Assessment Of Math

Definition assessment:

Educational assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs. Assessment can focus on the individual learner, the learning community the institution, or the educational system as a whole. "Studies of a theoretical or empirical nature addressing the assessment of learner aptitude and preparation, motivation and learning styles, learning outcomes in achievement and satisfaction in different educational contexts are all welcome, as are studies addressing issues of measurable standards and benchmarks"

Source: Wikipedia


Teachers need to ask themselves with math assessment:

The following are two very important questions that teachers have to ask when teaching.

Is what I am doing helping children to develop a desire to learn mathematics?

Is what I am doing teaching children to become numerate?


Types of assessment in math:


There are two main ways in which to assess children

Formative assessment in math.

Summative assessment in math.

Formative assessment is assessing a learner while the learner is forming the new knowledge.

Example for formative assessment in math:

An example of formative assessment would be sitting with a learner while he or she is doing a task (say using a number line to count in groups), watching how the child goes about the task and asking the child to explain how and what he or she is doing. In this way, you find out what strategies the child is using and developing and what strategies you should be helping the child with; you are getting direct and instant feedback on hoe the child is coping and you are able to respond to the situation immediately through re-teaching and explaining again, asking anther learner to help, or planning another lesson on that need for the next day.

Summative assessment is assessing a learner at the end of the lesson, section, topic, quarter or year as a summing up of what the learner knows. Therefore, tests and exams are summative versions of assessment.

In math, when both formative and summative assessments are used, that is continuous assessment. In an outcomes-based education system, continuous assessment is used. The teacher studies the learning outcomes required of the learners and then plans lessons to teach to achieve these outcomes. During the lessons, the teacher observers what children are doing and saying and how children are doing a task. The teacher asks for explanations from the children as to what and how they are doing a take. The teacher helps those learners who are confused and continually monitors which learners are gaining control of the skills and concepts. Once a child can do something independently within the number range for that learner, a teacher can say that that child has learnt what was intended by the lesson and so can record that performance as a desired learning outcome for that child

What is Median in Math

Introduction to what is median in math:

Let us see what is median in math. In general, median in math is the middle value in a set of data. Statistically median is defined as a measure of central tendency which gives the value of the middle-most observation in the data. The median in math is obtained by arranging the given list of data in ascending order. Median separates the higher value and lower vale. This article deals with what is median in math and how to find median with examples.


How to find median in math:


To find median initially we have to arrange the data values of the observations in ascending order. Then,

If n = odd {n= number of data} ,

Median = `(n+1)/2` th observation

If n= even,

Median = `(((n/2)th data ) + ((n/2) +1)th data) / 2 ` {which means average of ((n/2) + (n/2)+1)th data }


Example Problems to find median in math:

Example 1:

What is the median of the given observations 50, 125, 10, 210, 50, 24, 175

Solution:

Ascending order of given data,

10,24,50,50,125,175,210

Here the number of observations= n= 7

n= odd,

Median = `(n+1)/2 ` th observation

= `(7+1)/2`

=` 8/2`

= 4th observation

Hence median is 50.

Example 2:

Find the median of the given observations 20, 7, 9, 12, 7, 9, 5,3,15, 15

Solution:

Ascending order of given data,

3, 5, 7, 7, 9,9,12,15,15,20

Here n= 10 (even) ,

Median = `(((n/2)^(th) data) + ((n/2) +1^(th) data)) / 2`



=   ((10/2)th data) + ((10/2)+1) thdata)) / 2

= `(5^(th) data + 6^(th) data) / 2`

= `(9+9 )/ 2`

= `18/2`

= 9

Hence the median is 9.

Example 3:

What is the median of this observation 20, 29, 28, 33, 42, 38, 43, 25?

Solution:

Ascending order of given data,

20, 25, 28, 29, 33, 38, 43, 42.

Number of observation = n= 8

N= even ,

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Median = `(((n/2)th data ) + ((n/2) +1)th data) / 2 `

=((8/2)th data +(8/2)+1 th data )/2

= `(4^(th) data + 5^(th) data) / 2`

= `(29+33)/2`

= 31.

Hence the median is 31.

Example 4:

Find the median of the observation 6 ,28, 24, 15, 2, 4, 1 ,20,5

Solution:

Ascending order of given data,

1,2,4,5, 6, 15,20,24,28

Here the number of observations = 9

n= 9 (odd)

Median =`(n+1)/2` th observation

= `(9+1)/2`

= `10/2`

= 5

Median is the 5th observation.

