Fractions in Grade III

Hi kids,Earlier we have discussed about history of rational and irrational numbers and today we are going to learn about an important chapter in math called as  math fractions and simplifying fractions for Grade III of cbse syllabus. Fractions form an important part of math. A fraction is formed if it has a combination of the two terms which means a numerator and a denominator. A fraction is generally written in the form of a/b where a is numerator and b is denominator. To be more precise fractions can be defined as the ratio between a numerator and a denominator. Any common fraction is an example of math fraction like 2/3, 5/6 are all examples of a fraction. In words we can write 2/3 means 2 parts out of three. Let us take a simple example. Let's suppose A score 80 marks out of hundred in maths,  we can represent his marks in the form of a fraction as 80/100. It means eighty marks out of hundred.
Math fractions has its application in ratios as well as in division. In general we can classify fractions in two forms Proper and Improper fractions. A fraction is said to be a proper fraction if the numerator is less than denominator. Moreover a fraction is said o be an improper fraction if denominator is less than the numerator. Further we can say that the fractions form an important part of mathematics. Like numbers are the basic step to start with maths, fractions are the basis of maths as it is important in calculations and in understanding many things.(want to Learn more about ,click here),
Fractions  is a wide topic and there are many calculations and problems related to it. To sum up it can be said that fractions can also be of various types like mixed fractions, compound fractions, decimal fractions to name a few.
This is all about the Fractions and if anyone want to know about interpret data
then they can refer to Internet and text books for understanding it more precisely. You can also refer 4th Grade blog to learn about Factors and products. 

Equations and Inequalities in Grade III

Hello friends, Previously we have discussed about is 2 a rational number and in today's article we are going to discuss about the problems in equations and inequalities for grade III of CBSE math Syllabus. Here, I am going to tell you the best way of understanding the equations and inequalities problems. Start with the definition of equation, when two expressions are joined with the help of equal symbol then, it is called as equation. For example: x + 5=2, x + 4=1. Let me clear one thing that when we add, subtract, multiply, or divide the same number on both the side of the equation, the equal sign of an equation does not change. On other hand two algebraic expressions or two real numbers related by the symbol ‘<’, ‘>’, ‘<=’ or ‘>=’ form an inequality. For example: x-3>5. In inequalities perform addition or subtraction by the same number on both sides. Multiply or divide by the same number on both sides but if we divide or multiply by a negative number, we must reverse the inequality sign.
Now I would like to tell you that how would you solve the equations and inequalities problems. Firstly we are going for Problems in equations.
Example: Solve the equation for the variable y: y - 20 = 40
          Solution: y - 20 = 40
         Firstly we add 20 on both sides of the equation
          y – 20 + 20 = 40 + 20
         y = 60
        So, the answer is y = 60.
Example: Solve the equation for the variable: (y/3) + 50 = 40
            Solution :(y / 3) + 50 = 40
           Subtract 50 on both sides of the equation
          (y / 3) + 50 - 50 = 40 - 50
         (y / 3) = -10
        Multiply 3 on both sides of the equation
        (y / 3) * 3 = -10 * 3
        y = -30 so, the answer is 30

Now I am discussing about how to solve inequalities problems. Some examples are given below.(want to Learn more about Inequalities ,click here),
Example: Solve the inequality: 8x + 4 < 6x +7.
Solution: We have, 8x + 4 < 6x +7
Subtract 6x on both sides of the equation
8x – 6x + 4 < 6x + 7 – 6x
2x + 4 < 7
Subtract 4 on both sides of the equation
2x + 4 – 4 < 7 – 4
2x < 3
Divide by 2 on both sides of the equation
x < 3/2
So from the above all the real numbers are greater than 1. Hence, the solution set is (-infinity, 3/2).
Example: Solve the inequality: -2x – 7 < 7
Solution: -2x-7<7
Add 7 on both sides of the equation
-2x - 7 + 7 <7 + 7
-2x < 14
Divide by-2 on both sides of the equation and you will see the inequality sign is to be reversed.
x > -7
So from the above all real numbers are greater than -7 and hence, the solution set is (-7, infinity).

So this is all about equations and inequalities and if anyone want to know about

Time in terms of unit fractions then they can refer to Internet and text books for understanding it more precisely. You can also refer 4th Grade blog to study about Multiplication and division situations.

Numbers and Whole Numbers in Grade III

Hello friends,Previously we have discussed about real numbers definition and in today's session we all are going to discuss about one of the most interesting topic of mathematics, number system. In grade II of maharashtra board we learn counting of numbers(1,2,3,4,5,6,7…….) in mathematics, but we have not learnt about type of numbers. So in grade III we are going to learn What are numbers and  definition of whole numbers and how to solve math problems related to it.
First of all, we discuss what is numbers? Numbers are mathematical object which is used to count and measure different things. In mathematics there are so many numbers between    positive numbers (1,2,3,4………), negative numbers(-1,-2,-3………).
………………-9 -8 -7 -6 -5 -4 -3 – 2 -1 0 1 2 3 4 5 6 7 8 9………………………
But from algebra point of view, all numbers are defined in a set which is called as a real numbers and we divide real numbers into two types of numbers

• rational numbers
• irrational numbers

So, first of all we discuss about rational numbers  :(want to Learn more about Whole Numbers ,click here),
We know rational numbers are represented as (a/b) where a and b are integers and b is not equal to zero, but when b is equal to 1 then all numbers are represented as rational numbers . There are following numbers which is a part of rational number set (Q)  -

• Whole Numbers (W) - In algebra, whole numbers can be represented by a set of numbers which is starting from 0 to infinity .

