## Linear Function

There are many key features that you will learn during math career. The first and most basic function is a linear function. A linear function is used to describe the relationship of a straight line. This can be any straight line at any angle or any position. The general form of these operations is as follows;

y = m * x + b

Lets take a look at what all these terms mean. It is important to have a thorough understanding of what each of them means in mathematics and understanding.

First off we can bring our two variables in this equation x and y. X is the independent variable and it is represented on the horizontal axis of the graph. Y is the dependent variable (since its value depends on the value of x) and is represented on the vertical axis of the graph.

The letter ‘m’ is the slope. Graphically, this will give you the angle of the line. The higher the slope, the steeper the angle with the x-axis. The slope can be determined which of the two place on the line. You will simply sub force of the equation ;.

m = y2 – y1 / (x2 – x1)

This calculation is usually fairly easy and can be done on a calculator

last term, b, is the intersection of the line . This is the point where the line crosses the y-axis. If you have a graph of the line you can simply read values ​​directly from the graph. If you have the slope, you can prepare in every place on the line, rearrange and solve algebraically for the intersection.

So as you can see is a linear function not very complicated. It is a good place to start when learning about operations.

## Multiplication Table – Vedic mathematics’ Simple Technique Helps to remember it easily

to remember the multiplication table, consider the sum of the multiplicand and multiplier.

Remember the value for the sum of 10 (all other values ​​multiplication table) with basic techniques of Vedic mathematics.

The method we follow here is very simple to understand and easy to follow.

The method is based on “Nikhilam” Sutra of Vedic mathematics.

method will be apparent from the following examples

Example 1: ..

Suppose we have to find a 9 x 6

First write one below the other

9

6

Then we reduce numbers from 10 and write the value (09/10 = 1; 10 -6 = 4) to the desired character with ‘-‘ to between

9 -. 1

6-4

The product has two parts. The first part is Cross difference (here it is 9-4 = 6-1 = 5).

The second part is vertical product the right digits (here: 1 x 4 = 4)

We write parts separated by a slash

9 – .. 1

6-4

—–

5/4

—–

So 9 x 6 = 54

Let us see. one example

Example 2 :.

Suppose we have to find the 8 x 7

First write one below the other

8

7

Then we reduce numbers from 10 and write values ​​(8.10 = 2; 10-7 = 3) to the desired character with ‘-‘ to between

8 -. 2

7-3

The product has two parts. The first part is Cross difference (here it is 8-3 = 7-2 = 5).

The second part is vertical product the right digits (here it is 2 x 3 = 6)

We write parts separated by a slash

8 – .. 2

7-3

—–

5/6

—–

So 8 x 7 = 56

Let us see. one example

Example 3 :.

Suppose we have to find a 9 x 9

First write one below the other

9

9

Then we reduce numbers from 10 and write the value (09/10 = 1; 10-9 = 1) to the desired character with ‘-‘ to between

9 -. 1

7-1

The product has two parts. The first part is Cross difference (here it is 9-1 = 9-1 = 8).

The second part is vertical product the right digits (here it is 1 x 1 = 1)

We write parts separated by a slash

9 – .. 1

9-1

—–

8/1

—–

So 9 x 9 = 81

In the next example, the second part has two numbers

Let’s see how to deal with the issue

Example 4 :. .

To find a 7 x 6

First write one below the other.

7

6

Then we reduce numbers from 10 and write values. (10-7 = 3; 10-6 = 4) to the right of the numbers with a ‘-‘ to between

7-3

6-4

product two parts. The first part is Cross difference (here it is 7-4 = 6-3 = 3).

The second part is vertical product the right digits (here it is 3 x 4 = 12)

We write parts separated by a slash

seven – .. 3

6-4

—–

3/12

—–

Second bit, here are two digits.

of keep the digit unit (2) carry over the number (1) to the left of

seven -. 3

6-4

————–

(3 + 1) / 2 = 4/2

—— ——-

So, the answer will be (3 + 1) / 2 = 4/2

Thus, 7 x 6 = 42.

Example 5 :.

