Learn vocabulary related to nature of shapes Eg. Shapes, round, corner, edge, surface, plain, long & short.   Introduction to basicshapes (2D) Introduction to spatial orientation- 3D dimensional ·         To observe objects in the environment and gets an intuitive feel for their geometrical attributes   Identification of 2D shapes and 3D objects in everyday life ·         To identify the basic 3D shapes such as cube, cuboid, cylinder, cylindrical, cone, conical, sphereand spherical by their names. Introduction to properties of shapes ·         To trace the 2-D outlines of 3-D objects. ·         To Observe and identify these 2-D shapes viz., rectangle, square, triangle, circle by their names with 3 D objects ·        To describe intuitively the properties of these 2- D shapes. Creating 2 – D shapes ·        To create shapes through paper folding, paper cutting ·        To identify 2-D shapes. ·        To describe the various 2-D shapes by counting their sides ,corners (vertices)and diagonals ·        To make shapes on the dot- grid using straight lines and curves. Tangram ·        Create shapes using tangram pieces ·        Matches the properties of 2D shapes by observing their sides and corners (Vertices) ·        To tile a given region using a tile of a given shape ·        Distinguishes between shapes that tile and that do not tile constructing 3 – D objects ·        To be able to draw 3-D objects. ·        Describe the various 3D shapes by counting their sides, corners and diagonals Properties of 2 – D shaped objects ·        To learn names of shapes like triangle, square, rectangle, pentagon, circle etc., ·        To recognize these shapes in the objects around them. ·        Able to draw circles using objects like bangles , bottle caps etc., ·        Able to draw a 2D shapes free hand and with geometry tools. ·        To identify centre, radius and diameter of a circle. ·        To identify sides, diagonal, perimeter for a quadrilateral objects. ·        To measure and find out the differences among different quadrilateral objects ·        To understand the properties of 2D objects     Creating shapes by combining different 2 – D shapes ·        Uses Tangram to create different shapes. Drawing 3–D shapes from 2–D Shapes ·         To get the feel of perspective while observing drawings of 3-D objects in 2-D. ·         Able to explore intuitively rotations and reflections of familiar 2-D shapes. ·         Able to explore intuitively symmetry in familiar 3-D shapes like in alphabets. ·         Able to make the shapes of cubes, cylinders and cones using nets especially designed for this purpose Introduction to angles ·         To get the feel of an angle through observation of objects in their environment and paper folding.
 ·        To know basic names of shapes like square, circle, oval, rectangle, triangle ·        To observe and describe objects from the surroundings having different sizes and shapes like pebbles, boxes, balls, pipes, bottle caps, pencil and eraser. ·        To draw the border of objects and represent in 2D (Eg. Draw rectangle with border of eraser/pencil box) Introduction to draw straight lines ·        To draw horizontal, vertical and slant lines (free hand) ·        To draw /represent straight lines in various orientations(vertical, horizontal, slant) Differentiating,Sorting and classifying object based on shapes, locations and space ·        To collect objects from the surroundings and differentiates, Sorts, classifies and describes those objects on the basis of shapes and other observable properties Eg .Sound produced by group of students within outside the class, same done by one child (within the class and outside the class). ·        Observes and describes the way shapes affect ·         To identify objects by blind folded and to use the vocabulary such as curve, straight line, circle, cylinder, sphere, cone, square, rectangle, triangle, circle , corner etc. Introduction to draw different kind of lines and figures of 2D and 3D.     ·         Identifies and makes straight lines by folding, straight edged objects, stretched strings and draws free hand and with a ruler ·         To distinguish between straightandcurved lines ·         To identify objects by observing their shadows ·        Able to fill space using tiles of geometrical shapes using one or two shapes ·        Able to choose a tile among a given number of tiles that can tile a given region both intuitively and experimentally.     Properties of 3 – D objects ·        To create 3D objects using Clay and paper foldinggiven nets ·        To compare and differentiate 2D and 3D objects   Introduction to Symmetry   ·        Able to explore intuitively the reflections through mirror, ink blots, paper cutting and paper folding. ·        Able to draw top view, front view and side view of simple objects. ·        To observes from the surrounding and from day to day life situations and identifies symmetrical objects. Eg: Vertical dissection of human body (externally), butterfly, petals of flowers, design of a fabric, starfish etc. ·        Collects/ records symmetrical objects whenever/ wherever they see ·        To draw such symmetrical objects and naming the same. ·         To learn the names of angles like acute, obtuse and right angle. ·         Able to identify right angles in the environment. ·         Able to classify angles into right, acute and obtuse angles. ·         To represent right angle, acute angle and obtuse angle by drawing through tracing. Area and perimeter( to be given in activities only) ·         to determine area and perimeter of simple geometrical figures (such as rectangle/square using standard units)   Introduction to Fractals ·         Observes and understands fractals Create model of fractals using clay, paper, glue and match sticks

 movements like rolling and sliding. Iterative patterns in shapes ·        Able to draw circles, spirals, ovals; ·        To differentiate and to compares the shapes drawn. ·        To explore visual examples of repeating patterns. NUMBE RS Numbers from 1 to 9 ·        To observe objects and make collection of objects ·        To arrange the collection of objects in order by –         Matching and –         One to one correspondence ·        To count the number of real objects in a collection.(concrete) ·        To count the number of objects by representing them in the form of pictures(semi-concrete)   ·        To make collection of objects corresponding to a specific number   ·        To recognize and speak numbers from 1 to 9.   ·        To use numbers from 1 to 9 in counting and comparison. (Real objects and repeated events like clapping/jumpingto be used for counting) ·        To read and write numerals from 1 to 9. ·        To identify the ordinal Numbers from 21 to 99 ·         To learn numbers by rote from 21 to 99. ·         Write numerals for Twenty-one to Ninety nine.   Counting ·         Group objects in category.(eg: group the names based on alphabets) ·         Count the objects in each category(eg: count the number of number of students name starting “A”, number of students name starting “B”…) ·         To group objects into ’tens’ and ‘ones’ ·         To draw representation for groups of tens and ones ·         To group a number into tens and ones ·         To identify the predecessor and successor up to 99. ·         To identify numbers” in between” Eg: 24, _ _, 26. ·         To skip count by twos forward to backward up Numbers sequence up to 1000 ·        To read and write all 3-digit numbers. ·        To expands a number with respect to place values ·        Counts in different ways – starting from any number Compare Numbers ·        To identify odd and even numbers with respect to ones place upto 3 digit numbers ·        To be able to forms greatest and smallest numbers using given digits. ·        To be able to sort an array of numbers into ascending and descending order Ordering ·        To arrange things in different orders for a given solution.