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Teaching of Mathematics in nursery should be started only after 3 to 4 weeks of students in the class. First oral counting of concrete objects should be taught using solid object from the classroom environment adopting question answer method. As show the fans in classroom. Ask students what is this. How many are these. Count yourself and ask students to repeat with you. One fan, two fan, three fan. four fan. Similarly show any other colourful and attractive object as balloon, marble and teach counting. Also tell you have two ears, two eyes, one nose, one tongue, two hands, two legs, five fingers etc.
When students have perfected counting objects up to 10 introduce gradually shapes of 1, 2, 3 etc. Give practice of each number at least in 3 to 4 pages. That 1 in 3 pages, 2 in 4 pages, 3 in 4 pages, 4 in 4 pages and so on. Dont make haste student will learn very slowly. Teach at their sped of learning. Until one shape is perfected do not over on to the other shapes.
Some strokes as vertical line, horizontal line, slanting line, circle, half circle must be taught for at least first 30 periods. Students should be given sufficient opportunity to use blackboard, drawing copy to make drawing, scribbling and perfecting the coordination of their eyes and hands before starting formal teaching. Students should be guided the correct posture while writing, correct way of holding pencil, size of the pencil should be sufficiently large for firm and good grip. Lead of the pencil should be neither too soft nor too hard. Normal good quality HB pencil should be used. Teacher should ensure the minimum use of eraser by the students. Teacher should be watchful that no student writes with his or her left hand. However, even if the best efforts of the teacher to persuade a student to write with right hand fails to give the desired result and the student continues to write with his/her left hand, let him/her write as he/she finds it easy.
Counting up to 50. Oral, written and dictation. Counting of solid objects. Concept of big, small, more, less, far, near, light, heavy, comparison of objects as which one is heavy, light, big, small, far, near,
matching of numbers and pictures of objects after counting the objects. Matching similar numbers.
Concept of straight lines, slanting lines, half circle, circle, vertical lines, horizontal lines.
Syllabus of Mathematics for LKG
Number up to 100. Counting, reading, writing and dictation in any order. Reverse counting up to 20.
Spelling on numbers up to 10.
Counting of solid objects. More practice of the concept of big, small, more, less, far, near, light, heavy, comparison of objects as which one is heavy, light, big, small, far, near,
matching of numbers and pictures of objects after counting the objects.
Matching similar numbers.
Concept of straight line, slanting line, half circle, circle, vertical line, horizontal line.
Addition of one digit numbers such as add 5+4, 3+2, 8+0 etc.
Subtraction involving one digit numbers as subtract 7-5, 8-2, 9-5. Sums should be given both vertically and horizontally.
as add 4 add 5+5 = 10 and also
+5
Addition or subtraction should be taught by using concrete objects as seeds, marble and not by drawing lines to add or subtract. Children should be instructed to bring seeds or marbles with them for doing addition and subtraction sums.
Table of 2 and 3 as do the sums 3x2= 2x7=
Concept of ones and tens as in 34 there are 3 tens and 4 ones. 3 tens are 30 and 4 one are 4 so 3 tens are more than 4 ones.
Addition should be taught first by solid objects without saying add or plus. e.g.
3 toffees and 2 toffees are how much? 5 toffees.
Show the students 4 marbles and ask how many are these.
Now show the students 3 more marble and ask to count and tell how many are these.
Now ask one students to mix up these 3 and 4 marbles and count it again and tell you how much these are now i.e. after mixing.
The student will tell you that these are now 7.
Now tell students
4 marbles and 3 marbles are 7 marbles. Write this statement on the black board.
4 marbles and three marbles are 7 marbles.
Continue practicing of this type of statements for about a week. Now you can replace and with plus sign and explain what plus sign mean and replace are with equal to sign and explain what does it mean.
4 marbles and 3 marbles are 7 marbles
4 marbles + 3 marbles = 7 marbles.
Give practice of this type of question for another full week and then replace concrete objects with abstract numbers
4 marbles and 3 marbles are 7 marbles
4 marbles+ 3 marble = 7 marbles
4 and 3 are 7
4+3 =7 read aloud 4 plus 3 equals to 7
4 plus 3 is equal to 7
Now give at least 50 exercises to make it perfect. Continue this exercise for about 15 periods with at 5 to 8 sums in each period.
Similarly teach subtraction first with concrete object then with abstract numbers.
Keep 7 marbles in box and ask a students to count and tell you how much these are.
