Probability Survey

Author: nitin.p070

The probability survey is the way of expressing an event that will occur. The probability survey is the event, the experiments that are repeatedly done under some predefined conditions. The results for one or more experiments are not equal. These types of experiments are called as the random experiments or simply experiments. The probability includes the sample space, trail and different forms of events.

Terms present in the probability survey:

Sample space indicates the total number of possibilities for an experiment.
Trial corresponds to the experiment is performed.
Event specifies the outcome of the experiments.
Exhaustive events are an event which contains all the necessary possible outcomes of the experiment.
Mutually exclusive events are the two events that cannot occur simultaneously.
The probability certain likely defines the equally likely event in the probability. Equally likely event means that the two or more events have an equal probability. For example while tossing the die the probability for getting the tail and also the probability for getting the head are the equally likely events. The equally likely event determines the equal probability for the events.

Example problems for probability survey:

Ex 1 :A jar has 6 gray and 9 red marbles. What is the probability to get one gray marbles from the urn without replacement?

Sol:

The number of marbles in the jar is 6 gray and 9 red marbles.

The total numbers of marbles are 15 marbles.

The possibility for getting a gray ball is 6.

The required probability is 6/15 .

Ex 2 : While tossing a fair die, find the complementary probability of the numbers greater than 3.

Sol:

The sample space for the die is S= {1, 2, 3, 4, 5, 6}

The total number of sample space =6.

A is the event for getting the number greater than 3.

A= {4, 5, 6}

The number of events greater than 3 is n (A) =3

P (A) =n (A)/ n(S)

P (A) = 3/6

P (A) = 1/2

The probability for getting the numbers greater than 3 is 1/2 .

The formula for the complementary probability is 1- P (original probability).

The required probability = 1-P (A)

The required probability = 1- 1/2

The required probability = 1/2

The complementary probability for the numbers greater than 3 is 1/2 .

Survey of probability of certain likely events:

Some examples for probability certain likely:

Probability for getting the head and the tail when a coin is tossed only one time.
The probability for getting the number 3 and number 4 are equally likely events.
If an urn contains 5 white balls and 5 red balls. In that the probability for getting the single white ball and also the probability for getting the single red ball are the equally likely events.

Ex 3 : A jar has 5 gray and 7 green marbles. What is the probability to get one gray marbles and also probability for getting 1 green marbles? Determine whether the above events are equally likely events.

Sol:

The number of marbles in the jar is 5 gray and 7 green marbles.

The total numbers of marbles are 12 marbles.

The possibility for getting a gray marble is 5.

The probability for getting one gray marble is 5/12.

The possibility for getting a green marble is 7.

The probability for getting one green marble is 7/12.

The probabilities are 5/12 and also 7/12. These two probabilities are not the equally likely event because the probability of that two events are not same they are different.

Ex 4 : A single six face die is rolled. Find the probability for getting the number 6 and also 3. Determine whether these two events are equally likely events are not.

Sol:

The sample space for the die is S= {1, 2, 3, 4, 5, 6}

The total number of sample space is 6.

The probability for getting the number 3 is 1/6 .

The probability for getting the number 6 is 1/6 .

The probabilities for the two events are 1/6 and 1/6 respectively. The probabilities for the two events are equal. So these two events are equally likely events.

Practice problems:

Two coins are tossed at the same time. What is the probability to get two tails?
Ans: 1/2 .

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Educational Games: Stimulating Brain Growth and Development

Author: A Fist Full of Coins

Scores of children all over the world suffer from learning disabilities. Learning disabilities can affect a child in a variety of ways. From bad academic performance to poor social skills, children with learning disabilities face a wide range of problems. Kids with learning difficulties often need extra help. While the help and guidance provided by a medical professional can go a long way when it comes to helping children cope with learning difficulties, there are many other ways to help a child.

There are many games that can help children with special needs. These games have a strong scientific basis and can successfully assist children with neurological disabilities. Serotonin and dopamine play an important role in brain development. When children laugh and play these games, dopamine is released into the brain. This promotes brain development and greatly assists in the learning process. These games are of special help to children with memory problems. These games are designed in a way that they improve memory, stimulate the brain and promote growth. Many of these games also aim to develop social and interpersonal skills in children.

Brain improvement games are particularly helpful for children dealing with learning difficulties and attention problems. While many of these games are aimed towards children with ADD, ADHD and other brain disorders, they are also beneficial for adults with brain injuries and brain degenerative issues. In fact, there are many adult brain games that are designed specifically for adults. Most of the brain workout games available in the market suit the requirements of children as well as adults. The best part about memory improving games is that they are not just beneficial for children with learning problems but are also fun to play! Most of these games are designed in a manner that they are able to hold the attention of the players and provide relaxing time. As they have a positive impact on children's mood, they promote the creation of dopamine in the brain. This ultimately leads to brain development and growth.

In the recent years, with advancements in medical sciences, more insights have been made available to those dealing with learning disabilities. Educational fun games are developed using scientific research and methods. For this reason, they can go a long way when it comes to promoting brain growth and development. Countless children all over the world have benefitted from fun educational games. You can easily find an exciting brain improvement game in the market. If you're a concerned parent of a child with learning disabilities, you can easily find a quality educational toy and game in the market. A Fist Full of Coins and other educational games prove to be greatly helpful for children.

