The syllabus of 6th grade math (also covered in 7th grade math) is designed in such a manner which is easily adapted by students of this class. Everyone knows that to make students understand any topic, it has to be explained in more practical way and that’s why moderate teaching aids are being preferred in present time by teachers whether it is school or any other online tutoring website. Some of these features are Video seminars for better explaining of any term, Online chat with tutors through remote connection to help in homework and various more. These tricks work mostly for earlier classes students because while giving them lessons, the key thing is to involve them some how and because of these friendly features this is done by ease. Math topics of 6th grade include Algebra, geometry, number system and Mathematical reasoning based questions. All these topics are pretty newer for this class students that’s why the math syllabus only includes some basic problems by which the meaning of the term Algebra or geometry gets cleared. In this session we will elaborate the algebra topics of 6th grade students.
When students has to deal with algebra then they have to learn one thing very strongly which actually defines the meaning of algebra. That important term is formation of mathematical expression. Math is an important part of our daily life which is used in almost every task we do or happens by own. We study mathematics to get aware of these tasks related to us and for that the situation has to be represented in an equation of we can say mathematical expression and this is what students learn in 6th standard. To form any algebraic equations variables and coefficients are interrelated through arithmetic operators.
Let us first elaborate these terms, Variable is a letter or symbol whose value can be changed in the equation and coefficient or constant is a fixed value. The presentation of both these terms must go through one point “ satisfaction of the equation”. Means left hand side value of the equation must be equal to the right hand side value.
Suppose an algebraic equation is as : ( x + 2 = 5)
Now here 'x' is a variable whose value is unknown for us yet and 2, 5 are constants. These terms are related through addition operator. Equation represents that (x+2) is equal to 5 it means the equation is satisfied but for solving this algebraic expression, students has to determine the value of 'x' which is done as:
x + 2 = 5
Shift the constant term into one side of the equation
x = 5 - 2
x = 3
In grade VI, there are some formulas included whose implementation is being learnt in factor and proportion section of the math syllabus. But actual use of those formulas are implemented in algebraic equation evolution. This evolution concerns with the normalization of the algebraic equation into such stage that the further composition can't be done. Let us take an example of Algebraic equation and see how its normalization is executed with the help of predefined standard formulas:
x2+ 5x+ 6= 0
the above can be written as
x2 + 3x + 2x + 6 = 0
It looks easy but this is done according to a rule which states that” the decomposition of first order derivative is to be done in such factors that the product of coefficient of the derivatives results the constant term of the given equation”.
Here '5x' is the first derivative and 6 is the constant term of the equation, that’s why '5x' is decomposed as ( 3x +2x) because (3 X 2 ) results the desired constant term .
Now exclude the common factor as:
x( x + 3) + 2( x + 3) = 0
By executing the previous step again
(x + 3) ( x + 2)= 0
This equation can't be decomposed further so this is the solution of the given algebraic equation. While solving any algebraic equation the final step is always to determine the numerical value of unknown variables of the equation, so accordingly here the value of 'x' has to be obtained as:
(x + 3) ( x + 2)= 0
This means one of the factor should be zero to satisfy the equation,
if (x + 3) = 0 than x = -3 and if ( x + 2) = 0 then x = -2
There are some more fraction principles which you will learn in fraction section of grade VI syllabus.
Once students get aware of evaluating procedure of algebraic equations then the next chapter adds one more factor in algebraic equations which is formation of equations from given word information. As said earlier 6th standard is the stage where students learn the formation of the problems in mathematical equations rather then their proper solution fundamentals. So now for making more clear that “ what actually word information is and how to form mathematical expression with it?” let us take an example for word problems for class VI:
James’s savings is 4 times as much as Sam’s savings, so find following:
What is the ratio of James’s savings to Sam’s savings to their total savings?
What fraction of their total savings is James’s savings?
What fraction of James’s savings is Sam’s savings?
If both boys save a total of Rs. 120, how much does James save?