To find the 8 x 3

By following the above procedure, we may write as follows

8-2

3-7

—–

2/14

—–

first part = 8-7 = 3 – 2 = 1

The second part here is 2×7 = 14

It has two digits. of keep the digit unit (4) and carry over the number (1) to the left of

8 -. 2

3-7

————–

(1 + 1) / 4 = 2/4

—– ——–

So, the answer will be (1 + 1) / 4 = 2/4

Thus, 8 x 3 = 24 .

let’s see one last example

Example 6 :.

to find 6 x 5

By following the above procedure, we can write that.

6-4

5-5

—–

1/20

—–

first part = 6-5 = 5-4 = 1

The second part here is 4×5 = 20

It has two digits. of keep the digit unit (0) and carry over the number (2) to the left of

6 -. 4

5-5

————–

(1 + 2) / 0 3/0 =

—– ——–

So, the answer will be (1 + 2) / 0 = 3/0

Thus, 6 x 5 = 30.

Thus, we can come to any value up to 10 x 10

## Hypnotize yourself now – 10 Steps to Hypnotize Yourself Today

I want to show you a very interesting technology to Hypnotize yourself. It is known as the Betty Erickson technique as she devised it to hypnotize yourself. Betty’s husband Milton Erickson is someone I have referred to several times in the work of famous hynotherapist and psychiatrist and someone whose work seems to hypnotize me all the time. This technique to hypnotize yourself is entirely attributed to her.

Hypnotize Yourself Betty Erickson method

This approach to hypnotize yourself is based on the following assumptions and ideologies. But there are a number of countermeasures example of these ideas, they will be of value in understanding and utilizing this method to hypnotize yourself.

We believe our thoughts into pictures, sounds and feelings.

When we think of we would refer to external things we see and interior images we create. This includes a minimum of images (“What is your bedroom like?”), Synthetic images (“What would it look like if it were renewed?”), As well as the actual, real things that we see around us .

When we think of the sound these are things that we hear and internal sound that we create. This includes a minimum of words or sounds (“Think of your favorite pop song”), imagined words or sounds (“Imagine the song is sung by someone else”), and also includes internal dialogue as well as all real, real , live music around us.

Third, what we believe. This can be a real physical sensations or imagined ones. Can you imagine being on the beach and paddling in cold water

Most of us use one of these thinking more than others ?; however, both have to use all three of them. Since this is usually the case, a person who “thinks” in images would not Hypnotize’s best simply by visualizing

attention :.

stereotype of hypnotists holding watches or other fixation devices for customers to stare at are the result of the great misconceptions about hypnosis. I for one have long exile velveteen smoking jacket and my watch chain for more modern methods of hypnotic induction! The experience of hypnosis is usually internal focus to move away from the environment around us and turn our attention inward. This technique to hypnotize yourself to make it even more

Hypnotize Yourself Technique :.

Step 1: Find a comfortable position and get themselves relaxed and settled. Get in position that you will be able to maintain easily for the time you are going to hypnotize yourself. It may sit or lie down, though sitting is recommended to prevent you from falling asleep. Get yourself centered, just looking in front of you and breathing slowly and surely. Let yourself relax

Step 2 :. Think about how long you plan to spend in this situation and make a statement to yourself about things like “I’m going to hypnotize me in 20 minutes …” (or however long you want) You will be delighted to discover how well you “internal clock” can keep track of time for you

Step 3 :. What do you get out of this? Make a statement to yourself about why you want to hypnotize yourself. In this process, you allow your unconscious mind to work on the issues rather than give proposals, (which is another technology) so our purpose statement should reflect that fact. Here’s how I recommend you linked it to yourself “. I’m going to hypnotize me, in order to allow the unconscious my mind to make changes that are appropriate to assist me in _____________”

Filling in the blank with what you want to achieve such as “developing more confidence in social situations.” The actual words are not nearly as important as the fact your statement acknowledges that you are turning this process over the unconscious mind

Step 4 :. Facing front of you, take three, one at a time, you see. Go slowly, pausing for a moment on each. Preferably, they are small things, such as a spot on the wall, door knob, the corner of the picture frame, etc. Some will include the items as they look at them – “I see the hinge on the door frame”

Step 5 :. Now turn your attention to the auditory channel and notice, one by one, three things that you hear. (You will notice that this allows you to incorporate sounds that occur in the environment rather than being distracted by them.)