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Looking for kids & adult brain improving and fun learning games in Canada? Welcome to A Fist Full of Coins Game, A creative board game proven to optimize brain function.

What Is Loyalty?

What Is Loyalty?
By Jennifer Ruth Russell

How to teach your child about loyalty?

As your children begin elementary school they learn a lot about relationships. Your daughter's best friend today may betray her trust tomorrow. Or possibly your son wants to leave his basketball team because there's someone he doesn't get along with.

How do you help your child when you see her blindly following a friend or a trend? Or maybe your son keeps leaving a friendship whenever someone more interesting comes along or things become a little difficult.

What about talking behind someone's back?

This is the perfect opportunity to teach about how to practice loyalty. Without loyalty we change our commitments as often as we change our socks.

What is loyalty? The Virtues Project gives a simple and clear definition. "... Loyalty builds relationships that last forever."

Loyalty is standing by what you believe in, even when someone else may not agree with you.

Loyalty helps you listen closely to your own heart. Loyalty keeps your heart safe. If you can't stand up for something, maybe it doesn't ring true to your heart. Your heart will always tell you what is true for you.

When you practice loyalty it's important to choose wisely. The way you begin a relationship sets the tone for the way it will continue to be.

Take the time and really listen to your heart. Ask some important questions: is this someone that I can be myself with? Can I see myself being a good friend? Is this someone/something that I can stand up for? What is loyalty? What does my belly (your gut) say about this person?

Loyalty keeps you faithful (true) to your friends and family. It helps you to set your heart on things that really matter. Telling your true feelings to people who are close to you is practicing loyalty.

Loyalty helps you to protect what is important to you.

Here's an inspirational children's song that I wrote, that will give you a good definition of loyalty:

Stand by what you believe in.

Listen closely to your heart.

Be careful and choose wisely, loyalty keeps safe your heart.

Loyalty is the guardian (keeper) of my soul (spirit);

It sets my heart on things that matter.

It keeps me faithful to my friends and family.

I'm loyal. I am secure.

So let's ask the question again. What is loyalty? It's choosing wisely what you give your heart to.

Jennifer Russell is an award winning songwriter, founder and director of This is Where I Live Community Sing-along. She has written empowering & fun songs that bring out the best in our children. http://www.rembakids.com

To date, This is Where I Live Community Sing-along, has reached over 10,000 children in 500 schools throughout the world. The very nature of the songs themselves creates a recognition of, and participation in global citizenship awareness.

http://www.rembakids.com/

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What You Should Know About Teaching Special Education

What You Should Know About Teaching Special Education
By Michelle B Parreno

Special Education for me is a challenging vocation for it caters to individuals with disabilities. Through this type of education, students with disabilities are educated effectively.

I read a line from an article years ago that states: "It is said that a society can be judged by the way it treats those who are different."

In a democratic society it is believed that every individual is valuable in his own right and should be afforded equal opportunities to develop his potentials. The provision of special education will empower families to build future for their children, normal and special alike.

It was said that "teaching" is what special education is most about.

The role of the Special Education (SPED) teacher is very crucial. The SPED teacher has the responsibility not only to teach the regular classroom stuff like reading, writing, math etc, but also Activities of Daily Living and peer socialization.

An important part of a special education teacher's job is the early identification of a child with special needs, intervention is vital in educating children with special needs because as time goes on children who are not coping or who struggle in the general curriculum can be negatively affected.

A SPED educator's job is also challenging. Special education teachers work with children and youths who have a variety of disabilities. I also find this vocation fulfilling, for, it provides the opportunity to establish meaningful relationships with special kids.

Although helping these students can be highly rewarding, the work also can be emotionally and physically draining. SPED teachers work under the threat of litigation against the school or district by parents if correct procedures are not followed or if they feel that their child is not receiving an adequate education.

A SPED educator should be well-guarded by the laws. Understanding and practicing the laws will ensure a safe and legal environment for both the special child and SPED teacher.

A special educator's battlecry should be "commitment". Commitment spells equitable and excellent classroom. Without commitment to the chosen vocation, one won't be able to do his/ her job well.

But, teachers cannot do it alone. Teaching is a collaborative effort between the educator, student, parents/ family and the community. SPED educators, should express desire to be the parents' partner in the development of the special child.

As teachers, trying to reach out beyond the school to promote trust and understanding, and build partnerships with all segments of the school community is significant. Being active in associations/ causes supporting the special child/ special education can be a good start.

I would like to quote Robert Pasternack, Ph.D., Assistant Secretary Office of Special Education and Rehabilitative Services,U.S. Department of Education. He said:

"Some of the kids that are in special education are not, in fact, kids with disabilities. They are, in fact, instructional casualties. They are, in fact, kids who haven't been taught successfully using scientifically validated instructional approaches and research validated curricula in the general education system and general education settings."

With that, I have the following implications to education of children with special needs:

• States will put a premium on Reading --- to deliver scientifically validated and scientifically based reading research, validated curricula and instructional strategies in classrooms.
• Continuous and more additional trainings for teachers. If professional development will be given to teachers, if it's sustained, if it's systematic, if it's embedded in what teachers do, then, in fact, we can go ahead and improve the capacity of teachers to address the learning needs of the heterogeneous groups of kids that they have in front of them on a daily basis.