First of all form the equation according to the first sentence,
If J is used to represent James and S is for Sam then
(J= 4 X S ):(Jame’s savings is 4 times as much as Sam’s savings)
One thing also gets clear that total units of saving is 5, four of James and one of Sam.
1. so ratio of J and S is :
J= 4 X S
J/S = 4.
Ratio of James savings to total saving is as 4 : 5
so James's saving is 4/5 of total savings.
3. ratio of Sam savings to James's saving is 1 : 4
so Sam saving fraction to James is ¼.
4. total 5 units are there so
5 units = 120 ( total saving)
so value of I unit = 120/5 = 24
James's share is = 4 X 24 = 96
Sam's share is = 1 X 24 = 24.
That’s how the equations are formed from given word information and easily being resolved.
In general, Algebra covers vast portion of mathematics and traditionally included in every class, so it is important to be good in Algebra and understand its concept because when students move to their higher classes than the Algebra based questions are not there but eventually students has to use Algebra tricks to solve various other math topics. Apart from algebra, students of 6th standard also deal with number system and geometry problems. All the math units of grade VI only include problems which just introduces the different mathematics branches to students. These problems gets complicated as students moves into his higher studies.
When students get proper assistance in solving their math problems only in that case students easily build their math skills. That’s why online math tutoring services are getting the prior success because they provide that immediate assistance for every class students and explain the things according to student’s mind level. Online math tutoring websites spread its service with the help of expert and proficient online math tutors who are available on the website 24 x 7 for solving your math queries. For making math sessions more interesting, these online tutors use some math games in which queries of different types are put on the screen with various options and student has to pick the right one, this phenomenon increases the focus of students and the competition feeling improves their performance. This trick works for 6th standard like earlier classes because this is the stage at which students generally not show their interest in books but same thing is when explained or presented in any graphical mode or with any game scheme then they actually get too much interacted. Online math tutors arrange various worksheets in which queries are related to awareness of standard principles. These worksheets solving is really worthy for students because they learn more about standard principles and problems implementation of these principles through worksheets which makes their math basics sharp. Most of the students prefer online tutoring because this service gives all which you expect from your tutor. They give all the relevant data to study and always being with you virtually through Internet platform. All the 6th grade topics are covered by these tutoring websites and students can arrange a regular math lesson session for himself. By participating in Online test programs students can compare his math skills with other students globally. So this is how the math syllabus of grade VI actually goes on for students in a flow.
In upcoming posts we will discuss about Syllabus of VI Grade. Visit our website for information on class 8 ICSE syllabus
When students has to deal with algebra then they have to learn one thing very strongly which actually defines the meaning of algebra. That important term is formation of mathematical expression. Math is an important part of our daily life which is used in almost every task we do or happens by own. We study mathematics to get aware of these tasks related to us and for that the situation has to be represented in an equation of we can say mathematical expression and this is what students learn in 6th standard. To form any algebraic equations variables and coefficients are interrelated through arithmetic operators.
Let us first elaborate these terms, Variable is a letter or symbol whose value can be changed in the equation and coefficient or constant is a fixed value. The presentation of both these terms must go through one point “ satisfaction of the equation”. Means left hand side value of the equation must be equal to the right hand side value.
Suppose an algebraic equation is as : ( x + 2 = 5)
Now here 'x' is a variable whose value is unknown for us yet and 2, 5 are constants. These terms are related through addition operator. Equation represents that (x+2) is equal to 5 it means the equation is satisfied but for solving this algebraic expression, students has to determine the value of 'x' which is done as:
x + 2 = 5
Shift the constant term into one side of the equation
x = 5 - 2
x = 3
In grade VI, there are some formulas included whose implementation is being learnt in factor and proportion section of the math syllabus. But actual use of those formulas are implemented in algebraic equation evolution. This evolution concerns with the normalization of the algebraic equation into such stage that the further composition can't be done. Let us take an example of Algebraic equation and see how its normalization is executed with the help of predefined standard formulas:
x2+ 5x+ 6= 0
the above can be written as
x2 + 3x + 2x + 6 = 0
It looks easy but this is done according to a rule which states that” the decomposition of first order derivative is to be done in such factors that the product of coefficient of the derivatives results the constant term of the given equation”.