(eg: finding out different ways to prove that 3 and 5 make 8, by arranging numbers in different orders)   Addition and Subtraction within 1000 ·        Able to add and subtract numbers by writing them vertically in the following two cases: (Sum should not exceed 1000) Number Sequence up to 10000 ·        To read and write 4 – digit numbers (including odd and even numbers) ·        To write numbers with respect to place value expansion. Comparing numbers ·        Able to sequence an arbitrary array of numbers in ascending and descending order. ·        Able to form greatest and smallest numbers using given digits     Addition and subtraction within 10,000 ·        To add and subtract up to four digit numbers by writing them vertically in the following two cases: without grouping, with grouping (sum should not exceed 10,000). Multiplication (up to 2 digit number by 2 digit number and 3 digit number by single digit number) ·        Able to do elementary multiplication of 2-digit by 2- digit and 3- digit by single digit numbers using lattice algorithm and the standard Numbers beyond 10000 ·         to know numbers beyond 1000 being used in real life situation Place value and comparing numbers ·         To find place value in numbers beyond 10000. ·         Able to sequence an arbitrary array of numbers up to five digits in ascending and descending orders. ·         To form the greatest and smallest numbers using four and five digits. Numbers and operations ·         To appreciate the role of place value in addition, subtraction and multiplication algorithms. ·         To multiply 3 digits by 2 digits ·         to use informal and standard division algorithm ·         To divide 4 digits by 2digits
 numbers from 1 to 9 ·        To match the ordinal numbers with objects in order of size     Concept of “Zero” ·        To introduce the concept of “no objects” give the symbol zero to represent it. ·        To approach zero through real life situation (such as there are 5 papers lying on the floor, how many remaining? Or there are 5 waste papers lying on the floor, ask the child to put in the garbage bin one by one. Let the children count and say eg: 1 in the bin, 4 on the floor, ….finally nothing or zero on the floor, 5 in the bin). Introduction to Number 10 To know and use the number 10 Counting ·        To count the objects.(Eg: count the number of books in the bag; the child should be able to tell the total and ensures that the child has counted everything once) ·        To estimate, verify and justify the counted value. ·        To be able to count the objects, mentally & silently; ·        To be able to relate last number counted with the to Ninety-nine. ·         To skip count by threes forward to backward up to Ninety-nine ·         To introduce odd and even numbers Ordering ·         To arrange numbers till hundred in ascending and descending order ·         To able to form the greatest and the smallest 2-digit numbers with and without repetition of given digits. ·         To arrange things in sequential order. (eg: arrange names of the classmates, alphabetically).   Place value and comparing the numbers ·         To expand a number with respect to place values. ·         To count and regroup objects into tens and ones ·         To use the concept of place value to compare numbers   Ordinal and Cardinal numbers ·         To indicate and identify the position of an object in a line ·         To learn ordinal and –  Without regrouping. –  With regrouping. ·        To use the place space value in standard algorithm of addition and subtraction. ·        Able to solve addition and subtraction of simple problems in different daily life situations presented through pictures and stories. ·        To frame problems for addition and subtraction facts. ·        To estimate the sum of, and difference between, of two given numbers   Multiplication ·        Multiplies a given number by another number in various ways such as: -by drawing dots -by re-grouping -by repeated addition -by using multiplication facts ·        Explains the meaning of multiplication ·        Identifies     the sign               of multiplication. ·        Able to construct the multiplication tables of 2, 3, 4, 5 and 10 ·        To use an appropriate number operation in the life situation of the child / in the child’scontext ·        To multiply two digit numbers using standard algorithm and Lattice (column) algorithm ·        Able to reason out the results of operations down on specified numbers ·        Able to write tables up to 10 × 10.   Division: up to 4 digit number by single digit number. ·        To divide a given number by another number in various ways. ·        To apply the four operations to life situations. ·        To frame word problems. ·        To estimate sums, differences and products of simple two digit numbers to nearest tens or hundreds. Mental Arithmetic ·        Able to add and subtract multiple of 10 and 100, mentally. ·        Complete multiplication facts by adding partial products, mentally (e.g, 7×6 = 5×6+2×6) Introduction to square numbers ·         to understand the term square numbers ·         to find out square numbers up to 100 Factors and multiples. ·         Understand the meaning of factors and multiples ·         To identify least common multiple(LCM) Mental Arithmetic ·         Able to estimate sums, differences, products and quotients up to two digits numbers and verifies using approximation. Systematic ordering: ·         Logically find out something based on the condition.(Eg: the child should be able to investigate and find the number of possible routes from one location to another on a map/maze; find out different words that can be made using five given letters; meaningful)
 and ones through pictures. ·        To group a number orally into tens and ones ·        To identify the predecessor and successor up to 99. ·        To identify numbers” in between” Eg: 24, _ _, 26. ·        To skip count by twos forward to backward up toNinety-nine. ·        To skip count by threes forward to backward up to Ninety-nine[Ensure that this part(Numbers from 21 to 49/99 is an optional, so as to consider the pace of the learner]   Mental Arithmetic ·        To add two single digits numbers up to sum of 10 mentally PATTER NS Patterns in Sounds ·        To identify the patterns in sounds ·        To make pattern through sounds   Patterns in Colours   ·        To identify the patterns in colours. ·        To make pattern through colours.   Patterns in Shapes ·        To identify the patterns in Patterns in Sounds ·        To observe and extend patterns in sequence of sounds. Eg: Patterns of sounds can be extended by tapping benches, feet, clapping etc. ·         To create   patterns   by mixing sound and body movements   Patterns in Colours ·        To observe and extend patterns in sequence of Patterns in shapes ·         Creates patterns of regular irregular shapes by stamping (eg: by drawing leaves, ink blot diagrams) ·         Searches for patterns in different ways of combining colours sounds, 2D and 3D shapes ·         To recognize simple symmetries in shapes and patterns. ·         To create patterns and designs from straight lines and other geometrical Patterns in shapes ·        Observes shapes sequence from kaleidoscope ·        Identifies the patterns in a sequence of shapes ·        Creates Patterns using shapes sequence Patterns in numbers ·        Able to identify patterns in multiplication and division: multiples of 9. ·        To cast out nines from a given number to check if it is a multiple of nine. ·          Able to identify patterns in Patterns in shapes ·         To create patterns using different colours and shapes Patterns in numbers ·         To identify patterns in square numbers and triangular numbers ·         To relate sequences of odd numbers between consecutive square numbers Patterns in Geometry ·         Able to make border strip and tiling