W = ( 0 , 1 , 2 , 3 , 4 , 5 , 6 ………………………………….)
here W shows Whole Numbers set .

• Natural Numbers (N) - From algebraic number system, natural number is a set of number which include all whole numbers except 0.

N = ( 1, 2 , 3 , 4 , 5 , 6 , 7 ………………………………………)
here N is natural number set.

• Integer Numbers (I) - From algebraic definition, integer numbers are set of numbers which include all negative, positive and zero number except decimal numbers.

                 I = ( ……… -7 -6 -5 -4 -3 – 2 -1 0 1 2 3 4 5 6 7  ………)
                 here I represent set of integer number
Now further we are going to discuss our second type of real numbers irrational numbers.
Those numbers which are not part of rational numbers are part of irrational numbers or we can say that those numbers which are not represent in (a/b) form are called as a  irrational numbers like sqrt(2),  sqrt(5) etc.
At last, this picture represents whole story about Numbers
  
So, my friends this all about our Grade III mathematic topic Number System. I hope guys you enjoyed today's session and if anyone want to know about Models for multiplication then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Multiplication and division situations in the next session here.

Properties of numbers in Grade III

Hello Friends,Earlier we have discussed about real numbers examples and in today's session we all are going to discuss about an interesting topic of mathematics which is properties of numbers for grade III students of gujarat secondary education board. These properties include commutative and associative properties. Here I am going to give you the best free math answers and way of understanding these terms.
Arithmetic operations on the numbers follow the basic properties commutative property, associative property, distributive property. But here we will only study about two of them. Now start with the Commutative property.
Commutative word originally comes from the word “commute” which refers to move the stuff around. In addition of two numbers, this rule is represented as "p + q = q + p", which means 5 + 9 = 9 + 5. In multiplication of two number, this rule is represented as "p x q = q x p", which means 5 x 9 = 9 x 5. Let’s understand it in this way
Addition of numbers can be done in any order.
For example: 2 + 13 = 13 + 2
                      p + q = q + p
Multiplication of numbers can be done in any order.
For example: 12 x 6 = 6 x 12
                       p x q = q x p
Subtraction of numbers can’t be done in any desired order, since it is not commutative
For example: 6 – 2 ≠ 2 – 6
                      p - q ≠ q – p
Division of numbers can’t be done in any desired order, since it is not commutative
For example: 6 ÷ 2 ≠ 2 ÷ 6
                      p ÷ q ≠ q ÷ p

Let’s now move to associative property
Associative word originally comes from the word “associate” which refers to the grouping of numbers or objects. In addition of three numbers, this rule is represented as "p + ( q + r ) = ( q + p ) + r", which means 5 + ( 9 + 12 ) = ( 5 + 9 ) + 12. In multiplication of three number, this rule is represented as "p x ( q x r ) = ( p x q  ) x r", which means 5 x ( 9 x 12 ) = ( 5 x 9 ) x 12. Let’s understand it in this way

Addition of numbers can be done in any order.
For example: 2 + ( 13 + 9 ) = ( 2 + 13 ) + 9
                      p + ( q + r ) = ( q + p ) + r
Multiplication of numbers can be done in any order.
For example: 12 x ( 6 x 14 ) = ( 12 x 6 ) x 14
                       p x ( q x r ) = ( p x q  ) x r
Subtraction of numbers can’t be done in any desired order, since it is not associative
For example: 6 – ( 2 – 4 ) ≠ ( 6 – 2 ) - 4
                      p - ( q - r ) ≠ ( q - p ) - r
Division of numbers can’t be done in any desired order, since it is not commutative
For example: 6 ÷ ( 2 ÷ 4 ) ≠ ( 6 ÷ 2 ) ÷ 4
                      p ÷( q ÷r ) ≠ ( p ÷q  ) ÷r

This is a brief introduction about commutative and associative properties for the grade III students and if anyone want to know about Steps in problem solving  then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Probability and Statistics in the next session here.

Different Patterns in Multiplication Facts

Hello friends,Previously we have discussed about 3 digit subtraction with regrouping and now we are back again with one more algebra 1 topic for grade III of icse board. Our today’s topic is very much interesting. Today we will learn Patterns in multiplication facts.
There are many students who put lots of efforts and time to memorize facts in earlier grades. And there are a few who can really recall them easily. When some multiplication questions are assigned to them there may be only 2 or 4 students who can solve all of them quickly with cent percent accuracy. Other still take time to solve them after putting so much efforts.
 Multiplication facts help you to memorize table and also make it easy to create any number’s table with little effort.
Multiplication facts are easiest to learn when we find some pattern or relating something with other we already know.(want to Learn more about Patterns in Multiplication ,click here)

First we start with what is multiplication. I know you all must be laughing! We all know what multiplication is.

Multiplication is simply a fast way to add group of equal size.