Hence median = 6.

New Math Division

Introduction for new math division:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) widely used in day to day life. In these articles we are going to see about new math division. Division (÷) can be considered as repeated subtraction or equal distribution.

The following division methods are all based on the form Q = N / D where

• Q = Quotient

• N = Numerator (dividend)

• D = Denominator (divisor).

Specifically, if c time’s b equals a, written: c x b = a, Where b is not zero, then a divided by b equals c, written: a / b = c. In the above expression, a is called the dividend, b the divisor and c the quotient.

(Source: Wikipedia)


New math division and long division definition and steps:


Definition for division:

Division is defined as an arithmetic function, which is the opposed process of multiplication. From the process of division, the proportion or ratio of two numbers be capable of be calculated.

Otherwise, the process of decision how many periods of one number is included in a further one. Symbol of division is ‘/’ or ‘÷’. If we divide a number by another number, then

Dividend = (Divisor * Quotient) + Remainder

Long division:

Division plays a key role in our day to day activities. Long division is one of the usual methods of solving the division problems. Long division is usually studied in elementary classes. In this article, we are going to see about long division with remainders.

Steps for division math facts:

Step1. Division of two integers by the related signs resolve be positive sign

a) Positive ÷ positive = positive

b) Negative ÷ negative = positive

Step2. Division of two integers by the unlike signs will be negative

a) Positive ÷ negative = negative

b) Negative ÷ positive = negative.



Example problem for new math division:


Problem 1: Jack built a tower of blocks forty-nine inches high. Each block in the tower is seven inches tall. How many blocks were used to build the tower?

Solution:

Jack built a tower of blocks forty-nine inches high.

Each block in the tower is seven inches tall.

So, total blocks =   `49 / 7`

Therefore total blocks used to build the tower = 7 blocks

Problem 2: The school's Internet connection transferred thirty eight megabytes of data in two seconds. How many megabytes can it transfer in just one second?

Solution:

The school's Internet connection transferred thirty eight megabytes Data in two seconds.

So, therefore total megabytes can it transfer in just one second

=   `38 / 2`

= 19 megabytes.

Problem 3: There are four soft drink machines in the university. They hold sixty - four cases of soda altogether. How many cases does each machine hold?

Solution:

There are four soft drink machines in the university.

They hold sixty - four cases of soda altogether.

Total cases of soda machine hold =` 64 / 4`

= 16 Cases of soda.

Arithmetic Problem Examples

Introduction to Arithmetic:

Arithmetic is the most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.

- Source: Wikipedia


Example Arithmetic Problems:


Addition:

Arithmetic Problem example 1: In a vegetable basket 18 tomatoes and 17 potatoes. How many total vegetables are there in the vegetable basket?

Solution:

No. of tomatoes in the basket = 18

Number of potatoes in the basket = 17

Total vegetables in the basket = 18 + 17

Total vegetables in the basket = 35 fruits.

Subtraction:

Arithmetic Problem example 2:  There are 67 seats in a compartment. 61 seats were occupied by the passenger. How many seats were not occupied?

Solution:

Total no. of seats in the class = 67

No. of seats occupied by the passengers = 61

No. of seats not occupied = 67 – 61

No. of seats not occupied = 6 seats.

Multiplication:

Arithmetic Problem example 3: A notebook cost 2 dollars. What is the price of 12 notebooks?

Solution:

Price of 1 notebook = 2 dollars

Price of 12 notebooks = 12 x 2

Price of 12 notebooks = 24 dollars.

Division:

Arithmetic Problem example 4:  5 trousers price is 25 dollars. What is the price of 1 trouser?

Solution:

Price of 5 trousers = 25 dollars

Price of 1 trouser = 25 / 5

Price of 1 trouser = 5 dollars.


Practice Problems in Arithmetic Problems:


Addition:

Problem: There are 15 pens in an Office. Davina is going to put 16 of them in the Office. Totally how many pens will be there?

Answer: 31.

Subtraction:

Problem: There are 25 students in a computer science class. 22 students got pass in computer science. How many students failed?

Answer: 3.

Multiplication:

Problem: George delivers 40 letters in a day. How many letters does she deliver in 5 days?

Answer: 200.