Step 6: Next, attend to your feelings and take three perception you can find now. Again, go slowly from one to another. It is useful to use sensations that normally are outside of awareness, so that the weight of the glasses, feeling wrist watch phone, the texture of your shirt on the body etc.

Step 7: Continue the process with two images, then two auditories and two kinaesthetics. Then in the same manner, continue (slowly) with one.

You have now completed the “external” part of the process to Hypnotize yourself. Now it’s time to start “internal” part of

Step 8 :. Now close your eyes. Now, bring a picture in your mind. Do not work too hard at this; this is fun, remember? You can construct a picture or simply take what comes. There may be a point of light, it can be a beautiful beach, or it could be a car or apple. I will not scare you with the ideas that randomly pop up in my mind. If something happens to you, just use it. If nothing comes, do not hesitate to put something in your mind

Step 9 :. Pause and let the music come to your awareness or generate one and name it. While this is technically the internal part, if you should hear a sound outside or in a room with you, it’s okay to use it. Remember, the idea is to integrate what you experience rather than being distracted by them. Typically, in the absence of environmental sound; I imagine often hear the cry of Hallelujah from gospel choir; do not ask me why, it just happens in my mind

Step 10 :. Become aware of the feeling and name it. It is preferable to do this internally – use your imagination. (I feel the warmth of the sun on my face) But as the hearing, if you actually have a physical sensation that gets your attention, use it.

repeat the process with two images, then two sounds, then two feelings. Repeat the cycle again with three images, three sounds, and three feelings

Then to complete the process, open your eyes when alloted your time is up -. It is not uncommon to feel a little “spaced out” or wander off somewhat. At first, some people think they have fallen asleep. But in general you will find yourself coming back automatically at the end of the allotted time that you have set before you choose to hypnotize yourself. Trust that you were not sleeping and that your unconscious mind was doing what you asked for it.

Many people do not get all the way through the process. It is perfectly fine. If you should finish before the time is up, just continue with 4 images, sounds, feelings, then 5, and so on. There is a simple way to just get you know how to hypnotize yourself.

## Math Secrets Revealed

There is nothing spectacular about KS1 and KS2 maths. Average child should be able to solve problems from the solutions. However, children are being stopped by even trying … How they have to solve a simple equation (a standard question from the test) if they have never been exposed to that ?!

Two years ago, I asked my son to do some solutions. He was not able to solve a large amount of them, even if they do not result in higher mathematics. He just was not even introduced to this type of questions. If you are expecting 9 years to resolve the issue yourself, you live in a dream land … Basic knowledge needs to be taught to children. They need to get homework every day, they need to practice math. What happened to equal opportunity for all? The children used to be prepared by the schools of their tests, without parents having to worry about it, without additional classes, teaching … what went wrong?

Mathematics nowadays is made up of a complex. I do not think any new routes add / subtract / multiply help but add to the confusion. It was enough to watch TV programs on improving standards of education in secondary schools using three colored cups (use red to stop the teacher when you do not understand something) to start to worry about your child. Who comes up with these ideas? They may work in schools, the elementary schools do not need anything more than more math lessons and parents interested in learning. If teachers do not receive parental support, they will not be able to achieve higher standards. Children need to spend more than 10 minutes to learn or go home. Nowadays pupils are not expected to compete, as it is bad for them, they just have to spend time in school to play most of the day (I’m speaking from experience my children |).

They return home frustrated, they learned nothing and they sit down to do some more math … with me.

I am sorry, but I believe in old-fashioned training and competition. Times board still has to learn by heart if you want to progress in mathematics, there is no way around it. Competition needs to be able to compare results and improve.

Let’s assume, the child is not thinking about GCSE in mathematics. He’s just going to get through the math to keep teachers happy. Then he begins to live his life without having any knowledge of the risk of interest rate, credit cards and loans. Citizen without basic ideas of what life is about. Why do you think we have so much crime? Because young people, frustrated (lack of knowledge), head for easy ways of getting money and goods … stealing, robbery, drugs. Plus the wrong example at home. Or no examples at all.

Schools became a free child-minding places. You copy the child of 9, record 3 and you only have a few hours when you have to spend time to do something for the children. for example, cook or wash their clothes. It’s not that having children is all about.