If you are looking for a school that: Is committed to enriching the lives of our diverse population; Works to meet learner and community needs in a mutually supportive partnership; Has competent teachers, therapists, staff & facilities; Is accessible and safe; and

Has lots of student activities;

visit http://www.carouselschool.com

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How to Improve Your Math Skills

How to Improve Your Math Skills
By Amit Kothiyaal

Very few people are aware that mathematics is a branch of science; science enhances technology and technology makes life easier. In fact, if you compare our lifestyle to that of the previous generations, we can call ourselves luxurious. You have math to thank for that, because the right ingredients can be destructive when used in wrong amounts.

If that is not enough reason for you to want to improve your math skills, then let's zoom in to your personal life. Nothing in the market is for free. Aside from the basic addition, subtraction, multiplication, and division you perform in designating your budget, there are discounts to consider and promos to join. How many miles can the gas in your car tank take you? How many yards should the carpet you have to buy be? Did your secretary compute yesterday's expenditures correctly? How can you check? You see, there are plenty of reasons you should invest time in improving your math, because it will give you more confidence in dealing with numbers in daily activities. No, you don't have to throw yourself back in college or in review centers. There are simple and effective ways you can do this without the additional stress or expenses.

An Early Math Challenge

We're not sure where the wacky alarm clock ideas originated from (we bet the Japanese influenced them anyway) but that doesn't really matter as much as the fact that they work. One of these ideas is to require the sleepy-head to answer ten sets of equations in basic mathematics for the alarm to stop ringing. They can get annoying, especially if you are not a morning person, so just concentrate on its benefits. First and foremost, by the time you finish and silence resumes, your brain would be too awake to be seduced back to sleep.

Second, you will become more alert the longer you undergo this morning math surprise, and third, you will master the basics of math without even knowing it. Time pressure and noise will no longer be enough to distract you from coming up with the correct solution.

Download this kind of applications and install them in your mobile phone. Make sure your thread of patience is long enough before you attempt this. Otherwise, your poor phone might end up on the floor, crushed to pieces.

The Advantages of Lending a Hand

The next time your son or daughter asks you to help them with their math homework, say yes and give it your best shot. Learning more about math is never a loss, and in this instance, your interest in numbers may influence your child to do better at school.

Teenagers can offer after-school tutoring for free or for a certain amount of money. Getting paid for assisting others in math education can be an effective motivation to study it further. You wouldn't want to teach others the wrong things, wouldn't you? The people you teach may also add to your current bank of knowledge. Math is like a maze, there can be more ways than one to get to your destination.

A Virtual Learning Experience

Math help need not be boring, and the first two examples are proofs of that. The worldwide web is anything but dull. Online mathematics courses create a suitable playground for modern minds. Lessons are commonly presented in the form of game, puzzles, and trivia, keeping users easily engaged. Similar to the approach of the first examples, your attention is diverted from improving your math skills to interacting with an entirely different and enjoyable game.

During your free time, you can boot up your laptop or bring out your mobile gadgets to access these math applications. Killing time has never been this fruitful.

The Brain is a Powerful Tool

A computer system is patterned after the human brain. If you think the former is impressive, then you should be in awe of the latter. But to maximize your brain's greatness, you have to exercise it. Avoid using calculators when doing your grocery of summing up your monthly bills. Calculate mentally whenever you can, and bring out your gadgets only to check whether you are correct.

This practice makes you less reliant on tools and more confident in your skills. It also saves time, energy, and space in your bag. The next time you see numbers, get excited and start jogging your brain. You will be shocked by the results.

The author loves writing on various subjects like Math, English and Science. He also writes about the advantages of online math courses, and how virtual Math lessons can act as an effective medium to learn the trickiest concepts.

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New Teachers - Lecture Tips That Will Keep Students Interested

New Teachers - Lecture Tips That Will Keep Students Interested
By Mackenzie Kerby

You've all seen the Charlie Brown episode where the teacher is lecturing and all the students hear is "wa wa wa wa wa wa." We remember watching that as kids. Unfortunately, seeing this as kids taught us that this was what school was like. Now, as we are adult teachers, we are constantly afraid of becoming the teacher from Charlie Brown. Well, what if we could avoid this? What if we could use this knowledge to create inspiring and organized lectures using Best Practices? I have developed 6 tips for you to help you in creating fun and memorable lectures that will leave your students with long lasting knowledge.

1. Create an objective. We have heard this before from our administrators. Often times we hear this when the administrators come to observe us in the classroom. Write your objective on the board! Say it at the beginning of class! Say it at the end of class! Well, they're right! By telling the students what they are to be learning and why they are learning, they are more apt to pay attention and way more apt to remember what you're talking about. It will also help them when coming up with what they should actually be writing down.

2. Have your students do something productive. Your students should not be just sitting there. If you are engaged in best practices, your students should be doing something active with their learning while they are listening to your lecture. More often than not, this means that they will need to be taking notes. But give them structure. Maybe this meaning Cornell notes or maybe it's powernotes. It's your call!

3. Break it up. Break your lecture up into different segments. I would say no more than 4 or 5. This way, those who have difficulties processing long bits of information will be able to compartmentalize what you are telling them easier.