 shapes ·        To make pattern through shapes. Patterns in Numbers ·        To identify the patterns in numbers. (using elementary examples- single digit numbers) Patterns in body movements ·        To identify the patterns in body movements Iterative patterns and processes ·        To observe and collect similar objects from surroundings such as flowers, leaves; ·        To draw similar objects and to compare them colors. Eg: Patterns of colors can be extended by mixing different colours.     Patterns in shapes ·         To create block patterns by stamping thumbprints, leaf prints, vegetable prints, etc. ·         To create patterns of shapes of a)       Regular(eg: in grid) b)       Irregular and c)       Combinations of a and b   Patterns in numbers ·         To observe patterns in different ways of splitting numbers or combining numbers.   Iterative patterns and processes ·         Able to draw simple rangoli(eg:3 by 3 pulliKolams) shapes.   Patterns in numbers   ·         Able to identify patterns in the numerals for odd and even numbers and in adding odd and even numbers. ·         To identify patterns in multiplication with, and dividing by 10s.   Iterative patterns and processes ·         Able to draw complex rangoli with condition.(eg:drawing more pullikolams, atleast one kolam which is a single curve.) ·         To explore number patterns obtained by adding different numbers. ·         To understand through patterns that multiplication is repeated addition, division as repeated subtraction. multiplication and division by 10s, 100s. Patterns in Geometry ·        Able to identify symmetry in geometrical patterns patterns. ·         To make patterns of shapes using different number of angles/ types of angles. ·         To get introduced to rotation of angles. ·         To find patterns by rotating angles ·         To make patterns using rotational angles   Iterative patterns ·         Able to find patterns in a collection of words MEAS UREMEN TS Introduction to Length   ·        Comparison of Objects Using Length through Non Standard Units.   ·        To distinguish between near , far,thinthick,longer/taller,s horter,high, low,lighter, heavier, bulk Introduction to measuring (Length) through Standard units ·         To estimate and measure lengths/distances using uniform non-standard units like a pen cap/pencil, eraser, feet etc ·         To appreciate the need for standard tool for measuring length, by Length (using standard units – cm., m.,) ·        Able to appreciate the need for a standard unit. ·        To measure length of objects in their environment using simple aids. ·        To express appropriate standard units of length by choosing between centimeters and meters. Length (m., cm., addition, subtraction, conversion and estimation of distance) ·        To understand relationship between meter and centimeter; ·        Able to Convertmeter into centimeters and vice versa. ·        To solve problems involving length and distances. ·        Able to estimate length of an Operations on Measured distance mass and capacity ·         Able to apply the four operations in solving problems involving length, weight and volume. ·         Able to relate commonly used larger and smaller units of length, weight and
 ·        To seriate objects by comparing their length and mass. ·        To measure short lengths in terms of non- uniform units( in the context of ‘games eg., ‘Kittipil’ ‘goligundu’, ‘naadupudiaatam’ or by leaping, jumping, etc.,) ·        To estimate distance,measureslength and verifies using non uniform units ( e.g. hand span, cubit, etc.,) finding differences in non-standard tools. ·         To Use a ruler to measure lengths of different objects Introduction to standard tool for measuring (weight ) ·         Compare and identifies relationships between two or more objects by their weight. ·         Appreciates the need for a simple balance ·         Compares weights of given objects using simple balance Introduction to volume ( capacity) ·         compares and orders containers as per their capacities on the basis of perception & verifies by pouring out,etc., ·        To understand order of magnitude between cm. , m., and km. as units. ·        To estimate the length of given object in standard units and verifies by measuring. ·        To use a ruler to measure length of items used in daily life. ·        Able to relate centimeter and meter ·        Appreciate the need for standard tool for measuring length, by finding differences in non-standard tools Weight (using non-standard) ·        Able to weigh objects using non-standard Units. ·        To understand the concept of conservation of weight(in gm and kg) that applies in a simple balance   Volume (capacity -(using non- standard) ·        Able to measure and compare the capacity of different containers in terms of non- standard units. ·        Appreciate the need for standard tool for measuring volume, by finding differences in non-standard tools objects in their surrounding up to 1 meter and distance between two given locations in their environment up to 100 meters   Weight (Using standard units Kg., gm., addition subtraction) ·        Weighs objects using a balance and standard units ·        Estimates the weight of an object and verifies using a balance Volume (Using standard units L., ml., addition subtraction) ·        Able to measure volume of given liquid using containers marked with standard units ·        Able to estimate the volume of a liquid contained in a vessel and verifies by measuring Volume and converts one to the other. ·         To appreciate the volume of a solid body: qualitatively and also by informal measurement. MONEY Notes and coins ·        To identify common currency notes and coins ·        To put together small amounts of money Notes and coins ·         To add and subtract small amounts of money mentally. ·         To identify currency – Relating rupee and paise ·        To understand the relationship between rupee and paise ·        To add and subtract amounts Estimating cost ·        Able to convert rupees to paise. ·        To add and subtract simple amounts of money in Operations on money ·         To apply four operations in solving problems involving money.
 notes and coins ·         Puts together amounts of money not exceeding Rs. 100/- ·         To transact an amount using three to four notes. ·         To compare the rate of same product but different prices. ·         To use the vocabulary as more amount, less amount, expensive, in- expensive involving rupees and paise amounts of multiples of 10 without re-grouping.   Making bills ·        to collect bills for goods/items bought ·        To make rate charts andsimple bills denominations of rupees and paise which are multiples of ten using column addition and subtraction with regrouping. ·        To learn to use operations to find totals, change, multiple costs and unit cost. ·        Able to estimate roughly the total cost. Comparing cost ·         to collect bills of items bought and compare costs of same items ·         to find and reasons out for being expensive and inexpensive ·         to use the vocabulary such as expensive, costly, cheap, affordable, luxurious, inexpensive[Textbook writer has to note the usage of these words, such as when, where and why with examples of using these words in real life situations]. TIME Comparison of events based on time ·        To Distinguish between events occurring in time using term- earlier and later, old, new, less time , more time, shorter period or longer period, fast, slow , morning, evening, day and night ·        To observe changes in the position of sun throughout the day with time intervals     Organizes events based on time ·        Narrates the sequence of Days, seasons & months ·         Able to draw time- Cyclic events( such as day – night; days of the week; events of the day starting from brushing the teeth to sleep) ·         To get familiar with the days of the week and months of the year. ·         To get a feel for sequence of seasons. ·         To be able to sequence the events occurring over longer periods in terms of dates/days. Reading date and time (calendar, hours, minutes, am, pm) ·        to read a particular day and date ·        to understand the manufacture and expiry date of different products ·        To read the time correct to the hour (both digital and analogue). ·        Tells morning, noon, afternoon, evening, night and midnight. ·        To sequence the events chronologically. Iterative patterns and Time manipulation ·        Understands days by week ·        to use knowledge of days of a week finds the day in previous or upcoming week ·        Computes the number of weeks in a year ·        Able to correlate the number of days in a year with the number of days in each month. ·        To read clock time to the nearest hours and minutes. ·        Able to express time, using the terms, ‘a.m.’ and ‘p.m.’[Ensure that the children learn the meaning of prime Time manipulation ·         To use addition and subtraction in finding time intervals in simple cases
