Powers and repeated multiplication in Grade V

Children we have already studied about the concept of how to solve a rational number, Now we will talk about repeated multiplications of any number and math question related to it.
Let us say 2 * 2 * 2. Here we observe that number 2 is multiplied 3 times.
So this expression can be written as 2 > 3. We call it 2 raised to the power 3. This method of multiplication is called the concept of powers and repeated multiplication and comes under CBSE Board Syllabus.
Suppose we need to find the value of x>n, it means x is to be multiplied n number of times.
So if we write 2> 2 = 2 * 2 = 4
            similarly 3> 2 = 3 * 3 = 9
                          4 > 2  = 4 * 4 = 16
 and if we write 3 > 4 , we call it 3 raised to the power 4
                               = 3 * 3 * 3 * 3
                               = 81
We should also remember while solving powers that any number raised to the power zero is always 1.
so 4> 0 = 1
      5> 0 = 1
and 0 raise to any number is always zero. i.e. 0 > 3 = 0 *0 *0 = 0
Now solve 3 >0  + 2> 0
        As we know  that   any number raised to the power zero is always  1,
so  3 > 0 = 1 and 2 > 0 = 1
Putting these values in the given problem we get
             3 >0  + 2> 0  = 1 + 1 = 2 Ans.
 Similarly solve: 4> 0 * 2 > 0
             As we know  that any number raised to the power zero is always 1,
so  4 > 0 = 1 and 2 > 0 = 1

Putting these values in the given problem we get
             4 >0   *  2> 0  = 1 *  1 = 1 Ans.
This is all about the Powers and repeated multiplication and if anyone want to know about Sampling errors then they can refer to Internet and text books for understanding it more precisely.Read more maths topics of different grades such as Decimals and Place Values in the next session here. 

Direct, Indirect, Standard, and Non-standard Units

Hello friends,Previously we have discussed about antiderivative of fractions and in today's session we all are going to discuss about one of the most interesting topic of mathematics, standard and non-standard units of measurement and how we measure these units in direct/indirect manner in our everyday life which comes under central board of secondary education books.
First of all we will discuss what is standard units of measurements and how to solve math word problems related to it?
We deal with many measurement issues in our day-to-day life like somebody asks us about our weight and height then we answer directly that my weight is 30 kg and my height is around 4 feet . Why we give our answer in kilogram and feet because kilogram is standard unit of mass  and feet is the standard unit to measure height. So, we can say that standard units are those units which are generally used in our everyday life. Some of the important standard units of measurement are as follows
length = meter (m)
weight = kilogram(kg)
Volume = liter (ltr)
Time = second(sec)
Height = feet(ft)
Now further we discuss what is non standard unit of measurement?
Non standard units are those units which are not generally used in our daily life like
antique, ancient, archaic units like fathoms, acres, cubits, miles, stones, hundredweights, pounds, pecks, bushels, gills, pints, quarts, gallons .
Actually standard and non -standard units of measurement are related to each other like length conversion of units
1 myriameter = 10 kilometer
1 kilometer = 10 hectometer
1 hectometer = 10 decameter
1 decameter = 10 meter
1 meter = 10 decimeter
1 decimeter = 10 centimeter
1 centimeter = 10 millimeter
1 foot = 12 inch
1 inch = 1000 mils
and next chart describes conversion of units in weight
1 metric ton = 1000 kilogram
1 short ton = 2000 pounds
1 stone = 14 pounds
1 kilogram = 2.2 pounds
1 kilogram = 1000 grams
These are some conversion charts which tells us about connection between standard and non - standard units of measurement.
Now we are going to discuss our next topic direct/indirect measurement of units
When we do measurement of unit with help of measurement devices like thermometer for measuring temperature, scale to measuring length and weight machine to measure weight then this type of measurement is called as a direct measurement of unit like we measure marble with the help of our measurement machine and we get measurement result like weight of marble is 5kg , length is 20 meter and height is 2 feet.
When direct measurement is not possible then we use indirect measurement, where Indirect measurement is a technique that uses proportions between similar figures to find a measurement, like we have two similar figures of tree, one is big tree and other tree is small and we have to find out height of tree, then here we use proportional technique between both similar tree figure to measure the height of big tree.