4. Separate the sections with different activities. Throughout your lecture, break up your talking by having the students do different activities. For example, have students turn to a near by partner and repeat the top 5 parts of the lecture they have heard so far. Doing this will help them to remember because they are actively participating.

5. Have them repeat through questioning. As you lecture, don't just talk. Question your students. Question them on different background knowledge that they will know information about. Tapping into this will help them to succeed in acquiring new knowledge.

6. Wrap it up effectively. At the end of your lecture have your students do something with the information. Perhaps its a quick little quiz on the board. Perhaps they will write a paragraph summary.

Whatever you lecture about, make sure to follow these 6 tips to have your students remain actively engaged. This will increase their knowledge and participation. No Charlie Brown Effect here!

Your first year of teaching can be a toughie. My eBook will give you 6 tips that you can put in place now to help you be an organized, diligent, creative, and relaxed teacher. I encourage you to activate these 6 tips in your teaching career to have a fulfilling year as a first-year teacher.

http://www.amazon.com/How-Hate-Your-Life-ebook/dp/B00CMHRVTC/ref=sr_1_12?ie=UTF8&qid=1367777079&sr=8-12&keywords=how+not+to+hate+your+life

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Online Basic Geometry Definitions

Author: Omkar

Introduction to online basic geometry definitions tutor:

In this article online basic geometry definitions tutor,we will learn some important geometry definitions they are necessary to understand geometry concept.Those basic geometry definitions are used to design a graph with the assistance of those terms. Tutor will teach to individual and guide them to get the solution for problems through some websites via online. Online is a tool for self-learning from websites.

Basic definitions- online basic geometry definitions tutor

Supplementary angles:

We can call any two angles as supplementary angles,if the sum up of them should be 180°

Complementary angles:

We can call any two angles as complementary angles,if the sum up of them should be 90°

Acute triangle:

An acute triangle means a triangle in which all three angles should be less than 90°.

Obtuse triangle:

Obtuse triangle means one type of triangle in this one angle must be greater than 90°.

Right angle triangle:

A right angle triangle means one type of triangle in which one angle must be a right (90°) angle.

Triangle Inequality:

The triangle inequality means the addition of any two side should be greater than the third side

Scalene Triangle:

A scalene triangle means a triangle with three different unequal length of side.

some more definitions- online basic geometry definitions tutor

Centroid:

The centroid means a point in which three lines will meet each other. This point is a center point of a triangle. If we cut a triangle corresponds to that center we will get three equal parts.

Circle:

In circle the distance between the center and to any point present in the outer line of a circle is same.

Radius:

Radius of a circle is the distance between the circle's center and any point present on the circle.

Circumcenter:

In a triangle three perpendicular line drawn from the three sides bisect each other . That point is called as circumcenter.From this center point we can draw a circle

Congruent:

Two figures are said to congruent when all the parameters should be same interms of length and angles.

Altitude:

An altitude means a line connecting a vertex to the opposite side.

Vertex:

Vertex means a point.

Transversal:

A transversal means a line which passes through two another lines there is a no issue that should be parallel.

Point:

A point indicates a single location

Plane:

Plane is a flat, two-dimensional object one.

Quadrilateral:

Quadrilateral is defined as a polygon and has exactly 4 sides.

Trapezoid:

A trapezoid means a quadrilateral which contain one pair of opposite side they should be parallel to each other.

Polygon:

A polygon means a two-dimensional geometric object.It is made up of a straight line segment those segments touches at the ends.

Rectangle:

Rectangle means a quadrilateral and should has 4 right angle.

These are the few terms for online basic geometry definitions tutor

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Comprehend more on about Graphing Linear Equations and its Circumstances. Between, if you have problem on these topics acute scalene triangle Please share your views here by commenting.

Types of Pentagon

Author: nitin.p070

A pentagon is a closed two dimensional figure that is the union of line segments in a plane. A pentagon has the five sides and five angles. The internal angles in a simple pentagon total 540°. A pentagram is an example of a self-intersecting pentagon. A regular pentagon has five Edges and five vertices. Internal angle of a regular pentagon is 108 degree. There are two types of pentagons : concave pentagon and convex pentagon.

In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover its five angles are equal.
Four intersecting equal circles arranged in a closed chain are sufficient to determine an equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remain vertex is determined by the intersection of the first and the last circle of the chain.

It is possible to describe any equilateral pentagon with only two angles a and ß with a = ß provided the fourth angle (d) is the smallest of the rest of the angles. Thus the general equilateral pentagon can be regarded as a bivariate function f(\alpha,\beta) where the rest of the angles can be obtained by using trigonometric relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane.

Types of Pentagon : Concave and Convex Pentagon:

Concave pentagon:

It is a five sided polygon. At least one interior angle is greater than 180 degrees.

This causes some of the vertices of the pentagon to points towards the center.

An alternate definition exists a line that will cut the polygon in 4 or more places.

The twelve concave pentagons can be get together to make a concave dodecahedron.

Convex pentagon:

It is a shape with 180degrees or less.

The regular pentagon is the example of the convex pentagon.

Let us see regular pentagon in detail.

Express your views on the topic 9th cbse sample papers 2011 by commenting on articles.