 events in a day Calculating time ·         By using different containers to measure volume observes and calculates time, by using the terms like quick/fast and slow.   ·         To apply the knowledge learnt in money and understands that different modes of transports can be used based on time and money processes–Time based ·        To draw time-Cyclic events of a year(Months, seasons, festivals) meridian and ante- meridian from geography/earth science] ·        Relates to 24 hour clock with respect to 12 hour clock ·        Able to estimate the duration of familiar events. ·        Able to compute the number of days between two given dates. ·        Use Calendar (interlinking with patterns) INTERC ONCEPT S – – – – Integrating distance, money and time   ·         Able to reason out in solving problems by comparing time, money and distance ·         Able to create problems integrating time, money and distance ·         To use fractions in the context of units of length,time and money. FRACTIO N – – – Introduction to natural fractions ·        Able to observe items being a part or parts of a whole ·        Able to find the fractional part of a collection. ·        To identify the notation of Compare fractions ·         Finds a number corresponding to part of a collection in the form of fractions ·        To Compare different
 fractions ·        Use the vocabulary as half , quarter, three-fourths, semi, partial and whole ·        Able to Define Fractions ·        To compare natural fractions and identifies greater and smaller Symbolic representation of simple fractions   ·        Relating parts to whole eg: Filling up water in a measured bottle partially / fixing up puzzles circularly/ vertically/ horizontally in places and completes the whole. ·        Identifies half, one fourth and three- fourths of a whole. ·        Identifies the symbols, ¼ , ½ , ¾ ·        Explains the meaning of ¼ , ½ , ¾ ·        to appreciate equivalence of 2/4 and ½ and of 2/2, 3/3, 4/4 and 1 simple fraction ( ½ , ¼, ¾ etc) ·        To identify the terms like numerator and denominator. ·         To know types of fractions : Proper , Improper, mixed , like, unlike, equivalent   Equivalent fractions ·         Able to compare like fractions with denominators up to 20. ·         Able to estimate the degree of closeness of a fraction to known fractions ( ½ , ¼, ¾ etc)     Operations of fractions ·         Able to do addition and subtraction of like fraction ·         Able to do multiplication of fractions by single digit numbers   Relationship between Fractions and Decimals ·         To introduce the concept of decimal ·         Able to express a given fraction in decimal notation and vice versa
 INFORM ATION PROCES SING 1.Systematic Listing ·        To collect simple data such as Mode of transport to School, Favorite TV program, favourite food items, Numbers of brothers and sisters etc., 2. Organizing simple data (shape and numbers) ·        To represents and interprets Simple data sets(eg: in Venn diagram)       3. Modelling Puzzles: ·        To visualize and arrange parts in order.(Eg: Picture of a dog torn into pieces like head, legs, tail, body. The child has to arrange neatly and form a complete picture of dog, by placing everything intact.) Making Connections: ·        To form a shape, by connecting the numbers in sequence/colors.(eg: Lot of colored dots could be given such that 7 red dots for one shape, 8 blue dots for another shape. Now, the child has to connect similar colored dots to form shape)     4.Following and Devising Algorithms 1.Systematic Listing   ·         Listing down all possible things for a given category. (eg: listing down all possible ways of dressing oneself; listing down any pairs of numbers that sums to 20) ·         Listing down all possible things for a given sub- categories (Eg: finding out all the possible ways of dressing using two shorts and three shirts;Listing down combination of two numbers whose sum is equal to 20) ·         To collect data throughmeasurement.   Reasoning ·         To compare, verify and justify the lists prepared and ensures that the list is complete.(eg: the child should be able to answer, how do you know that you have counted all the possible ways and ensures that it is counted without repetition?) 2.Drawing inference ·         Represents data followed by discussions ( eg.heights of children, months in which birthdays of the children in the class ) 1.Systematic Listing   ·        Listing down all possible things for a given category, with multiple conditions.(eg: listing down all possible ways of dressing using 2 half-pants, 1 half-shirt and 2 full-shirts, if full-shirts are not to be worn with half- pants; listing down the number of different four- block-high towers that can be built using blue and red blocks(with the condition that one color for each block); listing down all possible 3-5 letteredmeaningful words that starts with letter ‘R’)   2. Drawing simple apt graphs ·        To collect data and represent it in terms of pictograph   ·        Choosing appropriate scale and unit for display through pictographs   3.Drawing conclusion from the represented data ·        To draw conclusions from the data by discussing with the teacher   4. Modelling Map making: ·         Able to make map of known- areas.(Not necessarily scaled).Eg: Making map of 1.Systematic Listing ·        Listing down all possible things for a given category, satisfying for multiple conditions that has conditions for exclusions.(eg: finding out all the possible ways of dressing using 4 shorts and four shirts, one each of colours red, blue, white and black, such that the colour of shorts and shirt is not the same, building towers with blocks of multiple colors; with many different restrictions on how they cannot be arranged; listing down all possible 3-5 lettered meaningful words that starts with letter ‘R’ and shouldn’t end with ‘M’ and ‘T’) 2.Drawing inferences from the represented data: ·        To collect and represent data in the form of bar graphs and pie-charts ·        Draws Inferences by discussing with the teacher   3. Modelling Route map: ·        Able to locate short and long paths; ·        Able to find out and check for connectivity between places       4.Following and Devising Algorithms 1.Systematic Listing ·         Logically place numbers in a given condition.(eg:the child should be able to solve 4 by 4 Sudoku) 2.Graphical representation of data ·         To collect two- dimensional quantitative data ·         To represent the data in the form of a table To draw a bar graphs and to represent a data and interprets it   3. Modelling ·         Marking art using cutouts of circles, rectangles and triangles of different sizes ·         Create artistic chains with different coloured beads     4.Following and Devising Algorithms ·         To enable them to find out easy and difficult ways to solve tasksand justify with reasons the better way (eg. Arranging 50 books Ordered by number on them in 5 rows.)