Division:

Problem: Thomas has 30 chocolates. If he presents his friends 5 chocolates each, how many friends can he share his chocolates with?

Answer: 6.

Math Definition for Kids

Addition:

Addition means sum of two quantities. The sign used to do addition is ‘+ ‘.

If Joe has 2 black pencil and 3 blue pencil means then the total number of pencil is

2+3 that is 5 pencils.

Subtraction:

Subtraction means difference of two quantities. The sign used to do subtraction is ‘– ‘.

If Kayla has 5 rupees and she spent 2 rupees in a store then the amount she has left in a hand is 5-2 that is 3 rupees.

Division:

Division means sharing a number into equal parts. The sign used to do division is ‘/’.

If a mom has 6 chocolates and then if she wants to give those chocolates to 2 children means, then it is 6/2 that is 3 .So she will give 3 chocolates to each child.

Multiplication:

Multiplication means a number is added to itself a number of times. The sign used to do multiplication is ‘x’ or sometimes ‘*’.

2+2+2=6 which is same as 3 times 2 which is equal to 6


Types of Angles Definition


Acute angle: The angle which is less than 90 degree is an acute angle. For instance, we can say 45 degree is an acute angle.

Right angle: The angle which is equal to 90 degree is right angle.

Obtuse angle: The angle which is greater than 90 degree is an obtuse angle. For instance, we can say 75 degree is an obtuse angle. I have recently faced lot of problem while learning cbse 10th sample papers sa2, But thank to online resources of math which helped me to learn myself easily on net.

Ascending order: Arranging a list of given elements from smallest number to greatest number.

Consider, the given list of numbers are 9,4,8,2 then the ascending order of a given list is

2,4,8,9.

Descending order:

Arranging a list of given elements from greatest number to smallest number.

Consider, the given set of numbers is 9,4,8,2 then the descending order of a given list is 9,8,4,2.

Twice:

Twice means two times.

The twice of 4 is 2 times of 4 that is 8.

Arithmetic Homework

Introduction to arithmetic homework:

Arithmetic  is the fundamental theory in mathematics. It was mostly used to work out mathematical function of addition, subtraction, multiplication and division. It is specially for the mathematical operations. An arithmetic operation is not just deals with integers,it also deals with arithmetical calculation, actual numbers and complex numbers.

Several times Number theory is known as higher arithmetic.
Congruence theory is known as Modular arithmetic.
Arithmetic performed on actual numbers is known as floating point arithmetic.
Let us do some arithmetic homework problems.


Example for Arithmetic homework help:


Addition:

Sum of two or more numbers is called Arithmetic. The addition symbol is + (plus).  We know how to do the addition function for the all kind of values. Addition will increase the values.

Homework Example:

8 + 3 = 11

Subtraction:

Subtraction is also one of the fundamental arithmetic operations. Minimizing two or more numbers is known as Subtraction. The subtraction symbol is – (minus). Subtraction problems reduce the values.

Subtraction can do in the following way,

C = A - B

Where,

C is difference.

A is the minuend value.

B is the subtrahend value.



Homework Example:

5 – 3 = 2

Multiplication:

Multiplication is the range of 2 numbers. X (product) is the symbol for multiplication. Multiplication also performs by recurrence of addition. The term frequently used for multiplication is “times”.

Homework Example:

8 times 2 means 8 multiply with 2.

8 * 2 = 16

The other way of multiplication frequent addition,

7 times 2 = 14

2 + 2 + 2 + 2 +2 + 2 +2 = 14

Rational multiplication:

16 / 4 * 8 / 8 =?

4 * 1 =?

= 4

Division:

Division is same like as multiplication function. But it is the reverse of multiplication. The sign of division is ‘/ ‘(slash). The most important function of division is decreasing the value then it is also repeat subtraction.

Homework Example:

12 / 2 = 6


Arithmetic homework practice problems:


Add:

22 + 61 = 83
58 + 68 = 126
Subtract:

75 – 20 = 55
58 – 10 = 48
Multiply:

4 * 2 = 8
7 * 5 = 35
Divide

25 / 5 = 5
60 / 5 = 12

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Arithmetic homework problems with solution:


Add:

16 + 22 =
29 + 46 =
Subtract:

52 – 48 =
19 – 53  =
Multiply:

8 * 9 =
12 * 5 =
Divide:

68 / 2 =
12 / 4 =
Answers:

Add: 38, 75

Subtract: 4, -34

Multiply: 72, 60

Divide: 34, 3.