Now ask another students to take out ( away) 3 marbles from the box. Ask third student to come and count the remaining marble in the box. How many are left. This is the process of subtraction.
There are 7 marbles in the box.
3 marbles taken away
4 marbles left in the box.
3 taken away from 7 equal to 4
We write this as
7 3 = 4
Explain again and again with concrete objects and simultaneously matching them with statement written on the blackboard.
Give sufficient exercise to make students perfect. Continue teaching subtraction for 15 periods. Now give mixed exercises i.e. both addition and subtraction sums.
Dictate questions and ask students to write in columns and add or subtract as the case may be.
How to converse with the students while dictating the sums.
The teacher will say aloud addressing all the students.
All the students, take out your copies. Come out. Make line. i.e. sit one after another with sufficient gap between the two students.
Listen to me.
Addition sums.
write-3 plus 5, write 5 plus 2 and so on.
Subtraction sums
Write- 9 minus 4, 7 minus 5 and so on.
While the students are busy doing sums the teacher will supervise their activities. She should see that all the students follow her instructions and do sums using only marble, no student should count on finger tips or draw lines to do the sums.
Syllabus of Mathematics for UKG
More practice of the concept of more, less, far, near, light, heavy, rough, smooth, hard, soft, big, small, short, long, more than, less than, concept of ones and tens. telling of place value of digits at ones, tens and hundreds place.
comparison of numbers. telling which one is more or less using symbol of more than and less as, 7>5 and 7<9.
Reverse counting from any given number to any given number. Say from 70 to 60.
Telling what comes after, before or between.
For example what comes after 69, before 100 and between 88 and 90.
Writing numbers skipping in 2s, 3s, 4s etc. as write from 50 to 70 by skipping 5s. Writing numbers in ascending or descending order.
Numbers up to 999 i.e. hundreds place.
Addition and subtraction of two digit numbers with carry and borrow. Table up to 5. Multiplication sums up to table of 5.
Spelling of numbers up to hundred.
Syllabus of Mathematics for First
More practice of numbers up to 999. Addition subtraction with carry and borrow.
Spelling up to 20 and those of 30, 40, 50, 60, 70, 80, 90 and hundred. Spelling of other numbers will be automatically framed as 78 will be seventy-eight. (seventy from 70 and eight from 8).
Place Value up to hundreds place.
Table up to 10. Multiplication and division up to table of 9. Multiplication in which multiplicands are between 0 and 9 as
9 x 5 = , 4 x 0 = , 6 x 1 = , 7 x 7 = etc.
Division involving one step of division as divide 49 by 7, 48 by 6, 35 by 5 etc.
Arranging numbers in different orders ( ascending/descending). Writing missing numbers, What comes before, after, between..
using symbols of +, -, =, < and > in sums.
As write the correct symbol in the blanks. ( = , - , = , < or >)
4 { } 2 = 6 8{ } 3=5 8 { } 6 5{ }8
Concept of some shapes as triangle, square, circle, semicircle. More practice of concepts taught in UKG as more than, less than, smaller than, bigger than, lighter than, heavier than, harder than, softer than.
Syllabus of Mathematics for Second
Numbers up to thousands place i.e. 9999.
Place value of the numbers. Arranging numbers in order. use of less than and greater than with symbol.
Writing numbers in ascending and descending order. Expanded form. Compact form.
Writing numbers in words and vice a versa.
Table up to 15.
Addition, subtraction of numbers up to 999. Addition in three to four columns as
write in vertical column and add 345, 308, 47 and 8.
Multiplication up to 3 digit numbers as multiply 345 by 6.
division up to three digit numbers as divide 480 by 8. Division in which remainder also comes as divide 675 by 12.
Introduction of Rupees and paise, coins and notes of different denominations. Questions such as, How many 50 paise coins are there in a 5 rupee note.
Introduction of concept and need of measurement of mass, length and volume. We measure sugar in kilogram, length of our school field in metre and milk in litre. Students should be taught which unit is used to measure what kind of objects. Teacher should arrange to demonstrate using such units and measure in daily life.
Expressing addition as multiplication and subtraction as division and vice a versa, as-
2+2+2+2+2= 10 is also 2 x 5 = 10 and its reverse too.
and 14 2 = 12 (1st step)
12 2 = 10 (2nd step)
10 2 = 8 (3rd step)
8 2 = 6 (4th step)
6 2 = 4 (5th step)
4 2 = 2 (6th step)
2 2 = 0 (7th step) total 7 steps or 7 times subtraction.
14 divided by 2 = 7
and its reverse too.