I do not expect parents to teach mathematics (even in elementary school), but I do not expect children who want to learn, to get an education from the school on the ground allow them to go to any college they want. If the school is unable to provide this education, what is the point of the school?

Even if your child does not plan to go to college, he would still benefit from a good understanding of basic mathematics. So will his secondary.

There is so much easier to blame, if you have a class students, who can follow the lesson … When I whistle blower?

## Teachers – formative – Informal assessment Content students’ knowledge in mathematics

While there may be overlap between some types of formative and summative assessment, and while there are both informal and formal way to assess students in this article, I will first and foremost with suggestions for informal, formative assessment for math class, especially the first of the three categories suggested by Clarke & Wilson

1. mathematics content knowledge of the student.
2. mathematical process of the student, such as reasoning, communication, problem solving, and making connections.
3. mathematical measure of the student, such as attitude, perseverance, trust and cooperation skills.

If you agree with the idea that words are signs for concepts, then you will want to use 1, 2, 3, 4, 5 concept shown below:

Mark expertise words by writing 1, 2, 3, 4, or 5 in front of the word. The numbers signify the following five statements:

1. I’ve never seen the word / phrase.
2. I’ve seen the word / phrase, but I do not know what it means.
3. I know the word / phrase has something to do with …
4. I think I know what it means in mathematics
5. I know the word / phrase in one or more meaning, including the meaning of mathematics.

———— Unit 2: Taking Measures and Equations ————-

• continuous
• opposition
• line
• length of a segment
• Ray
• central angle of a circle
• complementary angle
• vertical angle
• right triangle
• solve equations
• rational number
• square
• odd
• scientific symbols
• endpoint
• midpoint
• angle
• right angle
• acute triangle
• level
• calculated equations
• irrational number
• perfect cube
• absolute value
• part
• congruent part
• vertex angle
• straight angle
• Congruent angles
• obtuse triangle
• solution
• root
• real number
• cube root

I prefer to use this as both informal both before and after meals. At the beginning of a new unit or section (and again at the end), I give students sheet similar to the one shown above, with a vocabulary of terms for the unit reported. [The first time you use this idea, it is necessary to cross the five different stages of word knowledge, but students easily understand the idea that there are words that they have never heard of the words they know in several ways (and everything between these two).] It is important to pronounce the words that students read them and give their own level of knowledge of the word because there are words that students know when they hear but do not recognize when they see them. Then the chemicals expertise, all words that students rated as 4 or 5’s, asking them to write a best understanding of what the word means in mathematics. This is not used in the classroom but, as formative to give an idea of ​​student understanding of concepts before and after teaching unit.

another way to assess students’ content knowledge, gives students a piece of paper with 5 rows and four columns at the beginning of the week. Then, every day, whether students enter the class, or the closing of the day, four issues of the lesson or homework first day is given, and students come every problem (and solution) in four spaces for the day. The teacher can check this quickly or series Series stop them. This may be collected every day or at the end of the week, depending on the program teachers to use information in the evaluation.

The third proposal on the formative content knowledge is performance evaluation. All articles (and books) have been written about the next proposal formative mathematics content knowledge, but even though I can not quite explain it in the context of this article, I would be remiss not to mention the idea of ​​performance evaluation. Evaluation results are assessments “that students demonstrate in various ways their understanding of the subject or topic. These assessments are judged on predetermined criteria” (ASCD, 1996, p. 59). Baron (1990, 1990b and 1991) in Marzano and Kendall (1996) identified a number of characteristics of the project, including the following:

• are based on the real situation
• involve sustained work and often take several days combined in-class and out-of-class time
• deal with big ideas and key concepts within the discipline
• not present routine, open-ended, loosely structured problems that require students both to identify the problem and to build a strategy to solve it
• students need to determine what data are necessary, collect data, report and show them, and report them to the sources error
• necessary for students to use a variety of skills to gain information and communication strategy, data and conclusions (p. 93)

## Perform like math genius!

Are Math Genius?

Have you ever wanted to be a math genius like the television that can give you an answer to 65 square or 97 x 103 faster than you can say for some time? Many wish they could be more confident with math but do not really believe that they can succeed in mathematics, let alone perform as a mathematical genius.

