Paired numbers

In this section, we will talk about Numbers and paired numbers for grade III. Numbers are fundamentals of mathematics. Numbers can be  integers (play subtracting integers worksheet here), rational, real etc.

When we talk about paired numbers it means we are talking about the patterns in them. Patterns are everywhere around us including sitting arrangement in the class. Your teacher always wants you to sit in proper arrangement in class.

By means of pattern we mean a certain rule is applied to some set of numbers and whenever we perform the reverse operation we get the numbers back and also when we apply the same operation on the result, numbers increase or decrease in same format. Improve your skills on converting of fractions to decimals

Let's take the simplest example to understand the pattern first.

Example:

1 + 2 = 3.

3 + 2 = 5

5 + 2 = 7

In the example above we apply the addition of 2. When we add 2 in 1 we gets 3 and applying the same operation (+ 2) in 3 we gets 5 same to get 7. It is clear that each number is two more than the previous. If someone ask us what would be the next number we can reply to this in no time, that the answer would be 9 (i.e. 7 + 2). We can say these numbers, that is 3, 5, 7, 9 are paired numbers.

As a grade III student you must be aware of 2's table. It also follows the pattern.

2 * 1 = 2

2 * 2 = 4

2 * 3 = 6 and so on upto

2 * 10 = 20

Now, let's discuss some real life numbers patterns. How many legs do dogs have? The answer is 4. So,

1 dog has 4 legs.

2 dogs have 8 legs (number of legs * no of dogs. That is 4 * 2)

3 dogs have 12 legs (4 * 3)

Now we have one more real life example:

Weeks and days also follow a pattern.

7 Days make a week. So,

1 week has 7 days

2 weeks have 14 days (number of weeks * 7, number of days in a week)

3 weeks have 21 days.

Now let's make those patterns bit tough.

Suppose your mom has a chart of your favorite cartoon stickers. She asked you 50 questions and for every 5 correct answers she promised you to give 3 stickers. How many stickers you get if you managed to give only 30 correct answers?

Solution: First we make a pattern for this problem.

For every 5 correct answers you get 3 stickers. For 10 correct answers you get 6. Similarly 9 stickers for 15 correct answers, and so on.

For 20 you get 12

For 25 you get 15

And for 30 you get 18.

So answer is 18 cartoon stickers for the 30 correct answers out of 50.

This is all about the paired numbers and their examples.

In upcoming posts we will discuss about Unit fractions in Grade III and Possible combinations. Visit our website for information on CBSE board physics syllabus

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.

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.

Number Sequence in Third Grade

Hello my dear friends, today we will learn the basic concepts of mathematics that we study in the primary class i.e. Third grade. Students in this class are very small and in this they don’t implement any concepts, but simply learn the concepts. Let’s start with the basic of mathematics and basic of Grade III. Numbers. What you understand by numbers. Numbers are the starting of mathematics that moves through the mathematics. Numbers are the mathematical object used for the purpose of count and measure. In math, the definition of number has been extended over the years and years. In mathematics numbers are of several types like zero, negative, rational, irrational (see irrational numbers examples here), and complex. Also try to know what are prime numbers?

In grade III kids learn the simple numbers like, 1,2,4,100… and with this they  learn how to write these numbers in the word form. Like mathematical 1 is written as one. In the same way 2 is written as two and 14 is written as fourteen. Writing numbers in word form is simple 1 to 10 numbers are so easy to write as one, two, three, four, five, six, seven, eight, nine and ten. In the double digit number like 11, 21, 31, 41 they all are written as eleven, twenty one, thirty one, forty one and so on. The numbers with one’s are written as shown above. And the number having zeros in last place are written as 30- thirty, ‘ty’ is the main thing that we use at the end of numbers with zero. 20 is written as twenty, 30 thirty, 40 is forty and so on.. This is applicable for 2 digits number only.

The method of expressing the other number is same like if we have 20- twenty then we can write the other number of after 20 and up to 29 as twenty one, twenty two, twenty three….twenty nine. In the same way we produce for 30 to 39 and so on. After, the initial number start putting numbers from 1 to nine as it is. The first three digit number i.e. 100 is written as hundred and after this again the same process starts like 101 hundred one, 102 hundred two and so on up to 999.

In the Grade IV students learn the concept of numbers in more depth and remaining things. Now, move to the other concepts related to numbers that students study in the same Grade i.e. Grade III. Even and odd numbers, even numbers are those numbers which are exactly divisible by two. The numbers that come in table of two are even numbers. And one important thing is that all even numbers end with zero, two, four, six and eight. Let’s see few examples of Even numbers. 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30, 32,34, 36, 38 an so on.
These numbers are even as they are containing 2,4,6,8, and 0 at the end.
Now, the other type of numbers i.e. odd numbers.  Odd numbers are those numbers that are not exactly divisible by two. Odd number includes, 1,3,5,7,11,13,15, and so on.