Types of Pentagon : Regular Pentagon

A shape with five equal sides and five equal angles are called as Regular Pentagon.

Properties of Regular Pentagon:

• It has five equal sides
• It has five equal angles
• It has five lines of symmetry

Angle of a Regular pentagon:

Exterior angle of any polygon is 360° and hence the exterior angle of a regular pentagon is 360°.

Regular pentagon has five sides so each exterior angle measures (360/5) = 72°.

Interior angle of a polygon is calculated by using the formula,
n - 2 (180)

Where n =number of sides.

Where n =number of sides.

Here for pentagon interior angle = (5 - 2) 180 = 540°.

For regular pentagon each side interior angle = 540 / 5 = 108°.

Area of any regular polygon is:

A = 5t2 tan (54) / 4

Derivation of the diagonal length formula:

D = T * (1+v5) / 2

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How Do You Teach Your Child to Forgive?

How Do You Teach Your Child to Forgive?
By Jennifer Ruth Russell

Why is it important for a child to learn about forgiveness? It keeps their heart clean and healthy. Which is just as important as keeping their body healthy and whole. It builds self- respect and community skills.

We are sensitive creatures and Elementary School is the school of bumps and bruises in learning how to relate to others. This week's best friend can quickly become the betrayer, the liar, the 'enemy'.

When a child makes a mistake, how do they make it right and move on?... with forgiveness.

Here is The Virtues Project definition of Forgiveness:

Being forgiving is giving someone another chance after they have done something wrong. Everyone makes mistakes. Instead of revenge, make amends. Instead of feeling hopeless after a mistake, decide to act differently and have faith that you can change.

This simple technique will give you something to do with your child that will help her/him learn how to forgive.

Remember we are all in this together and many times people don't know how they hurt us. We're not talking about justice, about who was right or who was wrong; we're making things right in our hearts.

Begin by letting your child tell the story. Let them have their feelings about what happened. Ask them if they are willing to forgive. The Course in Miracles tells us that willingness is all that is required of us.

1. Have them close their eyes and see in their mind's eye the person standing in front of them.


2. Have them repeat after you:
   
   I forgive ____________ (say their name or myself) for __________ (not being the kind of friend that I want right now, saying something mean, making a mistake, etc)
   
   I let God take this over now and to make it right. I trust God to heal any hurt I feel in my heart.
   
   I promise to love myself and stop thinking about this.
   
   I forgive and I am free.


3. With their eyes still closed have them lift this person (or themselves) up, in their mind's eye, and into the sky until they can't see them any longer. This simple motion will help them release.

Do this with your child as often as necessary, until they start doing it for themselves.

If there are amends that need to be made with another, start with this forgiveness exercise. Help your child decide on what would be appropriate. Keep it simple and in the heart.

Jennifer Russell is an award winning songwriter, founder and director of This is Where I Live Community Sing-along and Professional Development. She has written some excellent, empowering & fun songs to bring out the best in our children. http://www.rembakids.com.

The Virtues Songs A-Z received the Parents Choice Award and the National Parenting Center Seal of Approval. These songs make teaching a child about forgiveness, compassion, unity, respect and honesty, simple, easy and fun.

http://www.rembakids.com/

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Analyzing Issues of Overidentification in Special Education

Analyzing Issues of Overidentification in Special Education
By David Pino

Overidentification in special education has two potential meanings. First, it can mean that there are too many students being identified as needing special education in a school or district. Estimates of students in need of special education services have ranged from 3% to 8% of total students. Central office staff typically attempt to stay within the 10% range however, it sometimes reaches highs of 13% or more. Second, it may mean that a certain group of students is over represented in the special education population in comparison to their make up in the general population of students. Ideally, the proportion of the subgroup of students in the special education population should be identical to that of the general population.

Overidentification of students in need of special education services results in a number of negative outcomes for the students, the school district, and to a larger extent society. Students identified as needing special education services often don't receive the same rigorous curriculum as those not receiving services. Therefore, they are not as prepared for the demands of the next grade level as unidentified students. They frequently have lowered expectations placed upon them, may be socially stigmatized, may display greater behavioral problems requiring disciplinary action, and are more likely to not complete school or they complete school with less skills than other students.

Overidentified students place an unnecessary burden on already limited school resources and take away existing resources from those students who are really in need of them. Staff time is taken up in extra preparation for their daily needs, to go to extra meetings, and to complete evaluations. If discipline becomes an issue, then administrator time gets taken away from other duties.

In regard to potential impacts on society, overidentification's reduced demands, watered-down curriculum, and potential social stigmatization leaves students unprepared to continue with their education or lacking the skills necessary to take a productive role in the workplace and support themselves. When these students are unable to become productive members of society after school then their educational institution has failed them.

Some of the reasons for overidentification include:

• Poverty and income inequality
• Inequity in schools funding
• Inability to access early interventions
• Lack of training in regard to appropriate referrals to and placements in special education
• Lack of understanding of diverse populations

Research has found that students from impoverished backgrounds are more likely to be unprepared for the rigors of education and lack the background knowledge and experiences of their more affluent peers. The Head Start Program was developed in 1965 to meet this need, and to provide comprehensive services to low income families during the preschool years. However, while gains have been made, a gap still exists, and many families are unable to access these services for a variety of reasons.