Although there are many out there that are very, very good at math, there is also a ‘mathematical secret’ that many people who seem to like math geniuses use, and I would like to share it with you

secret is simple :. you and most of the people you know that have the ability to perform as a mathematical genius, but you may be lacking some very simple but very powerful ‘mathematical tools’ to people who are smart in math use all the time.

What are mathematical tools? Math tools are just ways of thinking about numbers. For example, did you know that there are actually many different ways to multiply the numbers? Yes there are more methods than just the normal way that most of us were taught in school, and some of these techniques are much more powerful and easier to use.

Do not believe me? It’s okay … it’s good to be skeptical. Let me give you an example of one of these methods.

A mathematical secrets for squaring numbers that end in 5

Suppose I asked you to find the answer to 85 square. It is 85 x 85 … not an easy feat to solve without using a calculator or pencil and paper … or is it? Let’s think about it:

5 x 5 equals 25, right? So we know the answer to 85 square ends in 25. So far so good – now, here comes the fun part

What is the number to the left of 5 !? Easy, it is 8. Add 1 to this number. 8 + 1 is equal to 9. Now take the original 8 and multiply it by 8 + 1. It is just a fancy way to say multiply 8 by 9

8 x 9 equals 72

Now take 72 and put it next to the 25 to get 7225. The answer to the 85 power is 7225 !!

This process works to find the answer to any square number ending in 5 and there are literally dozens of other tricks equally impressive and fun math and secrets to help you perform like a genius. When you know some of these little tricks you will find that even the seemingly formidable mathematical problems can become incredibly easy. Curious to find more tips and tricks for math? Check out this collection of useful tips and tricks => http://www.vancouvertutoringservice.com/mathresources.html

## Why do we have to learn math? Discover 6 good reasons

Students often sit annoying questions of various types of teachers or parents. Often, these questions do not really matter at all, but more of a whining complaint supplied urge to spend time or sidetrack teachers lesson plans. Some of the spontaneous phone, off the cuff, answers can be: “Because I said so,” or; “Since we have a test tomorrow.” These words can slip out of our mouths, even if aware that these responses are inadequate. Sometimes, however, the question is legitimate. A question we may have even asked us every time. “Why do we have to learn math?” Below is a list of 6 good reasons to learn math. You can also project to give students to help them learn the reasons.

1. Simple math concepts build on itself. We need a simple mathematical concepts to work in more advanced mathematical concepts. Even if you get a job working with people, you will probably still need math. Advanced mathematics is needed for near infinite list of many popular activities such as:

• Computer areas
• Finance and banking
• Plumber
• Electrician
• Mechanic
• Sales
• Fashion
• Builder
• (fill in the blank …)

Jobs for unskilled labor are becoming harder and harder to come by. Get a good job with a good salary depends on the specific skills that not everyone can offer. Math is one of those skills. Even if your job involves working mainly with people, it is very likely that you’ll still have to use math. Learn math and get the job of your dreams.

2. Mathematics is needed when you have to decide how to create the best arrangement for furniture, equipment for large groups of people in work or for special occasions at home. Simple math concepts such as multiplying factors and manipulating ratios make it easy to adjust the cooking recipes number of people you want to serve. Learn mathematics and make personal life work better.

3. Mathematics can help you create art. Not only will you want to get the right sizes and colors blends math is used in almost every aspect of art. The main universities offer a category called “Mathematics in art and architecture.” Technologies such as tiling, tessellation, perspective, pattern and symmetry are some of the terms used in the art that require the use of mathematics. Do yourself and your world more beautiful. Learn mathematics.

4. People will often try to make you believe something that is not true and can use mathematics seem to prove what they say. If you know how to check the math, you can steer clear of being a fool. Shady companies use mathematics to lie is the subject of a classic book, “How to lie with statistics” by the author Darrell Huff. Written 50 years ago, most of misleading math tricks described in the book are still in use regularly. Even if someone is not trying to fool you, it is possible that an error was made. For example: A laboratory test can show that a person has a certain disease. If mathematical errors were made in the analysis, the person may not have the disease at all. It is important to be able to understand all the information that comes to you with a claim of “mathematical proof.” Do not be fooled. Learn mathematics.