 ·        To enable them to follow simpleand different types of procedure[example: simple treasure hunt games] ·         To record data using tally marks ·         Draws inferences from the data at the appropriate level eg. modes of transport chosen based on time and money can be drawn as a graph   3. Modelling Relations:older, younger ·         Understands relationship and expresses it orally (Eg: If Shalini daughter of Saravanan then Saravanan father of Selvi. Then the child should be able to tell what is the relationship between selvi and shalini.) Relations: Shapes and nature of objects ·         Correlates nature of objects with shapes of containers(eg: for a given pair of objects, the child should be able to tell which container holds what (through pictures))     4.Following and Devising Algorithms Framing and executing instructions ·         To equip them to make list of instructions; school, home, park, or any place ·         Able to mark routes for the given locations.   5.Following and Devising Algorithms ·        Able to devise instructions for going from one location to another on a map ·        Able to find the quick way of finding 10 more than an less than a given number ·        Able to find the quick way of adding and, subtracting a number. ·        Able to explore many tricks to quickly add and subtract. ·        Able to break down a big task to a list of small tasks(eg. A table to be moved to another room) ·        To equip them to write down a sequence of instructions; (eg: One group is to write down the sequence of task, one group is to carryout instruction; another group is to ensure that it is carried out correctly ·         Able to split bigger tasks into smaller, known tasks(eg. Multiplying two three- digit numbers)

 ·         To enable them to carryout instruction and toensure thatit is carried out correctly ·         To enable them to carryout a task in different ways(eg.dividing a pile of biscuits amongst students)

UPPER PRIMARY DRAFT SYLLABUS

 TOPIC CLASS VI CLASS VII CLASS VIII Numbers and operations. ·     Understand the concepts of Arithmetic of Integers ·     Understand addition and subtraction of integers using number line. ·     Able to add and subtract integers using real life situation. ·     Able to multiply and divide integers by whole numbers. ·     Understand that division by zero is meaningless. ·     Able to multiply and divide integers by integers. ·     Solve word problems usingthe four fundamental operations on integers and applies appropriate operations in word problems. Properties of Integers ·     Understand closure, commutative, associative, distributive properties (multiplication over addition), additiveand multiplicative identities, applied to integers. ·     Understand which properties hold for which operations, and illustrate difference from whole numbers (example: closure property for subtraction) Decimal Numbers ·        Recall the notion of decimal point. ·        Understand place value in decimals. ·        Learn the concept of decimals as fractions with denominators of tens and its multiples. ·        Represent decimal Numbers on Number line. Rational Numbers Rational Numbers ·     Understand the necessity for extending fractions to rational numbers. ·     To represent rational number on number line. ·      Understand that between any two rational numbers there lies another rational number   Arithmetic of Rational Numbers ·      To learn to perform all four operations on rational numbers. ·        Able to solve word problems on all operations. . Properties of Rational numbers ·      Understand the fourproperties of rational numbers, additive identity and multiplicative identity. Simplify Expression with three brackets ·           Able to simplify expressions with utmost three brackets. Powers ·           To express numbers in exponential form with integers as exponents. ·           Understand the laws of exponents with integral powers. ·           Able to calculate square and square roots of integers. –        Square roots using factor method and division method for numbers containing o     not more than 4 digits o     not more than 2 decimal places (in case of imperfect squares) ·          To recognize cubes and cube roots numbers (up to 8 digits), number names and numerals ·     Understands Indian and international representation of large numbers ·     Understands estimation as an important tool for large numbers (5 digits and beyond) ·        Identify smaller/larger numbers, compare using <, >, = symbols, arrange in ascending/ descending order. NUMBER SYSTEM – I ·        Perform the four fundamental operations (answers not to exceed six digits) and applies the right operation in word problems. ·        Perform operations in the right order using BODMAS rule Whole numbers ·        Understand extension of natural numbers to whole numbers ·        To represent whole numbers on number line. ·        Understand the four properties of numbers with emphasizing terminology (closure, commutative, associative, distributive properties over addition and multiplication identity of a numbers). ·        Identify     and     appreciate number patterns-ex: triangular numbers and
 square numbers. Test of divisibility ·        Recall the concepts of factors and multiples with the aid of multiplication tables up to 10. ·        Understand the rules of divisibility test and apply it to numbers 2, 3, 4, 5 and 10. Prime numbers ·        Recall the classification of even and odd numbers. ·        Understand the concept of Prime and composite numbers Factorization ·        To factorize 2-digit numbers. ·        To learn prime factorization of a given number Arithmetic of Decimals ·        Add and subtract decimal numbers. ·        Able to apply the appropriate operation in word problems- addition and subtraction of decimals. ·        Multiply and divide decimal numbers. ·        Able to solve word problems based on decimal numbers (all operations). (only factor method for numbers containing at most 3 digits). ·           To learn to estimate square roots and cube roots (Learning the process of moving nearer to the required number). ·           Able to calculate in easy ways and estimate the answer using all four fundamental operations ·           Able to approximate numbers up to three digits.   PATTERNS AND RELATIONS Playing with numbers ·        Understand patterns in Numbers ∑n, ∑n2 etc. Magic Squares NUMBER SYSTEM-II LCM & HCF ·        Understand the concepts of HCF and LCM ·        Understand the concept of co-prime numbers. ·        Calculate HCF and LCM by prime factorization method and division method. ·        Deduce the relationship between LCM and HCF and the product of two numbers. ·        Able to solve word problems with HCF and LCM
 Introduction of Integers ·        Understand the necessity for extension of whole numbers to negative integers. ·        Understand that the collection of positive integers, negative integers and zero forms integers. ·        Represent integers on the number line. ·        Compare integers and arrange them in ascending / descending order. Arithmetic of Fractions ·      Revise notion of fractions and fraction addition/subtraction ·      Understand mixed and improper fractions and convert from one to the other ·     Able to multiply and divide fractions by other fractions ·     To find the reciprocal of a fraction. ·     Able to solve word problems that involve fractions (with all four operations). II.Measurements Metric Measures ·        Recall the conversion of units of length, weight and volume restricting to the units mentioned below. (km, m, cm, mm and similarly units that are in common use in weight and volume). ·        Able to understand the use of decimal point to convert smaller to larger units ·        Able to add and subtract quantities with different unit with appropriate conversion Area and Perimeter ·        To revise the concepts of Perimeter and Area of Square, Rectangle, Right triangle and combined shapes. ·        To determine the area of Parallelogram, Rhombus, and Trapezium and regular hexagon   Circle ·        To determine the area and circumference of Circles and its parts. Area of Pathway ·        To calculate the area of Pathway inside and outside the given rectangles and circles applying the concept of area of rectangle and circle respectively. Circle ·      To introduce the concept of segment and chord. ·      To find the length of arc, area of sector. Area and Perimeter of combined Plane Figures. ·        Recall the concepts of area & perimeter for various quadrilaterals ·        Calculate the area of simple combined figures (Not more than three figures placed in juxtaposition) 3-Dimensional Shapes ·        Understand representation of 3-dimensional shapes in 2D ·        Understand representation of 3D objects with Cubes.