Arithmetic Reasoning

Introduction for arithmetic reasoning:

Arithmetic reasoning is a branch of mathematics that deals with the study of number especially with regard to basic operations such as addition, subtraction, multiplication and division etc and applications to solution of problems. Generally, we use arithmetic in our day-to-day life. The literacy rate is calculated by the 3 R’s namely ‘Read’, ‘wRite’ and ‘aRithmetic’. so arithmetic is an important role in our daily life. Arithmetic reasoning example and practice problems are given below. 


Arithmetic reasoning example problems:


1. A Washing machine costs Rs.5, 00,000/–. If the value depreciates 15% the first year, 13½% the next year 12% the third year and so on. What will be its value at the end of 10 years, the entire percentages applying to the original cost?

Sol:  The percentage of depreciation in value in consecutive years form an A.P.
Total depreciation (in %) = 15 + 13½ + 12 + … to 10 terms, Here a = 15, d = – 1.5
Sn = n/2 [ 2a + (n-1)d]

Sn = 10/2 [ 30 - 13.5 ] in % = 82.5%
Value of the machine after 10 years = 100 – 82.5 = 17.5%
Original cost of the machine = Rs.5,00,000
Value of the machine after 10 years = Rs.5,00,000 ×17.5/100 = Rs.87,500

2. Convert the following into percentages
(a) 2/5 (b) 3/4
Sol:
(a) 2/5 =2/5 ×100/100 =40/100 = 40%
(b) 3/4 =3/4 ×100/100 =75/100 = 75%

3. The monthly salary of Rani is Rs. 4000. She spends 80% of her salary every month. How much does she save every month?
Sol:
Rani's monthly salary = Rs. 4000
Expenditure = 80% of 4000
= 80/100 × (4000) = Rs. 3200
Savings = 4000 – 3200 = Rs. 800


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Arithmetic reasoning problems to practice:


1. Gilly deposits Rs. 2000 in a bank. The bank pays interest at the rate of 4% per year. Find the interest received by him at the end of 3 years. Also, find the amount to be paid at the end of 3 years.

Ans: Rs. 2240.

2. In a room there are 25 boys and 15 girls. What is the ratio between boys and girls?

Ans: 5: 3

how to do math arithmatic

Introduction to math arithmetic:

The basic math arithmetic properties are addition, subtraction, multiplication and division. Let discuss about how to do work with these arithmetic properties. In addition the sum of two or more numbers is said to be addition. Subtraction – it is the inverse of the addition. Multiplication is one of the major progresses in the math arithmetic. I like to share this Arithmetic Mean Formula with you all through my article.


math arthmatic addition and subtraction


math arithmatic addition:

The sum of one or more numbers is said to be addition.

For example:

Find the sum of the given values

22, 34

First arrange the numbers in the vertical format, and add the numbers at the right hand side.

22

34

_____

56

______

Another example for math arithmatic addition:

Find the sum of the given values

56, 78, 49, 34, 62.

Write the numbers in the vertical format.

Add the numbers from the right hand side. The remainder is placed in the head of the left side numbers.

(2) Balance

56

78

49

34

62

______

279

______

Subtraction:

Subtraction is the inverse form of the addition.

For example:

Find the difference between 78 and 32

Write the numbers in the vertical format

78

32

____

56

____

Another example for the subtraction:

Find the difference between the decimal values. 56.27 and 34.14.

Write the numbers in the vertical format.

56.27

34.14

_______

22.14

_______

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math arithmetic division and multiplication

Multiplication:

It is used to product of two numbers. It is another fundamental arithmatic operation. It is denoted as `xx` .

Example:

Find the product of the given values.

34 is multiply by 2

34 * 2

_______

68

_______.

Another example for the multiplication.

Find the product of the given values.

If 574 is multiplied by 6.

574 * 6

________

3444

_______



Division:

It is the opposite for multiplication. It is represented as /, `-:`

Example 1:

Find the values using division methods.

42 divided by 2.

21) 42 (2

4

____

02

2

______

0

______

Another example for the division.

The number 345 is divided by 5.

69) 345 (5

30

_____

45

45

______

0

_______

Calculating Half Life

Introduction to Original half life :-

The formula for Exponential decay is N = N0eKt

N0 is the initial population and the decay rate  is k

N is the final population after the time t with the decay rate k.