Example:
            5 x 3 =15
            (Number of groups) x (number of elements in each group) = total all together
One important thing is, the number of elements in each group must be same.

An important property of multiplication is Commutative property which states:
When we multiply two numbers their result is always same regardless of the order of the numbers.

Example:
            3x4 = 4x3 =12

“0” family facts:
            Any thing times “0” is 0.

            Examples:
                        0x1 = 0
                        0x2 = 0
                        6x0 =  0

“1” family facts:
          Any number times “1” is same number.
         
            Example:
                        1x4 = 4
                        5x1 = 5
                        9x1 = 1


“2” family facts:
          Any number times “2” is double the number.

            Example:
                        2x2 = 4
                        2x3 = 6
                        2x8 = 16
                        7x2 = 14

“4” family facts
          To multiply any number by 4 double it two times.
                     
            Example:
                        4x3 = 3x2x2 = 12
                        4x5 = 5x2x2 = 20
                        6x4 = 6x2x2 = 24


“5” family facts:
            To multiply any number with 5 we follow two steps.

            Step 1: Half the number we are multiplying.
                        Example: 5x3 = 1.5
                                        5x4 = 2
                                        5x5 = 2.5
                                        5x6 = 3
            Step 2: Again this step is further divided in two.

                        Step 2a: If number is even add zero.
                        Example:
                                        5x4 = 2 0
                                        5x6 = 3 0
                        Step 2b: If number is odd remove decimal.
                        Example:
                                        5x3 = 15
                                        5x5 = 25               

“6” family facts
                             For the even numbers only. That using this method we can only                                      multiply even numbers with “6”.

                                    Step 1: Half the number we are multiplying.
                                    Example:
                                                6x2=1
                                                6x4=2
                                                6x6=3

                                    Step 2: Put the number we are multiplying after the number(result                                                           of sep1)
                                    Example:
                                                6x2=12
                                                6x4=24
                                                6x6=36


                                             
“9” family facts
            To multiply any number with 9 follows two steps:
         
            Step 1:Half the number we are multiplying.
            Example:
                        9x3 = 2
                        9x4 = 3
                        9x6 = 5
            Step 2: Add a number with totals 9 with the first number.
            Example:
                        9x3 = 27 (2+7=9)
                        9x4 = 45 (4+5=9)
                        9x6 = 54 (5+4=9)

                                 
                     
“11” family facts
                   I will give you two methods to multiply numberswith“11”.
                     
                        Method 1: For single digit numbers.
                                         Number multiplied with 11 is just duplicated.
                                         Example:
                                                11x3=33
                                                11x5=55
                                 
                        Method 2: For two digit numbers.

·        Write the two digit number with space between them.  

                                                Example:
                                                            11x18=1_8
                                                            11x14=1_4

·        Add the both number and put result between the digits.

                                                 Example:
                                                            11x18=(1+8=9)=198
                                                            11x14=(1+4=5)=154

We have discussed some major patterns in multiplication facts. To get familiar with this will surely help you to complete your assignment and tests easily and in less time and if anyone want to know about Estimation in addition and subtraction then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Possible combinations in the next session here.

Understand Patterns in tables of Paired Numbers

Children today i am going to teach you one of the interesting topic of mathematical world that is algebra . In  grade  II of gujarat secondary education board we  learn  numbers(1,2,3,4,5,6,7…….)  and  addition  of  2 digits , subtraction  of   2 digits,  multiplication  on  2  digits  and   when  we   study  about  operations  like  addition , subtraction ,  multiplication,Factoring Algebra and  division  on   numbers,  then  this  kind  of  study  is  called  as  an  algebra 1 .In  grade III  we  have  to  study  about  Patterns  in  tables of paired numbers, where  paired  numbers  means  two  numbers  which  are  related  to  each  other  and  these  patterns are   useful  to  solve  similar  relative  problem  on   pair  numbers like  we have  cycle  and   their  wheels  relation  and  if  you  know  one  cycle  has  2  wheels  then  how  many  wheels  of   4  cycles .  In above  example  number  of  cycles  and  number  of  their  wheels  are  called  as  a  pair  numbers and we  have  to  make  a  table  pattern  to  solve  this  problem . So,   for   solving  these  kind  of  problems   we  have  to  study  about  Patterns in tables of paired numbers  and  when  we  define  paired  numbers  in  table  pattern  , where  table  pattern  is  known  as  a  row-column  pattern  and   these  kind  of  patterns  are  called  as  a  Patterns in  tables  of paired numbers(To know more about patterns click here).  So, initially   we  discuss  what  is  row-column  pattern - 

• row-column  pattern  ( table  pattern) :  in  this pattern, we  draw  two  intersected  lines  which is  combination  of  horizontal  and  vertical  line, where  horizontal line  is  known  as  a  row  and  vertical  line  is  known  as  a  column  . For  understanding  row-column  pattern  briefly  we have  to   take  an  example  from  real  life  scenario   – like  we  have  an  number  of  cats  and  number  of  legs  problem  in  table  pattern  

Number  of   cats                      Number  of   legs
            1                                                  4
            2                                                  8
            3                                                 12
            4                                                 16
            5                                                 20

so  when we  look  at  numbers ,   how  the   numbers  in  left  column   are  related  to   numbers  in     right   column ,  here  one  cat  has  4  legs  and  when    we  want  to  find  number  of  legs  of  2  cats  then  we  have  to  multiply  with  4  like  (2 * 4  = 8)  and  this  process  is  going  again  and again. So,  rule  of  this  pattern  is   multiply  by  4.