3/h = 6/24 write a proportion
6h = 3*24 find cross products
6h = 72 solve equation
h = 12
So the tree is 12 ft tall.
This example shows how indirect measurement is done with the help of proportions. This is all about direct / indirect measurement of units.
So in this session we learn about standard, non-standard units of measurement and direct and indirect measurement of units. I hope you learn many things about measurement of units from this session and if anyone want to know about equally likely events then they can refer to Internet and text books for understanding it more precisely.Read more maths topics of different grades such as Problems on sum of angles for Grade V in the next session here.

Unit Conversion and Measurement in Grade V

Hi friends, Previously we have discussed about number sense worksheets and today's session is here for measurement and unit conversion in grade V from Maharashtra Board Syllabus. While studying measurement, we simply talk about some standard measuring units and will know how to solve math questions based on it. In earlier times people used to measure the length with palms, feet. but the problem faced were that the palms and the feet of the kids varied from that of adults.
Let us imagine a situation, a man asked his son to bring the rope of length of 10 palms from the market. when he returned back with the rope, father took the rope and measured it. father got annoyed, did you know why? Yes, the rope he received was only 6 palms long. No children, it was not the fault of the son, but simply the difference that existed as the measure of the palm of the son and his father was different.
To overcome such problems of measurements, the standard units of measurements were developed. To do any of the mathematical calculations on the objects, it must be remembered that the units are same. It means that addition, subtraction, multiplication, and division can be done on the lengths only if they are having same units.
If the units are not same we convert one unit to another. This process of converting one unit to another is called Unit conversion. Unit conversion is very important role in mathematics. The standard unit of measurement is as follows (want to Learn more about Unit Conversion,click here),
For length we use Meter
For weight we use Kilograms
For  capacity we use Liter
The hierarchy of units are as follows:
Milli
Centi
Deci
UNIT
Deca
Hecto
Kilo
The upper one i.e. milli is the smallest and the last appearing unit i.e. kilo is the largest one. When we have to convert smaller unit to the bigger unit, we do division and when we have to convert the bigger unit to smaller unit, we do multiplication. Let us understand it more clearly by an example:
To change 24 millimeter to centimeter we divide 24 by 10
   = 24/ 10 cm
= 2.4 cm
Similarly  to convert 125 millimeter to decimeter we divide 125 by 100
 = 125 / 100 decimeter
= 1.25 decimeter
In the same way to change centimeter to millimeter  we multiply by 10
 Convert 23 cm to mm
= 23 * 10 mm
= 230 mm
To convert kilometer to hectometer, we multiply by 10
 Convert 12 km to hectometer
 = 12 * 10
= 120 hectometer
Convert 12 km to decameter, we multiply by 100
= 12 * 100 decameter
= 1200 decameter
Convert 12 km to meter, we multiply by 1000
 = 12 * 1000 = 12000 meters
Now we take an example
Say  we have to add 5 Km and 25 meters/ As the units are not same, they cannot be added. So we either convert 5 km to meters  or 25 meters to km so that the units become same and the mathematical operation can take place.
So 25 m = 25 / 1000 km
   = 0.025 km
Now we write add 5 km and 0.025 km
= (5 + 0.025) km
= 5.025 km
In the same way by bringing the units same, we can do any mathematical operation on them.
So this is a brief article about unit conversion and measurement in grade V. If you have any problem in solving unit problems,Steps in problem solving and Problem solving strategies then you can take help of online calculators.