Half- Life :-

In half life `N = N_0/2 `

Plug in the the value of  N as `N_0/2` in the initial equation we get .

`N_0/2``=N_0 e^(kt)`

Now canceling N_0 in both side and solving we get .

`1/2 = e^(kt)`

`2^-1 = e^(kt)`

Take ln on both sides of above equation we get

` ln (2^-1) = ln (e^(kt))`

Solving it we get

-1 ln(2) = kt.

Solving for t we get

` t = -ln2/k`

Half life time ` (t) = -ln(2)/k`

Now lets  see some solved problems in the topic origianl half life.


Original Half Life Solved Example Problem

The original half-life of an plutonium particle is 18,000 years. If 30 gram are present now, find how long it will take until only 20% of the original atomic particle remains.

Solution To Half life Day One Solved Example Probblem 1:-

The half period time is 18,000 years.

The initial amount is 30 gram..

We need to find the time it will take to make the 20% of original plutonium particle.

First we need to find the decay constant k.

The formula used for decay constant is

Plug in the values in the formula we get.

`18, 000 = - ln (2)/ k`

Now arraigning the above expression to find the value k we get

`k = - ln (2)/ (18,000)`

The value of ln(2) is 0.6931.

`= -0.6931 /( 18,000)`

`(-0.6931) / (18 000) = -0.0000385`

Therefore the value of decay constant is -0.0000385.

Now we have to find the time when there will be only 20% of atomic particle remains.

`6 = 30 xx e^(-0.0000385 t)`

Now divide by 30 on both side of the above expression.

`6/ 30 = (30 xx e^(-0.0000385 t))/ 30`

`0.2 = e^(0.0000385 t)`

Taking ln on both side of the above expression we get

`ln (0.2) = ln (e^(-0.0000385 t))`

`ln (e^(-0.0000385 t))` can be written as `-0.0000385 t.`

`ln(0.2) = -0.0000385 t..`

Now divide by `- 0.0000385` on both side of the above expression we get .

`ln(0.1)/ -0.0000385 = (-0.0000385 t)/ -0.0000385.`

By solving the above expression we get

`ln(0.2)/ -0.0000385 = t`

By solving the above fraction we get

41,803 = t

20 percent of  30 gram plutonium particle remains after 41,803 years.

Original Half Life Practice Problem

The half-life of an Barium particle is 16,000 years. If 40 gram are present now, find how long it will take until only 10% of the original atomic particle remains.

Answer:-

10 percent of  40 gram plutonium particle remains  after 40,859 years.

Definition of Scale in Math

Introduction to definition of scale in math:

In math a drawing that displays a real thing with accurate sizes without they have all been strong or distended by a exacting amount called as scale.

In math the definition of scale is showing as the length of the drawing, next that a colon (":"), and then the identical length on the real thing. Let, we learn about the how to do scale drawing ratio. This article shows the clear definition of the scale and  the how to perform the scale drawing  ratio with its examples.

Definition of Scale Drawing Ratio in Math:
In real situation, the length of the van is assumed as 300 inches. But, the length of a copy or print paper that you could use to outline this van is a little bit lower than 12 inches.

As 300/10 = 25, you will require about 25 sheets of copy sheet to formulate the length of the original size of the van.

In order to expand just one paper, you could then use 1 inch on your draft to specify 25 inches on the real-life things.

Therefore, we can write this as in ratio form of 1:25 or 1/25 or 1 to 25. Is this topic Division Operations hard for you? Watch out for my coming posts.

Examples of Definition of Scale in Math:

Example 1: The distance amid two towns measures 9cm on a map. What is the true distance if the scale is 1 : 40 000

Solution:

The True Distance = 9cm x 40 000

= 3600 00cm

We can shorten this by dividing the 360000 by 100 which gives us 3600m

and by again dividing the 3600m by 1000 we can simplify this to 3.6km

So the True Distance amid the two towns is 3.6km.

Example 2: The drawing of an Aircraft uses a scale of 1 : 5000 and if the aircrafts wingspan is 100m what length on the drawing actually refers this?

Solution:

Drawing Length = 100m ÷ 5000

= 0.02 m ( to change 0.02 to mm X 1000)

= 20mm

Therefore, the length on the drawing that refers the wingspan is 20 mm.