We   can  solve  many  problem  with  this  pattern  like  -   car  and  their  wheels ,  cow  and  their  legs , number of  weeks  and  number of days ,  number  of  shoes and  number  of  legs  relation   etc.    

In  everyday  life  we  see  many  patterns  like -  barbed  wire ,  grills  of   window ,  a  snake  etc  and  you  look  around  your   clothes  there  is  some  pattern  also  and  we  use  these   pattern  to  solve   mathematical  problems by relating   each  pair  number  in  certain  pattern  and   table  pattern  are  most useful  pattern  to  solve   mathematical  problem  which  is  in  pair  number form .So,  this  is  all  about  grade III's  important lesson of algebra - Patterns in  tables of  paired  numbers and You can also refer Grade III  blog for further reading on Division problems.Read more maths topics of different grades such as Algebra and Functions  in the next session here.

blog on grade III

Hello friends I am back again with a new topic. Algebra! Boring topic for some students but in today’s topic you will find it interesting. Our today’s topic is for Grade III students of cbse board who find difficulties in algebra 1. Today we will learn fact families, Patterns (practice patterns in Pattern Worksheet) in fact families.
 A grade III student is aware of basic a mathematical operation that is addition, subtraction, multiplication, division. Building his/her logic in the same, fact families are used. This enhances students’ ability to deal with these operations. Family means group of people related with each other similarly fact families means set of numbers and fact related with each other.
For a grade III student we only take 3 numbers in a family.
Addition and subtraction are part of one family. Similarly multiplication and division are part of same family. They are like cousins in family.
3 numbers two operators (+, - or /*) and an equal sign
(=) creates a family.For further details on algebra click here:

Example:
Numbers: 3, 5, 8
Operator: +, - and =.

Taking the above example let’s look at the Patterns in fact families.

Pattern 1: Add two numbers to get third number.
                        3 + 5 = 8
Pattern 2: Change the order of two numbers to get the same third number.
                        5 + 3 = 8
Pattern 3: Use the cousin operator here (-) and select the result of first two pattern and subtract one of the addend to get other one.
                        8 - 5 = 3
Pattern 4: Change the addend now to get other one.
                        8 – 3 = 5       

After discussing one family now we will move on the other family. Multiplication and division fact family. Multiplication and division is cousin operator.

Example:
            Numbers: 5, 4, 20
            Operators: *, / and =
         
Patterns in fact families

Pattern 1: Multiply two numbers to get third number.
                        5 * 4 = 20
Pattern 2: Change the order of first two numbers to get same third number back.
                        4 * 5 = 20
Pattern 3: Take result of first two patterns and select any one of remaining two numbers. Divide selected result from number to get third number.
                        20 / 5 = 4
Pattern 4: Use second number and again divide result of first two patterns from this.
                        20 / 4 = 5

You should ask me why cousin operators are used to define patterns in fact families. Cousin operators in the family has inverse property from each other.  So they are used to get the value from the result given by other operator of the same family. Confused!

Let’s take an example:
                                    Suppose we have 5,6,11 numbers and =,- operator

·        Addition of 5 and 6 gives 11

                  5+6=11

·        Now to get any one of addend from result we need cousin operator that family and one addend.

                  11-5=6

It must be clear to you now.
Now let’s talk about the usefulness of fact families. For a grade III student, an assignment is assigned by the faculty of algebra.
Andrew has 4 chocolates and Ricky gives him some more. Andrew now has 6 chocolates. How many chocolates did Ricky gave him?

Now if students are aware of fact families than they can easily solve this problem.
Andrew already has 4 chocolates.
After getting some from Ricky, Andrew has 6 chocolates.
Number of chocolates Ricky gave = after – already
                                                       =  6 - 4  
                                                       =  2

This is all about the algebra fact families and Patterns in fact families. Spend some time with them and I am sure you will find it easy and not so boring any more and You can get information about Odd and even numbers in grade III and Rounding numbers in Grade IV on Internet.

Place Value for Grade III

Hello friends, today we are going to learn about place value and whole numbers. Here I am going to tell you the best way of understanding place value and whole numbers which comes under the cbse board syllabus.
First we discuss about the Place value to calculate math answers. In our Decimal numbers system, the value of digit depends on its place. In the number each place has a value of 10 times the place to its right. A number in standard form is separated into group of three digit using commas. Each of these group is called period. Place value of digit is determined by its position in a number, the name of the place or location of a digit in a numbers. Place value is positional system of notation in which the position of a number with respect to a point determines its value. In the decimal system, the value of the digit is based on the number ten. Each position in a decimal number has a value that is a power of 10. A decimal point separates the non-negative power of 10 (10⁰=1 , 10²=100, 10³=1000). The idea of the place value is at the heart of our numbers system, First however, a symbol for nothing or zero had to be invented. Zero holds the place of particular value.  When no other digit goes in that position. For example the number “100” in words means one hundred. No one’s without a symbol for nothing our decimal number system wouldn’t work.To get more information about it click here:

Beginning with one place at the right, each place value is multiplied by increasing power of 10, the value of the first place on the right is “one ” the value  place to the left of it is ten which is 10 times 1. The place to the left of the ten place is hundred, which is 10 time 10. Place value number can be represented in many ways. But standard form is usually the shortest and easiest. Here are some numbers expressed in different form with their standard form show alongside.
We take one number 145, have three digits. Each digit is a different value in this value “1” refer to the hundredth place the “4” refers to the ten place and the “5” refers to the one place is succeeded.
Place value is an important concept that is often misunderstood and misplaced. Place value the particular power of the base of continue system that is represented by a particular position in a place value Notation for example: - unit, ten, hundred, etc. The definition correctly places the concept of place value as an attribute of positional system not solely the decimal one.  Place value the value given to a digit by virtue of the places it occupies in the number relative to units place. Importance of place value has been emphasized in the NCTM standards.  The place value is important to understand numeration system.

In above article we discuss about the place value and whole number and if you want to know about Properties of numbers in Grade III and Place value whole numbers then you can refer to the various sites available on Internet.

How to deal with Expressions in grade III

Hello friends, today we are going to discuss a very interesting topic, expressions, equations, and inequalities which are included in grade III of maharashtra state board of secondary and higher secondary education. Friends, as we all know study of mathematics is almost impossible without equations, expressions and inequalities, let’s start with expressions. An expression shows a math relationship between variables and constants, one interesting thing about expression is that it does not have a solution or answer if it is represented alone. It can only be evaluated by substituting the value of variable, we can solve an expression only if it is related by a equation or an inequality, for example: 5x +6 is an expression in one variable it can be evaluated by substituting different values of x, lets put x=5 then we obtain the value of expression = 31, this is called the evaluation of the expression.
Equation is nothing but a statement that shows two expressions are equal and expressions can be algebraic expression or any other, an equation consists of a number of variable and non variable, variables are the quantities which can have many possible values such as length, time, height etc. Non variables are those quantities whose value remain constant with time such as numerical digits whereas unknown are those quantities whose value is to be determine from the equation. Solution of an equation refers to find the value of unknown present in the equation. Friends, here we have an example of equation X+Y = 7, is an  linear equation having two variable whose sum is equal to 7, an equation can have a number of solutions, for example the solution for above equation can be found out by putting  x=2 and y=5,  other solutions to this equations are  (0,7) (-2,9)  and there can be a number of other solutions.

Now let’s know about inequalities, two expressions or real numbers separated by ‘<’, or ‘>’ , ‘<=’ or ‘>=’ sign form an inequality. Below are some steps on how to solve inequalities:

1. First we add or subtract the same number on both sides to reduce the size of the inequality
2. Then we separate the variables and constant of inequality
3. Then we multiply or divide by same number on both sides to get the solution of the inequality.

Now we consider few examples which will surely help you to understand the topic and for more information about this topic refer this:
Ex. Solve the inequality 8x+5 < 6x+7.
Subtracting 6x from both sides of the inequality, we obtain
8x-6x+5 < 6x-6x+7 or
2x+5 < 7 or
2x< 7-5 or 2x<2or
X<1 this is our answer.

Here we take another example:
Solve the inequality 4x +2 < -2x+ 14,
First of all we subtract 2 from both sides 4x+2-2 < -2x+14-2 or
4x < -2x +12 now we add 2x t both sides and we obtain

4x+2x < -2x +2x +12 or

6x < 12 now we divide both sides of the inequality by 6 and we obtain

x < 2 this is our answer.

Friends that is all for today and if you want to get information about Numbers and Operations and another topic from grade III that is  Fractions and decimals you all are advised to refer the internet.

Attributes of geometrical figures for Grade III

Hello friends we are back again. Today with a new topic of Geometry to provide geometry help for Grade III students of gujarat secondary education board. In today’s topic we will cover Geometry and Attributes of Geometrical Figures.

First, we will start with Geometry. Geometry has its own vocabulary. Geometry is all about shapes and sizes. Geometry shapes and Functions  are all around us, the thing is we did not notice.

Like the car and bikes we ride in, houses/buildings we live in, food we eat etc. Some of them can be touched and come can only be imagined. Geometry is based on four imaginary ideas or items upon which every thing else is designed – point, line, plane, space.

Some geometrical figures are: circle, rectangle, square, triangle, cube, cylinder, cone etc.

We will discuss attributes of some of them which are important to a grade III student.

For a Grade III student it will be good is he/she can identify and differentiate geometrical shapes.

Now we will discuss the Attributes of Geometrical Figures.To know more about Geometry click this.

Circle:

        

Attributes of the circle:

Center: All points on the circle are equidistant from the center.

Radius: Half the diameter. It is the distance from the center to any point on the circle.

Diameter: It cuts the circle into two equal parts.

Circumference: Periferi around the circle, just like perimeter of a rectangle.

Area: Region enclosed by the circle.

Chord: Line segment linking any two points on a circle.

Tangent: Line passing a circle and touching it at just one point.

Rectangle:

                 

Attributes of Rectangle:

                   Opposite sites are parallel and congruent.

                   Diagonals bisect each other.