Estimates of Measurements in Grade V

Hello Friends, in day-to-day life we deal with many measurement issues like somebody ask us about our weight and height and if you don’t  know about measurement of height and weight, then you don’t have answer. So it is required to know how we estimate measurement. So, in  today's session we all are going to discuss about one of the most interesting topic of grade V mathematics of tamilnadu education board, Estimates of measurements which is quite similar to the topic analytical geometry problems. 
First of all we discuss what is measurement.
Measurement is the process which is used to determine physical quantity in length, time, temperature etc. to standard unit of measurement like  length in meter, time in second or temperature in degree Celsius,You can also get math help online about  this topic.
Now further we discuss how we measure units of measurements.
Here we discuss measurement of five major units

• measurement of length : Basically measurement of length is done in meter and we have to know all basic conversions about length like  kilometer to meter, meter to centimeter etc. So I will show you a chart which shows how length conversion is done (want to Learn more about Measurements ,click here),

     1 myriameter = 10 kilometer
     1 kilometer = 10 hectometer
     1 hectometer = 10 decameter
     1 decameter = 10 meter
     1 meter = 10 decimeter
     1 decimeter = 10 centimeter
     1 centimeter = 10 millimeter
     1 foot = 12 inches
     1 inch = 1000 mils
If you know all these conversions about length then you can easily measure physical quantity in length term.

• measurement of weight : We generally measure weight in kilogram, but if we want to measure weight in grams and pounds , we have to  know all conversions about weight. I will show you a chart which shows all conversions about weight

     1 metric ton = 1000 kilograms
     1 short ton = 2000 pounds
     1 stone = 14 pounds
     1 kilogram = 2.20 pounds
     1 pound = 16 ounces
     1 kilogram = 1000 grams
With the help of this chart, we can easily measure weight.

• measurement of volume: We can generally measure volume in liter and we can also measure volume in other units of liter. We have to know all  conversions about volume and following chart makes it easier to do these these things.

1 liter = 1.057 quarts

1 milliliter = .001 liter

1 cup = 236.6 milliliter

1 ounces = 29.57 milliliter

With the help of this chart, we can easily measure volume.

• measurement of time : Basically we measure time in seconds, but if we want to measure time in millisecond or microsecond, then we have to know all things about time conversion and following chart shows all conversions about time

1 day  = 24 hours 

1 hour = 60 minutes

1 minute = 60 seconds

1 millisecond = .001second

1 microsecond = .000001 second

This chart teaches us how we measure time.

• measurement of temperature : Basically we measure temperature in Kelvin, but if we want to measure temperature in Celsius or other unit of  temperature, then we have to know all things about temperature conversion and following chart shows us how we do conversions of  temperature by using formulas

To convert celsius to kelvin : k= 273+c

To convert celsius to farenheit : 9/5C = F-32

To convert Farenheit to rankins : R = F+459.5

To convert Rankins to Kelvin : 9k = 5R

This chart teaches us how we convert temperature from Kelvin to degree Celsius and degree Celsius to Fahrenheit etc.

This is all about measurement of units and in this session we almost cover full concept of grade V mathematics topic Estimates of measurements. I hope you learn and use concept in your real life and If you want to know about Collect/organize/graph data then you can refer Internet.

Polygons in Grade V

Hello friends we are back again with another Geometry topic. Today we will have a look on Polygons, Triangles, and Quadrilaterals in grade V. We will learn what Polygons, Triangles and Quadrilaterals are their properties and types.
So let’s start with Quadrilaterals first. (also try quadratic formula calculator)
Quadrilateral is the combination of two words: quad means four and lateral means side. So Quadrilateral means four sides.
A Quadrilateral is the four straight sides, 2 dimensional closed shape.

Properties of Quadrilaterals:

• Has four sides or edges.
• Has four vertices.
• Interior angles has sum of 360 degrees.

Example:

         

The above shape is a quadrilateral and sum of angles are:
            118+94+80+68=360

Types of Quadrilaterals:
Rectangle has four sides and opposite sides are equal in length with every angle is right angle.


Parallelogram has parallel opposite side and are equal in length. Opposite angles are equal.

Rhombus: All sides are equal in length. Opposite sides and angles are equal. Diagonal of rhombus intersects each other at right angle.



Square: All sides are equal in length and all angles are equal 90 degree each. Opposite sides are parallel.