Statement problems on addition, subtraction and multiplication.
As Hamid has 48 toffees. His mother gave him 67 toffees. How many toffees now he has?
Solution:
Hamid has = 48 toffees
His mother gave = 67 toffees 48
Now, Hamid has = 48+67 toffees +67
= 115 toffees 115
A book costs Rs 45. How much will be the cost 8 books.
Solution.
since, cost of 1 book = Rs. 45 45
so, the cost of 45 books = Rs. 45x8 x8
= Rs. 360 360
Ans. cost of 8 books is Rs 360.
Use of scale to draw lines of 5 or 7 or 8 cm.
Forming smallest and biggest numbers using the given digit as write the smallest and biggest numbers using 3,2,5 and 0.
Introduction of fraction with the help of pictures and concrete objects. Only half, one fourth, one third, one fifth, one sixth etc.
Introduction of some geometrical shapes as circle, sphere, cube, cuboid, rectangle, square, kite, triangle, straight line, curved line, vertical line, horizontal line.
Telling time. Use and study of calendar.
Syllabus of Mathematics for Third
Numbers up to 99999. Writing numbers in both digits and words.
Writing numbers in expanded form. telling place value.
Roman numbers up to 39.
The four basic operations on these numbers. addition of three to five big numbers. Statement problem sums on these too.
Introduction of number line and use of it in the four basic operations.
Multiplication by three digit numbers as multiply 4057 by 345. Division by two digit numbers as divide 8972 by 25.
Multiplying by 10, 100 and 1000, 20, 200, 2000 etc.
Dividing by 10 and 100. telling remainder if a number is divided by 10 or 100 even without actual division.
Knowledge of terms as multiplicands, subtrahends, addends, divisor, dividend, quotient and remainder.
Concept of even and odd numbers. Test of divisibility of a number by 2 and 5 only.
Concept of fraction, How to write a fractional number, concept of comparing fractional numbers if their denominators are equal. Addition and subtraction of fractional numbers with equal denominator. Representing fractional number pictorially and vice a versa.
Fractional numbers as division as 1/5 is the same as 1 divided by 5.
Introduction of decimal in writing rupees and paise.
Introduction of Kilogram and gram, metre, centimeter and kilometre, litre and millilitre. Inter-conversion of these. As
5 kg = 5000 g 5600 g = 5 kg and 600 g.
Statement problem on all the four basic operation.
Time, Hour minute, second, inter-conversion of these units. As
5 hours = 5 x 60 = 300 minutes
Telling place value, Writing number in expanded and condensed form as 4578= 4000+500+70+8 and 7000+50+8= 7058
Forming biggest and smallest number using given digits as
Write the biggest and the smallest numbers using 2,5,3, 0 and 4
Answer The biggest number = 54320 and the smallest number is 20345.
Shape as triangle, square, rectangle, angle only shape, circle, perimeter of rectangle and square, introduction of shapes of solid objects as cube, cuboid, Ask students to make coulrful cut out of these shapes and models of three dimensional shape as cube, cuboid, pyramid.
Drawing lines of given size in cm. Measurement of pre-drawn lines.
Syllabus of Mathematics for Fourth
Large numbers up to crore. Writing numbers in words in Indian system as
4,25,07, 101 is four crore twenty five lakh seven thousand one hundred and one. Use of comma or space should be explained. In Indian system first comma is used after the first three digit from right, then commas are put after every two digit see the examples
125 no comma
4,125
44,125
4,44,125
44,44,125
4,44,44,125
44,44,44,125
4,44,44,44,125
In International system commas are put after every three digit from right. Every three digit represent one period.
Trillions, Billions, Millions, thousands and ones period.
123,456,789,123,111
One hundred twenty-three trillion four hundred fifty-six billion seven hundred eighty-nine million one hundred twenty-three thousand and one hundred eleven.
Roman numbers up to 100.
All the four basic operations on large numbers including statement problems. Concept of Natural Numbers and whole numbers.
Concept of even, odd, prime and composite numbers.
Test of divisibility of a number by 2, 3, 5, 4 and 8
Concept of multiples and factors of given numbers. Finding HCF of 2 numbers and LCM of three to four numbers but LCM should be within 100.
As find the HCF of 24 and 36.
Find the LCM of 4, 8 and 12.
Such question also as Find the least number which when divided by 8, 12 or 15 give remainder as zero.
Find the greatest number that can divide both 75 and 50 equally.
Finding HCF by writing all the factors of a given number then selecting the common factors and finally the highest common factor.