                   Diagonal are congruent.               

Square:

        

Attributes of Square:

Vertices: Every square has four vertices with internal angle 90..

Perimeter: Distance around square. All four sides are of same length so perimeter =4s.

Area: Length of one side multiplied by perpendicular height.

          That is s2.

Diagonals: Each diagonal cuts the other into equal part because they are the perpendicular bisector of the other. Length of each is = s√2.

Triangle

Attributes of triangle:

Vertices: Corner of the triangle. Each triangle has three vertices.

Base: Any one of the, usually the bottom one, used to calculate the area of the triangle.    

Altitude: Perpendicular from the base to the opposite vertices. As there are three base possible in a triangle so there can be three altitudes. The point where three altitudes intersects is called the orthocenter.

Median : Line from a vertex to the midpoint of the opposite side. The point where three median intersect is called the Centroid.

Interior Angle: Three angles at the each vertex inside of the triangle.

Exterior Angle: Angle between the side of the triangle and the extension of an adjacent side.

Cube:

                                                                      

Attributes of the Cube:

Face: Cube has six faces all are square. That is each face has four equal sides and all four interior angels are right angle.

Edge: Has 12 edges and all are of same length

Vertices: Point where three edges meet. And a cube has 8 vertices.

Face Diagonal: Are the line segment which links the opposite corner of the face. A cube has 12 face diagonal.

Space Diagonal: Line segment links the opposite corner of the cube. A cube has 4 space diagonal.

These are some basic figures of geometry and their attributes. As there are many other shapes as well. But for a Grade III student, these are enough to start with. You can take help of Internet or the other section to get complete knowledge about Numbers and Whole Numbers in Grade III and also Numbers in Grade IV.

Rounding Numbers Grade III

Hello friends, in this session we are going to learn about some of the mathematical topic related to grade III of maharashtra board. We are going to learn about the rounding numbers for grade III. The grade has its lot of interaction with the numbers. Rounding whole Numbers is just basic operation performed on the numbers in grade III.
Here in this session, we are going to learn about the Math problems on rounding numbers and the operation performed on them. Rounding a number is a process of making a decimal or any other whole number in to some appropriate form of the whole number. We replace the decimal number by another value that is appropriate or quite equal to that number. Rounding of a number is done for the purpose of making understandable and simpler form of any of the calculation. We replace the decimal value with their relatively nearest whole value. For example, replacing 87.5673 with 87.57, or some fraction number like 12 / 37 with 1 / 3, or the root of three (√3) with 1.7171. We make the rounding of any number because it becomes easier to work on it. It is not the exact value of the number and also we can’t get the exact result of the operation by approximating any number but it is only the approximation of any number and the result is also quite close to the exact result.
Now talking about the approximation of the whole numbers, the numbers that ends in 1 through 4 we replace them with next lower number that ends in zero. For example numbers like 61, 62, 63, 64, can be replaced with 60. Talking about other section of the whole number, the numbers that ends in 5 or more can be replaced with next even ten. For example, all numbers like 65, 66, 67, 68, 69, can be written in the approximation of 70.For more details and to know about the types of rounding numbers please refer this.
Talking about the rounding of other type of numbers can be understood by the help of some examples. For example, irrational number like √2 can be written as 1.414, fraction like, 4/7 can be written as 0.571. Fraction number can be replaced with some of the smaller numerator and denominator number for example 5123/10236 can be written as 1/2. A decimal number have also same rule for the rounding off. If the digits after decimal is 4,3,2,or 1, we have to simply drop that digits and if they are 5 to 9 we have to add 1 in the whole number for example, 1.83466897074 in to 1.83 and 1.83666897074 in to 1.84. For more clarification of the rounding off of the numbers, we have to take some more examples: if we want to keep only one decimal digit then the number 8.6480 will be 8.6 and taking two digits in consideration we will write it as 8.65, 6.997 can be written in 7.00 and
So, rounding of a number makes the operation simpler than the original operation and the result is also quite same to the exact result. If you want to know about Properties of numbers in Grade III and also about Mathematics in daily life then you can refer Internet.