 Measures of Time ·         Able to read time on a clock (Eg.1:15 min. as quarter pass one) ·         Use both 12-hour and 24-hour formats to read time and convert from one to another. ·        Able to find the duration between 2 time instances. ·        Able to convert from one unit of time to the other – seconds to minutes and hours and vice – versa, days to weeks, years, leap year and vice – versa.   Area and Perimeter ·        Understand the concept of area and perimeter of plane figures. ·        To learn to find the area and perimeter of square, rectangle, right triangle and combined shapes.   Conversion of Square units ·     To Convert Square units (Eg. cm2 to m2 ) III. ALGEBRA Introduction to Algebra ·        Introduction to variable through patterns and through appropriate word problems and generalizations. ·        To generate such patterns with more examples. ·        To solve unknowns through examples with simple contexts (single operations). Algebraic Expressions ·         Identify constants and variables in a given term of an algebraic expression and coefficients of the terms. ·     Identify like and unlike terms. ·     To learn to write the degree of expressions like x2 yetc. ·     Able to add and subtract algebraic expressions, with integer coefficients   ·        Able to form simple expressions with two Revision ·        To recall addition and subtraction of expressions. Algebraic Expressions ·        Able to multiply algebraic expressions with integer coefficients ·        Able to divide algebraic expressions by monomial ·        Able to understand and avoid some common errors (e.g. 2 xx = x, 7 xxy = 7 xy ) Identities
 variables. ·         To recall the identities for Solving simple linear equations ·     To solve simple linear equations (in contextual problems) (avoid complicated coefficients). Graphical representation of inequalities in a single variable. ·     To represent inequalities of a single variable graphically. (a + b)2 , (a – b)2 , a 2 – b 2 ·         Able to apply identities in problems ·         Deduce identities with geometrical proofs, numerical examples and applies it in sums Factorizations ·         Able to recognize (simple cases only) expressions that are factorizable of the following types (a+b)3 ,(a-b)3, (x+a)(x+b)(x+c) Exponents ·     Understand the laws of Exponents(through observing patterns and arrives at generalization.) Solving linear equations ·         Able to solve word problems that involve linear equations (with simple ·      aman = am+n where m,n ϵ N coefficients) ·      (am)n = amn where m,n ϵ N am =  m–n ·       an          a       where m,n ϵ N, m>n. Graphs: ·         Able to plot graphs of simple linear functions (ex: y=5x) ·     To find units digits of large numbers represented by exponents (ex: 2350) by observing patterns Algebraic identities ·     To deduce identities with geometrical proofs, numerical examples and apply it in sums (a + b)2 = a2 + 2ab + b2 , (a – b)2 = a 2 – 2ab + b a 2 – b2 = (a + b) (a – b). Able to recognize (simple cases only) expressions that are factorizable of the following types a(x + y), (x ± y)2, a2 –b2 IV. MODELLING Ratio and Proportion ·        Understand the concept of Ratio ·        Understand that Proportion is same as Recall: Ratio and Proportion ·     To recall the concept proportion. of ratio and Revision ·         Profit, Loss and simple interest. Application of percentage, profit & loss,
 the ratio of two. ·        Able to calculate the needed quantity using unitary method (with only direct variation implied). Shopping ·        Able to prepare a bill. ·        To verify the bill amount. Profit and loss ·        Able to calculate cost price, Selling Price and Profit/Loss. Indirect and Direct variation ·     Understand the concept of indirect variation ·     Able to differentiate direct and indirect variation and calculate the needed quantity using direct and indirect variation. Fraction and decimal into percentage ·     Understand percentage as a fraction with denominator 100. ·         Able to convert fractions and decimals into percentages and vice-versa ·     To   solve   word problems                   based on percentage. Simple Interest Able to calculate simple interest. overhead expenses, Discount, tax. ·        To solveslightly advanced problems involving applications of Percentages, Profit & Loss, overhead expenses, Discount, tax. Compound Interest ·        Able to find compound interest through patterns and use it in simple problems. (Compounded yearly up to 3 years or half- yearly up to 3 steps only). ·        Able to differentiate between simple and compound interest (The numbers used for calculation purpose should be easy – otherwise, calculator can be used.) Compound variation ·        To do problems on compound variation ·        To solve Time and Work problems– Simple and direct word problems. V.GEOMETRY Introduction to point , line, ray , segment and planes ·        Understand fundamental geometrical terms -points, lines, rays, segments and planes. ·        Understand collinear points and concurrent lines, point of concurrency ·        Understand parallel and perpendicular lines.   Angles and their types ·        Understand the concept of angles. ·        Identify vertex, arms and measure angles. ·        Understand right, acute, obtuse and straight angles. ·        Understand complementary & supplementary angles and find complementary and supplementary angles for the given angles.   Types of Triangles Properties of Parallel lines ·         Understand the properties of angles in intersecting lines, adjacent angles, adjacent angles on a straight line, parallel lines and transversal lines. Properties of Triangles ·         Able to apply angle sum property of a triangle. Congruence triangles properties ·         To know the concept of congruency and similarity of triangles. ·         To know the criteria for similarity of triangles. (SSS, SAS, ASA, RHS).   PATTERNS AND RELATIONS- Symmetry through transformation ·         To recall the types of Symmetry through diagram ·         To learn Symmetry through transformations (Translation, reflection, rotation and their combination) Properties of Triangles ·        To recall the properties of triangles. ·        Understand theorems based on properties of triangles and apply them to appropriate problems. ·        Understand Pythagoras theorem and solve problems using it.   Concurrent Points of a triangle with definition ·        Understand the concurrency of medians, altitudes, angle bisectors and perpendicular bisectors in a triangle.   PATTERNS AND RELATIONS Playing with numbers ·        Logical reasoning diagrams PRACTICAL GEOMETRY- Circles ·        Able to draw the parts of a circle and identify and compare the relationship between
 ·        Able to recognize different kinds of triangles based on (a) length of sides (b) measures of angles.   Symmetry ·        Able to find symmetrical objects in Surrounding. ·        To learn types of symmetry PRACTICAL GEOMETRY ·        To identify Geometrical instruments. ·        Able to measure and draw line segment. ·        Able     to     construct parallel and perpendicular lines using set square. ·         Able to draw given angles using protractor PRACTICAL GEOMETRY-   Construction using scale and compass. ·         To     construct     the perpendicular bisector of the given line segment. ·         To construct the angle bisector of the given angle. ·         To    construct    special angleswithout protractor – 90°, 60°, 30°, 120°. ·         Construction of triangles: given SSS, SAS, ASA. ·         To construct circles and concentric circles. radius and diameter.   Construction of Quadrilaterals: trapezium, parallelogram, rhombus, rectangle and square ·         Able to construct quadrilaterals: trapezium, parallelogram, rhombus, rectangle and square. VI.STATISTICS Introduction ·        Understand the necessity to collect data. ·        Organize collected discrete data using tally marks and a table. Pictograph ·        Able to interpret a pictograph and understand the need for scaling. Bar graph ·        Able to interpret data from bar graphs. ·        Able to construct bar graphs from the given data. Collection and organization of continuous data ·     To collect and organize continuous data. ·     Able to form a frequency table.   Mean, Median, Mode ·     To calculate Mean, Median, Mode of ungrouped data and understand what they represent Formation of frequency table ·        To recall formation of frequency table. Representation ·        To draw Histogram, frequency polygon for grouped data ·        To construct simple Pie- charts for the given data.   Measures of central tendency ·        Able to calculate mean, median and mode for discrete data.