Schools are not always funded appropriately with many schools requiring students to bring in their own work materials, lack resources for paraprofessional support, or lack the funds to have full day kindergarten or hire enough teachers to have smaller classes. When schools are funded appropriately, the district often determines where and when the money is spent, which may not always be on the biggest needs or those that will make the biggest difference in the long-term.

Unfortunately, some schools don't always make appropriate referrals or placement decisions. Sometimes they wait too long before making a referral and sometimes they make one too soon. The advent of Response to Intervention (RTI) may help in this area as schools should have data about how students respond to interventions before making a referral.

Lack of understanding about different cultures and the way children learn may also lead to students being over identified, especially for behavior concerns. Not every child is able to sit in a chair for six hours a day learning. There are many ways to learn and students need to be exposed to as many of them as possible before being identified with a disability.

Parents and educators need to be aware that over identification of students for special educational services has short and long-term consequences. These consequences affect the student, the school, and, potentially, society. It is the school's responsibility to keep an open mind, look at individual differences and all possibilities prior to identifying a student as in need of special education services.

For more information please visit http://dnpino.byethost17.com

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Pascal's Triangle and Polygonal Numbers

Pascal's Triangle and Polygonal Numbers
By Alec L Shute

Polygonal numbers are a kind of general set of patters, a sequence of sequences. Common examples include triangle and square numbers, but we can also have less well known sequences such as pentagonal, hexagonal, heptagonal etc. numbers, all of which are closely linked with Pascal's triangle.

First I will explain how all of these sequences can be formed. Triangle numbers are made from adding consective integers, or adding one more each time. The first few terms are 1,3,6,10,15,21,28,36,45,55. To get to the next term, you add 2 then 3, then 4 and so on.

The square numbers are usually thought of as the sequence made from multiplying numbers by themselves, for example the sixth square is 6 x 6 = 36. However, for the purpose of linking them to triangle numbers and the other polygonal sequences, we shall consider them in a slightly different way. Square numbers can be made by adding consecutive odd numbers - the sequence 1,4,9,16,25,36,49... has differences of 3,5,7,9,11,13... , which are the odd numbers.

Continuing this idea, the pentagonal sequence is 1,5,12,22,35,51... which have a difference of 4,7,10,13,16... , which are the multiples of 3 add 1, and the hexagonal numbers are 1,6,15,28,45,66... , which have a difference of 5,9,13,17,21... , which are the multiples of 4 add 1 (the hexagonal sequence also turns out to be every other triangle number). So an n-gonal number will have a first term of 1, then differences corresponding to multiples of n-2 add 1.

Now we can link all this in with Pascal's triangle. The triangle numbers 1,3,6,10,15... are famously found in the third diagonal in of Pascal's triangle, as shown in bold below:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 21 15 6 1

The square numbers (or any other polygonal sequences for that matter), however, are much harder to spot. The trick is to look in the same diagonal as we just obtained the triangle numbers from, but as they themselves don't appear there, we have to do a bit of adding to get them. The square numbers can be found by taking the sums of the consecutive values in this diagonal. So we get

(0) + 1 = 1

1 + 3 = 4

3 + 6 = 9

6 + 10 = 16 etc.

We apply a very similar process to create any polygonal sequence from Pascal's triangle. For the pentagonal numbers, we must multiply the first number by 2:

2 x (0) + 1 = 1

2 x 1 + 3 = 5

2 x 3 + 6 = 12

2 x 6 + 10 = 22 etc.

For hexagonal numbers, we multiply the first value in the sum by 3, for heptagonal numbers we multiply the first value by 4 and so on. This shows how we can create any polygonal number from Pascal's Triangle. This just goes to show how many patterns can be explored in Pascal's Triangle, as we have created an infinitely many sequences just from a single diagonal! For more information on some of the amazing patterns and properties of Pascal's Triangle, as well as a visual representation of the polygonal numbers, you are welcome to visit my site listed in the links below.

Pascal's Triangle

Pascal's Triangle

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Developing A Wide Subject Vocabulary-Guidelines for the Teacher

Developing A Wide Subject Vocabulary-Guidelines for the Teacher
By Richard D Boyce

As a teacher, your class will take its lead from you in all that you do. The use of language is the first place this will start. Your example of using the language of the subjects you teach must be at the highest possible level. That doesn't mean to use words whose meanings are not known to the class but rather ones which enhance a child's progress.

Obviously, any new terminology you use in each subject must be explained and used in ways to consolidate the new work to be learnt. Below are some ways you could enhance the students' understanding of the use of language.

• Colourful language. This does add interest or excitement to what you say or teach. No one says that when you teach you must use boring language. Use words that add colour and excitement to what you teach. Make it a goal of yours to look for ways to add colourful language particularly to the more difficult topics that you teach.
• Use the language of the subject discipline often. Teach the class the origin and meaning of each new term that you introduce.
• Create a spelling list of terms as you teach each topic. Some texts provide the lists for you.
• Have a quiz of these terms often. Have little spelling bees/contests.
• Have what I might call a definition test/quiz where the students write a definition of a subject term in simple language to explain its meaning to a person who has never seen the word before.
• In your own speaking, learn to say the same ideas in as many ways as possible to give constant examples to your class about how to use our language in a variety of ways.
• Insist that your students use the terms of the subject discipline in their answers to questions they write and in the questions or answers they ask or give.