Trapezium has one pair of opposite side parallel and non parallel sides and base angles are equal.


Kite has two pair of side. Adjacent sides are equal in length. One pair of opposite angles is equal. Diagonal intersect at right angle.



Polygons: It is a Greek word where Poly means “many” and Gon means “angles”.  Polygons are 2 dimensional closed shapes with three or more sides. All sides are straight. Polygons names are based on sides and angles they have.

Now let us discuss about types of polygons.
Simple and Complex
Simple polygons has only one boundary and does not intersect itself whereas complex intersect itself.


Concave and Convex:
                                    Convex has no internal angle more than 180 degree and if there is any internal angles greater than 180 degree than its is called Concave.

Regular and Irregular:
                                    If a polygon has all sides and all angles equal than it is regular. otherwise irregular.


Types of polygons based on the sides:
Triangle has 3 sides and internal angle sum of 180.


Quadrilateral has 4 sides.


Pentagon has 5 sides.

Hexagon has 6 sides.



Triangle: As we have seen above a triangle is simple polygon with 3 sides and 3 angles.
The sum of internal angle is 180 degree.

Triangles are classified on the basis of their sides and angles.

Classification based on sides:
Scalene has no equal sides and no equal angles.


Equilateral has three equal sides and equal angles of 60 degree each.


Isosceles has 2 equal sides and two equal angles.


Classification based on angles:

Right Angle triangle has one angle of 90 degree and the side opposite to right angle is called hypotenuse. This is the longest side of the right angle triangle.



Acute angle triangle has all angles less than 90 degree. That is all angle are acute.



Obtuse angle triangle has a one angle greater than 90 degree. That is one angle is obtuse.

           
Now you all are familiar with the Polygons, Triangles, and Quadrilaterals and types of Polygons, Triangles, and Quadrilaterals. Just spend some time with concentration and you can easily identify and differentiate them.

In next post we will talk on Estimates of Measurements in Grade V. For more information on syllabus of economics for ICSE class 12, you can visit our website

Measurement in Grade V

Hello friends, how are you all today? Previously we have discussed about properties of rational numbers ,Are you ready for today’s session?
Our today’s topic is an interesting topic of mathematics. Measurement is the topic what we are going to read. In measurement we include Types of Measurements,help with math measurements, Measurement Problems in grade V of andhra pradesh board of secondary education. So students let's start now.
Measurement is the process of calculating or determining result of quantities. When I was a kid and my teacher asked me first what you know about measurement. I always found difficulty to answer back. Let me tell you a fact that you also deal with measurement daily but the thing is that you are not aware of it.
When you said to one of your friend that you are taller than him and he claims the same than you both stood stand by each other or use a tape to determine who is taller.
That means you are calculating your height or we can say it as you are measuring your height.
We use some units to compute them. Like in our example the unit of height is inches or feet. Likewise unit of mass for example our weight is measured in kilograms. And time, you all are familiar with the unit of time. What it is? It is seconds, minutes or hours.
Now after knowing measurement we will move on to the types of measurements their units and measurement problems. In measurement problems we learn how to convert one unit into other.(want to Learn more about Measurement ,click here),

Let us discuss about mass measurement. Mass is the amount of material in an object that are not effected by        the environment.
Based on the International System (SI) the unit of mass is Kilogram often denoted as kg.
We have seven base measurements and kg is one of them.

Different units of mass and their conversion:

10 milligrams	=	1 centigram
10 centigrams	=	1 decigram
10 decigrams	=	1 gram
10 grams	=	1 dekagram
10 dekagrams	=	1 hectograms
10 hectograms	=	1 kilogram
1,000 kilograms	=	1 metric ton

We generally say weight in place of mass. But weight and mass are two different quantities.
Mass is a measure that how much material some object can contain whereas  weight is the measure that how strongly gravity pulls some object.

Now we will go through time measurement:
To determine time we need some measurement unit. Based on the International System (SI) the unit of time is minutes. We also have second and hour etc to describe time.