 VIII. INFORMATION PROCESSING Systematic Listing, Counting, Reasoning ·        Sudoku; solving sudoku. ·        Triangles with numbers on them adding to given sum; ·        Explore how many; how do you know you have counted all.   Modelling ·        Tree diagrams for numerical expressions; what regrouping does to the shape of the tree. ·        Representing carrom board and “strikes”.   Iterative patterns and processes ·        Euclid’s algorithm, Euclid’s game: (Ref:https://en.wikipedia.org/wiki/ Euclidean_algorithm)   Following and Devising Algorithms ·        Sorting given information on different attributes. ·        Disordering given ordered information. Systematic Listing, Counting, Reasoning ·        Tetraminoes: make all the shapes. How many up to rotationsand flips.     Modelling ·        Simple road map of town; roads carry costs; cost of routes; minimal cost paths. ·        Games like Sprouts and puzzles like 3-cup problem (Ref: Wikipedia)   Iterative patterns and processes ·        Given table, find the function. ·        Pascal’s triangle and Fibonacci sequences.   Following and Devising Algorithms ·        Making “best” schedules, time-tables, deciding order of tasks under given set of constraints. ·        Creating and using flowcharts. Systematic Listing, Counting, Reasoning ·        Determine the number of possible orderings of an arbitrary number of objects, describe procedures for listing and counting all such orderings.   Modelling ·        Games like SETS: https://en.wikipedia.org/wiki/Set_game ·        Map colouring using examples. ·        Making time tables. ·        Modelling 100 metre dash, long jump, high jump, javelin throw.   Iterative patterns and processes ·        Given description of simple physical/biological system, predict future behaviour. ·        Model of solar and lunar eclipse (imprecise but correct). ·        Devising and breaking simple codes.   Following and Devising Algorithms ·        Use of queues (e.g. at water taps, bus stops) ·        Best ways of packing objects into a bag / box. ·        Shopping to a budget, with constraints on money, weight, volume.

SECONDARY DRAFT SYLLABUS

 CLASS IX CLASS X Topic :Set Language   1.  Describing and representing sets   Able to describe a set in Descriptive, Set- builder and roster forms and through Venn diagram. Use symbols like Î,Ï,Æ, etc.   2.  Types of sets   Able to identify different kinds of sets. (Empty set, Finite set, Infinite set, Equal set, Subset, Power set, and Universal set, cardinality of sets)   3.  Set Operations.   Describes and illustrates – union, intersection, difference, symmetric difference and complementation.   Understands the commutative, associative and distributive properties of set operations-(restricted to three sets)     4.  Formula for set operations.   Formula for n( A È B ) and n( A È B È C) ; statement and verification of De Morgan law using Venn diagram. 5.  Application:   Solving simple word problems.   (Minimum number of problems illustrating the use of each concept in conformity with the number of periods allotted) Topic : Relations and Functions   1.   Defining Relations and Functions   Able to define and perform Cartesian product of two sets. To define a relation as a subset of product of two sets. To define function as a special relation and cite examples.   2.  Representation of functions.   Identifying a function through an Arrow diagram, a Table, a Rule or a graph. (Simple examples) The domain and Range. Vertical Line test.   3.  Types of functions.   Classifying functions as one-one, many-one, onto, into and bijection); (simple examples)   4.  Composition of functions (two and three)   Applying the results of one function on another. Examples for Commutative and associative nature of combining functions.   5.  Identification of some special functions   Identifying the graphs of Linear, Quadratic, Cubic and Reciprocal functions. Topic : 2. Real Number System   1.      Revision: Natural numbers, Whole numbers, Integers and Rational numbers. To recall the representation of natural numbers, whole numbers, integers, and rational numbers on the number line.   2.       Rational numbers. Topic : 2. Numbers and Sequences. 1.       Euclid’s division algorithm   Able to write Euclid’s division lemma for a division sum To find LCM and HCF using Euclid’s division algorithm   2.      Fundamental theorem of arithmetic
 Able to classify rational numbers as recurring / terminating decimals. To represent terminating / non terminating recurring decimals, on the number line through successive magnification.   3. Irrational numbers   To identify non terminating, non-recurring decimals leading to the existence and representation of irrational numbers such as    2,  3 and    5 on the number line. To do elementary basic operations on irrational numbers. Able to rationalize given irrational numbers of the type 1 (a + b   x ) and1 (   x +    y ) , where x, y are natural numbers and a, b are integers. 4.       Real numbers To identify a one–one correspondence between the real numbers and the points of a directed straight line. (The ratio of the examples for each concept to that of the exercise problems is 1:1) 5. Scientific notation ·           To understand the meaning of Scientific Notation. ·           To understand the importance and convenience of expressing numbers in scientific notation. ·           Able to convert larger/smaller numbers to scientific notation and vice – versa. Able to understand the fundamental theorem of arithmetic   3.       Modular arithmetic   To understand congruence modulo ‘n’, addition modulo ‘n’, and multiplication modulo ‘n’     4.       Sequences   To define sequence and to visualize a sequence as a function     5.      Progressions   To define an Arithmetic Progression and a Geometric Progression. (A.P. and G.P)   Able to find the nth term of an A.P and its sum to n terms. Able to find the nth term of a G.P. and its sum to n terms.   6.       Series   To determine the sum of some finite series such as Σn,Σn2,Σn3 Topic : 3. Algebra 1.     Polynomials To define a polynomial in one variable. Classification as monomial, binomial, etc. To Identify the terms, the coefficients and the exponents of a polynomial and its degree. Classification of polynomials as linear, quadratic, cubic etc. Evaluate a polynomial for given values of the variable. Identifies zeros of a polynomial. Learns to Add, subtract, and multiply polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication. 2.       Remainder theorem   To understand the remainder theorem via examples and analogy to integers and use it to find the remainder. Topic : 3. Algebra   1.       Simultaneous linear equations To recall solving a pair of linear equations in two unknowns. To solve a pair of linear equations in three variables by method of elimination only.   2.       Synthetic division   To determine the remainder and the quotient of the given polynomial using Synthetic Division. To use Synthetic division in the process of factorising a polynomial.   3.       Rational expressions   Able to simplify algebraic rational expressions (Simple Problems),   4.       Square root   To understand and compute the square root of a