Compose and Decompose Numbers in Grade III

Hello friends, today we are going to learn about Compose Numbers and Decompose Numbers for Grade III of central board of secondary education. We are discussing both Compose Numbers and Decompose Numbers one by one. So firstly compose numbers, compose numbers also called composite numbers. A positive integer which is not a prime number(what are prime numbers) is called composite or compose number that is n>1 which has factors other than 1 and itself also. Where n is a composite number. If it is not a Composite Number then it is called a Prime Number. In other words a number which can be divided evenly by numbers other than 1 or itself is called a compose number. The example of composite numbers is 4, 6, 8, 9, 10, 12, 14, and 15. what is prime factorization of these numbers its shown in the following table.
             n                             Prime factorization                       n                     prime factorization
            4                                     2²                                       20                            2².5
            6                                     2.3                                     21                            3.7
            8                                     2³                                      22                             2.11
             9                                    3²                                       24                             2³.3
           10                                   2.5                                      25                             5²  
           12                                   2².3                                     26                             2.13
           14                                   2.7                                      27                             3³
           15                                  3.5                                      28                              2².7
Now I am taking an example that may help you to understand composite numbers. We take two numbers that is 4 and 7. 4 can be divided evenly by 2 but 7 is not.
4 can be divided evenly by 2, as well as by 1 or 4,
4=1 x 4
4=2x2
But in the case of 7, we cannot divide 7 evenly by 2,3,4,5.
4 can be divided evenly so it is a Composite Number and 7 cannot be divided evenly so it is a Prime Number. 7 can only be divided evenly by 1 or itself. So from the above composite means something made by combining things like numbers.To know about highly composite numbers click here.
Now I am going to tell you about Decompose Numbers. Decompose Numbers is just reverse of composite numbers. In composite we combine things and made something but in decompose we separate or break down those things. Decompose is defined as the process of separating numbers into their components or to divide in to smaller parts is called Decompose. When we decompose a number then it is written as a product of prime factors and when  we decompose a fraction then it is written as a sum of partial fractions. For example      
356 can be decomposed as 356 = 300 + 50 + 6. I am taking one more example which may help you to understand the decompose numbers. We decompose 25,541.
Firstly, 25,541 = 20,000 + 5,000 + 500 + 40 + 1
= (2 × 10,000) + (5 × 1,000) + (5 × 100) + (4 × 10) + (1 × 1)
From the above, when we decompose 25,541 then we will get ‘2 ten thousands, 5 thousands, 5 hundreds, 4 tens, and 1 ones.
I want to tell you one more thing, when we multiply a list of prime numbers together, are equal to that number is called  prime decomposition of a number. For example 24=2x2x2x3, its prime decomposition is 2, 2, 2, 3.
From the above discussion I hope that it would be helpful you to understand the Compose Numbers and Decompose Numbers and to know about Numbers in Grade IV and Multiplication facts/tables you can refer to the various sites available on internet.

Counting Money in Grade III

Hello kids! How are you all today? Our today’s free online math tutoring session is going to be very interesting. Today we will learn Counting Money and Counting Numbers. A Grade III student always wants to know what his father and mother are doing with the currency. How they add up different kinds of them. What is the basic of counting it? Here we will learn how to count pennies, nickels, dimes, quarters, cents and dollars. It is very important for a grade III student to recognize them and know the value of their money. 1 penny, 1 cent are count by one.
That is we will count it as 1 penny, 2 penny, 3 penny and so on and same for cent.

1 nickel = 5 cents.
That is while adding (also play adding and subtracting integers worksheets) we count them as 5 cents (1 nickel), 10 cents(2 nickels), 15 cents(3 nickels) and so on.   
            5 pennies = 1 nickel
            1 + 1 + 1 + 1 + 1 (cents) = 5 cents = 1 nickel

1 dime = 10 cents and are counted by 10 to count them. That is we will count it as  10 cents(1 dime), 20 cents(2 dimes), 30 cents(3 dimes) and so on.
            10 pennies = 1 dime
                        And
            2 nickels = 1 dime

            5 cents + 5 cents = 10 cents = 1 dime
            1 nickel + 1 nickel = 1 dime

1 quarter = 25 cents and is counted by 5 to count them. That is we will count it as 25 cents, 50 cents, 75 cents and so on.
            25 pennies = 1 quarter
            5 nickel = 1 quarter
            2 dimes + 1 nickel = 1 quarter


1 dollar = 100 cents and is counted by 100 to count them. That is we will count it as 100cents, 200 cents, 300 cents and so on.
            100 pennies = 1 dollar
            20 nickels = 1 dollar
            10 dimes = 1 dollar
Dollar is represented as $.

Now we will look at some examples and get familiar with adding up money.
Example 1: how will you write 12 cents in dimes and pennies?
Solution: 1 dime and 2 pennies

Example 2: How many dimes are there in 10 cents?
Solution: 1 dime = 10 cents.

Example 3: how many penny and nickel you will need to count 6 cents?
Solution: 1 nickel + 1 cent = 6 cents.

Example 4: how many quarters are there in $1 or 1 dollar?
Solution: 4 quarter = 1 dollar


Now after discussing counting money let’s move on to Counting numbers. Before start learning counting we should know what are whole numbers. Whole numbers start with 0. That is whole numbers are 0, 1, 2, 3, 4, 5 and so on. Counting numbers are whole numbers but without zero. That is counting numbers are starts from 1.
The counting numbers are 1, 2, 3, 4, 5, 6 and so on.
Counting numbers includes positive whole numbers and also called natural numbers. The next number in counting numbers is generated by adding 1 to previous number.

We can also write numbers in words:
One, two, three, four, five, six, seven, eight, nine, ten.
1       2        3       4      5      6       7        8         9     10

Now just adding ten(10) in each next series can easily be generated.
1+10 =11, 2+10=12, 3+10=13 and so on
Eleven,         twelve,     thirteen.

Now we have discussed both how to count number and how to count money. Both are related with one another. Do you know how?
If we know counting numbers we can easily add up money and quickly move to the result.