Now, a question for you is 27 an odd number or even?  Yes, it is an odd number as it is not fulfilling any condition of even number. Now, here is other example, 51, 76, 89, 64, 65, 98. Find the even numbers out of the given series?

Answer: in the above question, we have 76, 64 and 98 as the even number. Because 76 contain 6 in last place, 64 have 4 and 98 is having 8 in the last place. And in the above section we have described that number ending with 2,4,6,8 and zero are even number. In the number system of the Grade III kids, also learn the skipping count puzzles. In skipping count puzzle students learn how to skip the same number in any sequence of number. Suppose we have 4,6,8,10 then what is the difference in them or we can say they are skipping by which number. In this series we are skipping two in between all the numbers of the series. Let’s see the other example of the skipping counting, 3,6,9,12,15... In this we are skipping three numbers at a time.

With the numeric value students of Grade III also learn word problems related to skip counting. Let’s have an example of this like John began at 68, he skip-counted until he reached 93. Could he have been counting by fours?
Answer: we know that John started 68 and skip- counted until he got to 93. We want to find out if he could have been counting by fours. Start counting like John, and on doing so we get, 68 +4 = 72 then again add 4 in 72,
72 + 4 = 76,
76 + 4 = 80,
80 + 4 = 84.
84 + 4 = 88,
88 + 4= 92,
92+ 4 = 96.
Thus the answer of the question is no. as if he proceeds like this then he will reach to 92 or 96 but not on 93.

Let’s have one more word problem of the skip counting to understand its concept properly so that my dear kids don’t get any problem in future and can easily solve the entire question related to skip counting.

Question: Alien start counting at 50 and finish when she reached to 80 what are the numbers that she go through while she was counting until she reached to 80 when she is counting by skipping 2.
Answer: let’s start with 50 and add 2 to each term every time so until we reach 80 so that we can easily find the total number of steps evolved to reach 80,
50+2 = 52,
52 +2= 54,
54 + 2 = 56,
56 + 2= 58,
58 +2 = 60,
60 +2 = 62,
62 + 2 = 64,
64 + 2 = 66,
66+ 2= 68,
68 +2 =70,
70+ 2 =72,
72 +2 =74,
74 +2 = 76,
76 + 2 = 78,
78 + 2 =80.
Thus, we can say that total step used to reach to 80 from 50 is 15. In this way students can learn how to skip the numbers and reach to other number.

In the above example I explained you the skip count in increment way in the same way we can skip in numbers in the reversed way. In this we are performing addition in the reverse we perform subtraction and do the work in the reverse way.  Let’s see one example to see the skip numbers in reverse way.

Question: Jas start counting in reverse way and from 33 and end with she reach to 6 then calculate the number of steps and the term that she skipped.
Answer, in this she is coming from higher to lower so we start subtracting the number, 3.
33- 3= 30,
30 – 3, 27,
27 – 3 = 24,
24- 3= 21,
21- 3 = 18,
18 – 3 = 15,
15 – 3 = 12,
12 – 3 = 9,
9 – 3 = 6.

In this we move 9 steps back to reach the level of 6 from 30 and in each step we have to subtract 3. In this students learn how to skip the numbers and with this they learn addition and subtraction easily. Skip count is something like game which is not so hectic and hard to learn. Students easily learn addition and subtraction with its help.

With this kids also learn number sequence in this class III. Number sequence is very simple concept as in this kids only learn how to determine the number which is missing in any sequence, which is very simple to adding or subtracting a number. Suppose we have a sequence as: 4, 14,_, 34, 44. in this we have to determine the number in the blank space? For doing such we see the difference between the other numbers like difference between 4 and 14,
14-4 = 10,
In the same way we find difference between 44 and 34,
44 – 34 = 10,
The difference between all the numbers is 10 so , add 10 in 14 and we get the number of blank place,
14 + 10 = 24,
To cross check the answer you can now subtract 34 from 24 and if difference is same as others then answer is right,
34 -24 = 10,
So the answer is correct.
Let’s have one more example of this so that you can understand the problem and its concept properly.
Question: 5, 10, 15, _, 25, 30, _?
In this question use the same method that we have used in the previous question if we subtract 10 from 5,
10- 5 = 5,
In the same way on doing this operation with other numbers we get 5, so add 5 to 15 and then to 30 and we get the missing numbers.
15 + 5 = 20,
30 + 5 = 35.
In this way you can easily determine the numbers which are missing in the sequence. For more help, take online help and enjoy math.

In upcoming posts we will discuss about Problems related to Angles in Grade III and math help online blog. Visit our website for information on ICSE syllabus for business studies