Different units of time and their conversion:

1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours
1 week = 7 days
1 year = 365 days

Now I will tell you about volume measurement. Volume is the measure to compute the capacity of the object.
For example: How much a water bottle can contain is the capacity of that bottle.
Unit of volume is liter we often use lt instead of liter. Except liter we also have milliliter, centiliter etc units to measure volume.

Different units of volume and their conversion
1 milliliter = 0.001 liter
1 centiliter = 0.01 liter
1 deciliter = 0.1 liter
1 kiloliter = 1000 liters

We can also simplify this table as:
1000 milliliter = 1 liter
100 centiliter = 1 liter
10 deciliter = 1 liter

These all are some measurements, their types, and some measurement problems. Do refer some exercises on measurement and get perfect and if anyone want to know about Measures of central tendency/dispersion
then they can refer to internet and text books for understanding it more precisely. Read more maths topics of different grades such as Mean and median in Maths in the next session here.

Whole Numbers and Place Value in Grade V

Hello friends,Previously we have discussed about probability worksheets and  today we are going to discuss one of the important topics of math grade V of cbse syllabus which is whole numbers and place value. Whole numbers are the set of familiar numbers (0, 1, 2, 3, 4, and so on). When they are called counting numbers, zero is not included. The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included) and they plays an important role to solve math problems.
The numbers 0, 1, 2, 3, ... etc.

There is no or decimal part and no negatives. We will begin our review of place values with a look at whole numbers. When writing large numbers it is a common practice to separate them into groups of three using commas as the separator. When separating into groups of three, start from the right and count toward the left.
Example: 3, 79 and 980 are all whole numbers.
Place value is the value of a digit as determined by its position in a number. The name of the place or location of a digit in a number. The ability to understand place values is an important mathematics skill measured in the Early Childhood Longitudinal Study. More specifically, students should be able to identify place values in integers to the hundreds place to achieve this skill. Simply the Place Value is the position of a digit in a number written in standard form determines the actual value the digit represents.This table shows the place value for various position (want to Learn more about Whole Numbers ,click here),

Place (underlined)	Name of Position
1 000	Ones (units) position
1 000	Tens
1 000	Hundreds
1 000	Thousands
1 000 000	Ten thousands
1 000 000	Hundred Thousands
1 000 000	Millions
1 000 000 000	Ten Millions
1 000 000 000	Hundred millions
1 000 000 000	Billions

We will take some examples for explanation.
Example:
The number 521092 has a 5 in the hundred thousands place, a 2 in the ten thousands place, 1 in the thousands place, 0 in the hundredths place, 9 in the tens place, and a 2 in ones place.
Example:
Four billion, sixty million, six hundred twenty thousand
4,060,620,000
And another example
9,568,125
Numbers, such as 9,568,125 have seven digits.  Each digit has a different place value.
The first digit is called the millions' place value. There are nine millions in the number 9,568,125
The second digit tells you how many sets of one hundred thousand are in the number.  The number 9,568,125 has five hundred thousand.
The third digit is the ten thousands' place. There are six ten thousands in addition to the nine millions and five hundred thousand.
The fourth digit is the one thousands' place which is eight in this example.
The fifth digit is the hundreds' place which is one in the number 9,568,125.
The next digit two is the tens' place.
The last or right digit is the ones' place which is five in this example.
Therefore, there are nine sets of 1,000,000, five sets of 100,000, six sets of 10,000, eight sets of 1000, one sets of 100, two sets of 10, and 5 ones in the number 9,568,125.

Example :In the numeral 7,015,384, what digit is in the...
  Ques                                                           Answer
a) Ones place ?                                                   4
b) ten thousands place ?                                     1
c) tens place ?                                                     8
d) millions place ?                                               7
e) hundreds place ?                                            3
f) hundred thousands place ?                             0
g) thousands place ?                                           5
So here we end with whole numbers and place value. I hope that this article will help you in solving problems related to whole numbers and place value and if anyone wants to know about Number systems in Grade V and Percentages in Grade VI then they can refer Internet.