In upcoming posts we will discuss about Compose and Decompose Numbers in Grade III and Mean. Visit our website for information on CBSE psychology question paper 2010

Expanded Notation in Grade III

Hello Friends, in today's session we all are going to discuss about the most interesting topic of mathematics, expanded notations which are usually studied in Grade III. Here I am going to tell you the best way of understanding this term. (Also you should read Function Notation to expand your knowledge)

The first question arises here is that what is expanded notation? Expanded notation is a way of representing the whole numbers as a sum of each digit multiplied by its place value ( units, tens, hundreds, thousands etc. ). Let’s understand by taking some examples:

1.    4345 = 4 x 1000 + 3 x 100 + 4 x 10 + 5 x 1

2.    372 = 3 x 100 + 7 x 10 + 2 x 1

3.    84957 = 8 x 10000 + 4 x 1000 + 9 x 100 + 5 x 10 + 7 x 1

Steps to convert a whole number from its standard form to expanded form:

1.    Let’s take an example to understand these steps easily. Let take 4257.

2.    Always start picking the digit of the number from the right side i.e. first pick 7 and multiply it by its place value i.e. 7 x 1.

3.    Now pick the second digit 5 and multiply it by 10 and so on multiplying all other digits from their place values i.e. 2 x 100, 4 x 1000.

4.    And finally arrange all the numbers with their place value using ‘+’ as a separator between them. Now the expanded form will look like:

                 4 x 1000 + 2 x 100 + 5 x 10 + 7 x 1
Let’s solve some questions related to expanded notation:
Q 1. Write the following numbers in their expanded notations.

a.    7458 = 7 x 1000 + 4 x 100 + 5 x 10 + 8 x 1

b.    48521 = 4 x 10000 + 8 x 1000 + 5 x 100 + 2 x 10 + 1 x 1

c.    169 = 1 x 100 + 6 x 10 + 9 x 1

d.    7879 = 7 x 1000 + 8 x 100 + 7 x 10 + 9 x 1

e.    15 = 1 x 10 + 5 x 1

f.     9586 = 9 x 1000 + 5 x 100 + 8 x 10 + 6 x 1

g.    12345 = 1 x 10000 + 2 x 1000 + 3 x 100 + 4 x 10 + 5 x 1

h.    741 = 7 x 100 + 4 x 10 + 1 x 1

i.      472 = 4 x 100 + 7 x 10 + 2 x 1

j.      74214 = 7 x 10000 + 4 x 1000 + 2 x 100 + 1 x 10 + 4 x 1

k.    2354 = 2 x 1000 + 3 x 100 + 5 x 10 + 4 x 1

This is all about the expanded notation and if still it is not clear to anyone they can refer to internet and text books for understanding it more precisely.

In upcoming posts we will discuss about Counting Money in Grade III and Possible outcomes. Visit our website for information on CBSE board fashion studies syllabus for class 11

Angles in Grade III

Hello Friends, in today's session we all are going to discuss about some of the most interesting topics of mathematics, angles and types of angles which are usually studied in Grade III. Here I am going to tell you the best way of understanding these terms.
Angle is formed when two rays starts from same point. Angles are the part of geometry shapes and the measuring unit of angles is degree. The point of meeting of rays is also known as vertex. Angles are usually assumed in 2D planes but they also presents in 3D planes. Two angles can be concurrent to each other only when they are identical in degree and the transformation of one angle from another completely overlap the another one. The size of angle is measured by the rotation of one ray away or towards the other one, therefore the angle is basically identified by the degree of rotation of rays. More more information read this resource.
To measure an angle a circular arc is drawn between two rays at the vertex with the help of compass. We can use the formula i.e.
       ÆŸ = k q
               p
Here ‘q’ is the length of arc drawn and ‘p’ is the distance of the arc from the point of meeting of rays also called as radius of circle and the last ‘k’ is known as the scaling constant which depends on the measurement unit chosen. From the above example we can conclude that ‘ÆŸ’ is independent of the arc size and the ‘q’ directly depends upon the ‘r’.
Now let’s move on types of angle:
What is an Acute Angle: Acute angle can be defined as the angle which is less than 90 degree.


Right angle: Right angle can be defined as the angle which is equal to 90 degree.


Obtuse angle: Obtuse angle can be defined as the angle which is greater than 90 degreebut less than 180 degree i.e. angle must be between 90 to 180 degrees.


Straight angle: Straight angle can be defined as the angle which is equal to 180 degree. Therefore these types of angles look like straight lines.


Reflex angle: Reflex angle can be defined as the angle which is greater than 180degree but less than 360 degrees i.e. between 180 and 360 degrees.
Adjacent angles: Adjacent angles can be defined as the angles which have common vertex and a common side.


Complementary angles: Complementary angles can be defined as the angles whose sum is equal to 90 degree and all together form a right angle.


Supplementary angles: Supplementary angles can be defined as the angles whose sum is equal to 180 degree.


Vertical angles: Vertical angles can be defined as the angles which have common vertex and their sides are formed by same lines and are opposite to each other.


When two parallel lines are intersected by the third line, eight angles are formed. Four of them are alternate interior angles and the remaining four are alternate exterior angles.

Alternate interior angles are pairs of angles on the inner side of the two parallel lines.

Alternate exterior angles are pairs of angles on the outer side of the two parallel lines.

Corresponding angles are pairs of angles which are similar in position and have face towards the same direction.

In upcoming posts we will discuss about Expanded Notation in Grade III and online math tutor help. Visit our website for information on CBSE board home science syllabus for class 11