Here '5x' is the first derivative and 6 is the constant term of the equation, that’s why '5x' is decomposed as ( 3x +2x) because (3 X 2 ) results the desired constant term .
Now exclude the common factor as:
x( x + 3) + 2( x + 3) = 0
By executing the previous step again
(x + 3) ( x + 2)= 0
This equation can't be decomposed further so this is the solution of the given algebraic equation. While solving any algebraic equation the final step is always to determine the numerical value of unknown variables of the equation, so accordingly here the value of 'x' has to be obtained as:
(x + 3) ( x + 2)= 0
This means one of the factor should be zero to satisfy the equation,
if (x + 3) = 0 than x = -3 and if ( x + 2) = 0 then x = -2
There are some more fraction principles which you will learn in fraction section of grade VI syllabus.
Once students get aware of evaluating procedure of algebraic equations then the next chapter adds one more factor in algebraic equations which is formation of equations from given word information. As said earlier 6th standard is the stage where students learn the formation of the problems in mathematical equations rather then their proper solution fundamentals. So now for making more clear that “ what actually word information is and how to form mathematical expression with it?” let us take an example for word problems for class VI:
James’s savings is 4 times as much as Sam’s savings, so find following:
What is the ratio of James’s savings to Sam’s savings to their total savings?
What fraction of their total savings is James’s savings?
What fraction of James’s savings is Sam’s savings?
If both boys save a total of Rs. 120, how much does James save?
First of all form the equation according to the first sentence,
If J is used to represent James and S is for Sam then
(J= 4 X S ):(Jame’s savings is 4 times as much as Sam’s savings)
One thing also gets clear that total units of saving is 5, four of James and one of Sam.
1. so ratio of J and S is :
J= 4 X S
J/S = 4.
Ratio of James savings to total saving is as 4 : 5
so James's saving is 4/5 of total savings.
3. ratio of Sam savings to James's saving is 1 : 4
so Sam saving fraction to James is ¼.
4. total 5 units are there so
5 units = 120 ( total saving)
so value of I unit = 120/5 = 24
James's share is = 4 X 24 = 96
Sam's share is = 1 X 24 = 24.
That’s how the equations are formed from given word information and easily being resolved.
In general, Algebra covers vast portion of mathematics and traditionally included in every class, so it is important to be good in Algebra and understand its concept because when students move to their higher classes than the Algebra based questions are not there but eventually students has to use Algebra tricks to solve various other math topics. Apart from algebra, students of 6th standard also deal with number system and geometry problems. All the math units of grade VI only include problems which just introduces the different mathematics branches to students. These problems gets complicated as students moves into his higher studies.
When students get proper assistance in solving their math problems only in that case students easily build their math skills. That’s why online math tutoring services are getting the prior success because they provide that immediate assistance for every class students and explain the things according to student’s mind level. Online math tutoring websites spread its service with the help of expert and proficient online math tutors who are available on the website 24 x 7 for solving your math queries. For making math sessions more interesting, these online tutors use some math games in which queries of different types are put on the screen with various options and student has to pick the right one, this phenomenon increases the focus of students and the competition feeling improves their performance. This trick works for 6th standard like earlier classes because this is the stage at which students generally not show their interest in books but same thing is when explained or presented in any graphical mode or with any game scheme then they actually get too much interacted. Online math tutors arrange various worksheets in which queries are related to awareness of standard principles. These worksheets solving is really worthy for students because they learn more about standard principles and problems implementation of these principles through worksheets which makes their math basics sharp. Most of the students prefer online tutoring because this service gives all which you expect from your tutor. They give all the relevant data to study and always being with you virtually through Internet platform. All the 6th grade topics are covered by these tutoring websites and students can arrange a regular math lesson session for himself. By participating in Online test programs students can compare his math skills with other students globally. So this is how the math syllabus of grade VI actually goes on for students in a flow.
In upcoming posts we will discuss about Syllabus of VI Grade. Visit our website for information on class 8 ICSE syllabus