5. Mathematics is essential in personal financial matters and budgeting. In life, you can use math to plan how to budget your money. In time you may need to plan how the company will spend money. Learn mathematics and grow rich.

6. Learn math and problem solving is a mental exercise that improves overall thinking ability. It’s like exercise for the brain. Want to be better in every way? Learn mathematics.

It should be obvious that there are many more than 6 good reasons to learn math. The next time math student asks, “Why do we have to learn this” do this simple task: “Why should we study mathematics”

Joly Colbert

## What is the Black Swan?

The Black Swan is a concept that you can hear in business and statistics, but what does it actually mean? First, I need to clarify what it is not. It does not just mean rare. Yes, it is a rare event, but something else is required. It is a rare event when an event occurs that was never expected to occur and that would result in a paradigm shift.

To give you an example, it was believed that swans are black could never. The term was thought to be almost like an oxymoron. To refer to something as such would be like referring to waterless flood. While in 1697 Willem de Vlamingh came across like a swan in Western Australia. This led to a paradigm shift; Black Swans present when thought they never could.

Something that would not be a Black Swan event would be to win the national lottery. Yes, it is very rare, but you expect that you could win. And if you win, it’s a nice surprise, but it does not change the way you think about or see lottery. It does not lead to a change in ideology.

What you might have figured out then you can never say something will be Black Swan event or you can see one coming. If you say that something could happen (but is unlikely to) the expression can not be used. It’s just something unlikely, and the fact that you have to consider that it means that it is part of your ideology.

The term is often wrongly used in the business. Recent decline from the sub-prime mortgage crisis was sometimes referred to as Black Swan event. It is not, as the collapse of the credit supply to them not to pay it (and derivative paper products that reduce the value of sub-prime mortgages). This was always the possibility of resulting crash sooner or later; it is part of the traditional economic theory (ideology we call).

Nassim Nicholas Taleb has written an excellent book on this event, and for those who want to understand more they should consider reading it.

## Beautiful Faces – A Historical Perspective of mathematics and beauty

Today, more than any other period in history, it’s overwhelming pre-job with beauty. For centuries, poets and artists have been unsuccessful in creating a consistent definition of “beauty”. There have been many artistic interpretations, but the comparison mathematical definition is not available and necessary.

Historically previous attempts food attractive biological standards have created a good tool, but not good definitions. According to the Pythagoreans in ancient Greece, “Everything is arranged according to the figures.” There was speculation that mathematics unifying force between life, art, God, and the universe. By viewing figures and the Pythagorean theorem, it was thought that perfection, harmony and balance would be revealed.

Leonardo Fibonacci, a mathematician in the 13th century Italy charted population of rabbits and discovered a number series from which the Golden Ratio is derived. The sequence of the series is the sum of the two preceding numbers. The number series begins with a series of “0, 1, 1, 2, 3, 5 …” and continues to infinity. From this series, Golden Ratio is produced by dividing each number in order of the number as before. The ratio continues and eventually converges what is known as Phi (1.618 …), named after Phidias, Greek sculptor.7,8 The mathematical concept of golden ratio has had a major impact on aesthetics because it argues for analysis. It does not, however, provide a definition of facial beauty.

Regardless of age or nationality, it’s all beautiful face, a certain proportion and harmony between the facial part. The proper equilibrium ratio between facial features is very pleasing to the eye. Consider locate brow, eyes, cheeks, nose, lip and chin to face height. According R.M. Ricketts, DDS, the ratio of the distance from the eyes to the nose base, and from the labial commissure to the chin, is 1: 1 in normal face. The ratio of the distance from the nose to the bottom of the labial commissure, and one of either of the two previous distances (0.618 …) This is an example of the golden face relationships. This golden ratio can also be used for analysis of the aesthetic contact face. Stephen Marquardt, DDS, has used the golden ratio to create a pentagram-based surfacing facial features are located, as an analytical tool, according to this ratio.

In today’s world, modern language computerized communication requires repetitive mathematical data. It is important for artists and surgeons to develop a mathematical equation that accurately assesses, defines and compares the face (a) beautiful, (b) attractive, (c) the average, or (d) unattractive.