Many modern syllabuses contain a requirement that communication as a skill in the subject must be assessed as part of the total assessment program. This implies that the student must use the terminology of the subject in their answers to all assessment tasks to show understanding of the language of the subject being tested.

The student needs a good base in the language of the subject to know what is required in each assessment task before they can begin to answer the question and answer in such a way as to show understanding of the subject.

During the last 16 years of his teaching career, our author, as Head of Mathematics, had to implement within his school's assessment program a new marking criteria in the assessment of Mathematics. That criterion was testing a student's communication skills in Mathematics. This meant he had to provide teacher inservice and make changes to the work programs to teach the students how to communicate in Mathematics. Go to http://www.realteachingsolutions.com for more information on this and other assessment issues.

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Power Lens

Author: johnharmer

Power of a lens

The power of a lens is its ability to converge or diverge the incident beam of light and is defined as the reciprocal of its focal length. Thus, P = \/f

Diptre is the unit of power. The power of a lens is said to be one dioptre (ID) if its focal length is one metre.

P(dioptre) =-?--

f(metre)

The power of a convex lens is positive while that of a concave lens is negative.

From lens maker's formula, — = (n-l)j — + — I

f I/?, R2 J

1 n-1 n-1 . „ n-1 n-1 i.e., - =-+- i.e., P =-+-

f R\ R2 R\ R2

Now, (n-l)//?] is the power of first refracting surface = P, and (n-])/R2 is the power of the second refracting surface = Pz

¦¦ P = Pi + Pz

Thus, power of a lens is the sum of the powers of its surfaces.

Magnification

When a linear object is placed perpendicular to the principal axis of lens, a linear image perpendicular to the principal axis is formed due to refraction through the lens. The position, size and nature of the image depend on the lens and position of the object with respect to the lens.

The ratio of the linear size of the image to the linear size of the object is defined as linear magnification of the image of the object formed due to refraction through the lens. It is denoted by'm'

linear size of image / Thus, m =--— -

linear size of object 0

In all cases of image formation due to refraction through a lens, it can be proved that

image distance v

m =- = —.

object distance u

I v

Thus, m = —

0 u

The object distance (u), the image distance (u) and the focal length (/) of a lens are related by lens equation. Accordingly

I + i-i

u v f

Using the lens equation it can be proved that

f v-f m =- and m =-.

u-f f

Note :

'm' is positive for a real image and negative for a virtual image.


Introduction to Photoelectric Effect Intensity:

It is the phenomenon of emission of electrons from the surface of metals when the radiations of suitable frequency and suitable wavelength if falling on the surface of the metal. The emitted electrons are called photo electrons and the current so produced is called as the photoelectric current. The intensities of photo electrons vary with material.

emission of electrons

photoelectric electrons

Materials that emit Photoelectrons

Different materials emit photo electrons when they are exposed to radiations of suitable frequencies or wavelengths. The whole range of the electromagnetic radiations from the ?–rays and the x–rays to the ultraviolet and the visible and the infrared rays produce this effect. For example the alkali metals like the lithium and sodium and potassium and cesium etc. show the photoelectric current with the visible light whereas the metals like the zinc and cadmium and magnesium etc. are sensitive only to the ultraviolet light.

Photoelectric effect was discovered by Heinrich Hertz in 1887. Further experimental study was undertaken by Hallwachs in 1888. Then in 1899 Lenard showed that the carriers of electricity emitted from a metal surface under the action of the ultraviolet light were the electrons and Einstein explains it successfully by the theoretical evidences.

Image of photoelectric emission on sodium

image of photoelectric emission on sodium

Effect of the Intensity of the Incident Light

The surface of the metal plate is illuminated by the monochromatic ultraviolet light. The accelerating potential difference between the metal electrodes is increased till the photoelectric current is maximum and this current is due to the flow of the photo electrons emitted per second from the surface of the metal. The experiment is repeated for different known intensities of the incident light and the variation of the photoelectric current with the intensity of the incident light is shown in the fig.1 which is a straight line.

Intensity verses photoelectric current

Fig.1 Intensity verses photoelectric current

Conclusion for the Intensity of Photoelectric Effect

From the discussion we had on the intensity of photoelectric effect on matter, we conclude that the straight line graph shows the number of  photoelectrons emitted per second by any metal surface is directly proportional to the intensity of the incident light i.e. if we need the large photoelectric current then the intensity of the incident light should be large.

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Polygon definition

Author: Matthew David

Introduction
Polygon

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. In geometry a polygon it can be traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners.

In geometry a polygon  is usually a plane shape  that is bounded by a closed  circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called edges or sides, and the points where two edges meet are the polygon's vertex or corners. A polygon is a 2-dimensional.Polygons is primarily classified by the number of sides.

Characteristics of Polygon

Convexity

Polygons may be characterized by their degree of convexity:

Convex: any line and it can be drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
Non-convex: a line may be found which meets its boundary more than twice.
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is the visible from and that is a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of that  polygon crosses itself. Branko Grünbaum calls these Coptic, though this term does not seem to be widely used. The term complex is sometimes that can be used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
Star polygon: it is a polygon which can be self-intersects in a regular way.