Find HCF of 24 and 36
First write all the factors of 24 = 2, 3, 4, 6, 8, 12, 24
now write all the factors of 36 = 2, 3, 4, 6, 9, 12, 18, 36
Now select common factors = 2, 3, 4, 6 and 12, these five factors are common to both 24 and 36
Now select the highest of all these five factors = 12
So, the HCF of 24 and 36 is 12. Answer is 12.
Expressing numbers as multiplication factors as 49= 7x7
or 48 = 2x24, 3x16, 4x12, 6x8,
Fractional Number: More examples with concept of denominator, numerator, comparison of fractional numbers with common denominators, comparison of two fractional numbers with different denominators, addition, subtraction and multiplication operations on fractional numbers. expressing fractions as division and vice a versa.
Introduction of Metric system. Kilo, deca-, hecto- , deci-, centi- and milli- with gram, metre and litre.
Inter-conversion of these. All the four basic operations on these units.
Introduction of decimal numbers. Comparison of decimal numbers. reading of decimal numbers. Conversion of decimal into fractional numbers as
0.5 = 1/2, 0.12 = 12/100 .01 = 1/100 etc. Telling place value of numbers involving decimal, addition, subtraction and multiplication involving both decimal numbers and whole numbers. As add 45.23+40.2+0.56, subtract 100-45.225, multiply 4.5x10, 458.52x1.2,
Statement problem sums on four basic functions
As-
The cost of 1m of a cloth is Rs.102. Find the cost of 78 m of the same cloth?
In 1 litre of petrol a car goes 12 kilometer. How much petrol will it require to go from Delhi to Lucknow, if Lucknow is 480 K from Delhi?
Problem on loss and profit, concept of cost price, sale price. Finding loss and profit.
Telling time. Concept of month, year, days, weak, hours, minutes, seconds, addition subtraction involving hour, minute and second. Leap year, days in a weak, month, year, leap year, in Jan, Feb etc..
Geometry:
introduction of angle, constructing angle of measure 20 to 180. Naming of an angle with letter. Concept of line, line segment, ray, parallel line, non-parallel lines. Perpendicular line. Slanting line. Concept of triangle, angle in a triangle, angles in square or rectangle, constructing a triangle, a square a rectangle without any given measure,
Perimeter. finding perimeter of a regular shape as triangle, square, rectangle or any other polygon. problem sums on perimeter, as
Length and breadth of a field are 80m and 60 respectively. How long will Mohan travel in making its four rounds?
Estimating and data handling. Concept of tally and chart.
Railway time table. Introduction and study of railway time table.
Syllabus of Mathematics for Fifth
Introduction of Indian and International system of expressing very large numbers .i.e up to billion. Operation on such large numbers.
Concept of LCM and HCF with statement problems on these. Method of finding HCF by division method and LCM by factorization method. Finding prime factors of big numbers as Find all the prime factors of 1024.
Rules of writing Roman numbers.
Introduction of I,V,X, L, C, D AND M.
Concept of decimal numbers, fractional numbers. Inter-conversion of these. Types of fractions simple, mixed, improper fraction. All the four operations on decimal and fraction. Division up to certain place and giving answer round to the third, fourth, etc place of decimal.
Problems on Unitary Method as
Cost of 4.5 m cloth is Rs180.00. find the cost of 2.5 m of the same cloth.
Such division as divide 1 by 64. 1 by 7 and give your answer correct to the third place of decimal.
Introduction of mixed operations and BODMAS. Explain order of operation.
Introduction of percentage, problems involving percentage, loss and profit, discount, finding percent of some number. Inter-conversion of percent, decimal and fractional numbers. As-
Change to %: 0.25, 1.25, 7/10, 1/75
Change to decimal 10% 8% 1/25 1 1/8
Change to fraction .25% .00145 1.25
Railway time table. introduction of 24 hour system. Ability to read and understand railway timetable.
Introduction of average. Simple questions on average. As
A player scored 45 runs in the first match, 36 runs in the second match and 66 runs in the third match. Find his average of runs in all the three matches.
Circle, diameter, radius, periphery, centre of circle, angles, kind of angles, constructing angle, naming angles, naming triangles, parallel lines, ray, line, line segment, drawing circle of given radius.
Perimeter of a closed shapes having only straight lines.
Problem on interest. (Optional)
Area- Introduction and finding area of square and rectangle only. (Optional)
Finding area of a shape regular or irregular using graph paper by counting number of squares it covers.( Optional)
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