 3.       Identities   To recall/understand the algebraic identities for (a + b)2, (a – b)2, a2  – b2,           (x + a)(x + b), (a + b + c)2, (a + b)3  and      (a – b)3.  (to be supplemented by visual illustration wherever possible)   Able to verify identities of the type, (x + a) (x + b) (x + c) and x3 + y3 + z3 – 3xyz and use them in problem solving.   4.       Factor theorem   To learn the statement and proof of the factor theorem and use it to find the factors of a given polynomial, in particular  (i)  trinomials  of  the  type a x2   + b x + c,   a ¹ 0 where a, b, c are real numbers and (ii) cubic polynomials. Learn to obtain the GCD and LCM of (at most three) algebraic expressions by factor method only.   5.        Linear equations in two variables   to recall linear equations in one variable to identify and solve linear equations in two variables by (a) Substitution (ii) elimination, (iii) Cross multiplication and (iv)Graphical methods to explore the possibilities for (i) unique, (ii) infinite or (iii) no solutions. Apply linear equations in two variables to solve problems from life situation.   6. Linear Graphs Able to draw straight lines, intersecting and non-intersecting straight lines. Solving linear equations using their graphs. polynomial. Able to correlate relationship between discriminant and nature of roots.   5. Quadratic Equations   Able to form a quadratic equation in the standard form a x2 + b x + c = 0, (a ¹ 0) , when the roots are given. To solve quadratic equations (only real root) – by (i) factorization, (ii) completing the square and (iii) using formula. Able to write and solve a quadratic equation, when given a word problem (related to day-to-day activities). To comprehend the relationship between zeros and coefficients of a quadratic expression.   6.       Quadratic graphs   Able to solve quadratic equations through graphs. Able to determine the relationship between the nature of the solutions and the graph of a quadratic function. 7.       Graphs of variations   To solve graphically equations y µ x, y µ 1 , xy = k , ” x, y > 0 . x 8.       Matrices   1.       Types of matrices   To introduce matrices through examples To identify the order and formation of matrices To recognize different types of matrices 2.       Matrix operations   Able to add and subtract the given matrices. To multiply a matrix by a scalar, and to find the transpose of a matrix. To multiply 2×2; 2×3; 3×2 Matrices. To evaluate the determinant of a 2×2 matrix and find the inverse of the matrix. 3.       Matrix equation To solve the equations of two variables – using matrix method. Topic : 4. Geometry 1. Properties of parallelograms (Theorems without proof)   To recall the theorems on linear pair, vertically opposite angles, angle – sum property of a triangle (interior and Topic : 4. Geometry 1.       Proportionality theorems To discover geometrical facts given by i.       *basic proportionality theorem* for a triangle and its *converse*
 exterior) and congruent triangles.   To classify quadrilaterals and parallelograms (through hands-on activities) and list their properties to use them in problem solving.   2.       Circle theorems   To understand that there is only one circle that passes through 3 non-collinear points . To learn about equal chords in a circle, the perpendicular from the centre to any chord, and congruent arcs. To discover the relationships between the angles at the centre of a circle, angles in Cyclic quadrilaterals, and angles at the circumference in the same segment. (All the above through practical work and not by theoretical proofs) Simple problems based on the above concepts.   3.       Practical Geometry Able to identify and understand through practical work, the centroid, orthocentre, circumcentre and incentre of a triangle. ii. angle bisector theorem and its converse To apply them to solve numerical problems only. 2.       Similar triangles   To discover properties of similar triangles by practical work. (theorems without proof) Pythagoras theorem* 3.       Circles and Tangents   To understand the facts (without formal proof) on lengths of tangents to a circle, angle between tangent and radius through the point of contact and alternate segment theorem. 4.       Concurrency theorems   States Ceva’s theorem and Menelau’s theorem (without proof).   5.       Practical Geometry   To construct tangents to circles. To construct triangle, given its base, vertical angle at the opposite vertex and (a) median or (b) altitude or (c) bisector. Able to construct a cyclic quadrilateral. Topic : 5. Coordinate Geometry 1.       Plotting Points on a plane To understand the concept of Cartesian plane with its axes. Able to plot the points on the plane and write the co – ordinates of a given point, 2.       Distance between two points Able to find the distance between two given points and make use of it in problems. 3.       Section formula To determine the point of division using section formula (internal division only) To find and use midpoint formula To find the centroid of a triangle by formula. 4.       Graph of a linear equation To examine linear equations of the type ax+by+c=0, writing it as y = mx + c and linking with the chapter on linear in two variables. Topic : 5. Coordinate Geometry   1.       Area of a triangle   To recall formulae for distance between two points, and the midpoint of two given points and the point of internal division (using section formula) . To calculate the area of a triangle using formula. To find area of a quadrilateral given its vertices. To determine the slope of a line (i) when two of its points are given, (ii) its equation is given.   2.      Forms of Straight line Able to find the equation of a straight line in: i.        slope-intercept form, ii.       point -slope form, iii.     two -point form, iv.     intercept form. Topic : 6. Trigonometry 1. Trigonometric ratios To understand the concept of trigonometric ratios using the relationship between the sides and the angles of the right angled triangle. To recognize the values of sine, cosine, tangent and their Topic : 6. Trigonometry   1.       Identities   Able to identify the Trigonometric identities and apply them in simple problems.   2.       Heights and distances
 reciprocals for specific angles 0° ,30°, 45°, 60° ,90° . To do simple problems based on these ratios. 2.       Complementary angles To use the concept of complementary angles in simple problems 3.       Trigonometric tables To understand the usage of trigonometric tables. To apply trigonometric ratios to calculate heights and distances. (Not more than two right triangles; (Angles of elevation or depression should be 30°, 45° or 60°.) Topic : 7.Measurement and Mensuration 1.      Area of a triangle Able to use Heron’s formula (no proof) to find the area of a triangle.                                                                         To apply the same idea to find the area of a quadrilateral.   2.      Surface Area and Volume of Cube and Cuboids To recall the 3 D shapes To find LSA , TSA and Volumes of cubes and cuboids. Topic : 7.Measurement and Mensuration   Surface Area and Volume of Solids   To determine volume and surface area of cylinder, cone, sphere, hemisphere and frustum (hollow solids to be omitted). To compute Volume and surface area of (not more than two different) combined solids) Problems involving conversion of solids from one shape to another with no change in volume. Topic : 8. Statistics & Probability   Statistics: 1.       Histograms.   To recall the collection of data, presentation of data in tabular form – ungrouped and grouped data. To recall histogram and frequency polygon To construct histograms (with varying base lengths).   2.       Measures of central tendency.   To recall Mean, median, Mode of ungrouped data. Able to calculate the Mean, Median and Mode for grouped data.   3.       Probability   Probability: an experimental approach   To study probability through empirical approach by considering experiments to be drawn from real-life situations. Able to calculate the probability of events like tossing coins and throwing dice. Topic : 8. Statistics & Probability   Statistics 1.       Measures of central tendency   To recall Mean for ungrouped and grouped data.   2.       Measures of dispersion   To understand the concept of Dispersion. To understand and compute Range, Standard Deviation, Variance and coefficient of variation   3.       Probability:   Probability-theoretical approach   To understand Random experiments, Sample space and use of a tree diagram. To define and describe Events – Mutually Exclusive, Complementary, certain and impossible events. To understand addition Theorem on probability and apply it in solving some simple problems.