A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc and it can be a different great circle and you have a digon. Regular Polygon Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.

Special Nmaesof Polygons

Some polygons have special names and that are depending on the number of sides they have.



Number of sides              Name of polygon

3                            Triangle

4                            Quadrilateral

5                            Pentagon

6                            Hexagon

7                            Heptagon

8                            Octagon

9                            Nonagon

10                           Decagon

Classifying Polygons:

There are two categories of polygon. They are convex and concave. Polygons are also classified by the number of sides they have. The following list shows that the polygon name and number of sides they have.  

Triangle - three-sided polygon.

 Quadrilateral - four-sided polygon.

 Pentagon - five-sided polygon.

 Hexagon - six-sided polygon.

 septagon -seven-sided polygon.

 Octagon - eight-sided polygon.

 Nonagon - nine-sided polygon.

 Decagon - ten-sided polygon

Regular polygon:

A regular polygon is a polygon which has equal angles  and equilateral . Regular polygons may be convex or star.
Regular convex polygons:
1. Introduction to Square:

A square is one of the regular quadrilateral.  it has four equal sides and four equal angles .All angles are 90 degree .The total internal angles of square is 360 degree.

Square
2.Introduction to Equilateral triangle:

An equilateral triangle is one type of polygon.it has three sides.They are equal in length and the total internal angle of triangle is 180 degree.All the three angles are equal.(each 60 degree).

Equilateral triangle

3. Introduction to Pentagon:

The five sided polygon is known as pentagon. The sum of internal angle of a pentagon adds up to 540 degree. The all internal angles are equal( each 108 degree)

Pentagon
4.Introduction to Hexagon:

The six sided polygon is known as hexagon with equal length (regular hexagon).the sum of internal angle of a hexagon adds up to 720 degree. The all internal angles are equal (each 120 degree).

Hexagon

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Celebrating Earth Day With Your Children - 5 Top Tips to Teach Your Children About Kindness on Earth

Celebrating Earth Day With Your Children - 5 Top Tips to Teach Your Children About Kindness on Earth
By Jennifer Ruth Russell

April 22 is Earth Day's 40th anniversary. Yippee, a day set aside just to celebrate our amazing mother earth. Her beauty and generosity are inspiring.

Earth day is a wonderful opportunity to teach children about kindness.

Here are 5 Top Tips to Teach your children about Kindness on Earth Day

• Play a game with these questions. There are many answers to these questions, let your children use words, pictures, charades and body sculptures to express their ideas.

What is kindness? What are some ways that you show kindness to others and to yourself? How can you show an animal, a plant or the earth kindness? How does reduce, recycle and reuse show kindness to the earth?

• Kindness Challenge:

Have a contest, with your children, to see how many acts of anonymous kindness they can do in a day. Ask them to think of several things he/she could do that would bring a smile to someones face. Include the earth in the acts of kindness. What would bring a smile to her face? Start them off with a few of your own ideas. Let your children keep track of their own progress. Keep a chalkboard or a piece of paper eye level to mark each act. Tally the total in the evening and celebrate the kindness that you have brought to the earth and the people on it.

• Visit a Recycling Center and discuss how recycling helps the earth.
• Visit the Animal Shelter in your area. Find out what it takes to adopt an animal and take care of it. Ask them about their rescue program.
• Sing-along with the song Kindness

I am kind to the earth, I am kind to the animals, all of creation deserves to be treated with kindness

Verse: I look for ways to help others, and show kindness to all that I see

When I reach out to another, I become sensitive, to the world around me

Repeat Chorus

Verse: I care about the earth; the air, the land and the deep blue sea

Reduce, recycle and reuse, I'm connected to the world around me

HAPPY EARTH DAY!

Jennifer Russell is an award winning songwriter, founder and director of Remba Kids Songs & This is Where I Live Community Sing-along. She has written some excellent, empowering & fun songs to bring out the best in our children. http://www.rembakids.com

To date, This is Where I Live Community Sing-along, has reached over 10,000 children in 500 schools throughout the world. This program addresses issues such as bullying, fighting, lack of courtesy and disrespect. The very nature of the songs themselves creates a recognition of, and participation in global citizenship awareness.

This tips are included in the Character Building Music Kit called Together We Can Do Great Things.

http://www.rembakids.com/

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Educating Children With Attention Deficit Disorder - Importance of Establishing a Dominance Profile

Educating Children With Attention Deficit Disorder - Importance of Establishing a Dominance Profile
By MaryEllen Jirak

What Are Dominance Profiles and How Can They Be Used

I'd like to begin with a Paul MacLean quote from his book, The Triune Brain In Evolution: "If uniqueness were an indispensable requirement for an evolving society, every person would be indispensable."

Unfortunately uniqueness is not something that we highly treasure in school yet it is what we most admire in our greats in all walks of life. In other words, there is a large disconnect in how our educational system treats those that learn differently.

Lateral dominance is our natural and innate way of learning from and processing information. Dominance Profiling is a technique for assessing a person's learning style. Each of us has a preferred way of taking in and learning from the world. Understanding your child's (or your own), learning characteristics can assist you to see why we each act and learn in certain ways especially when under stress. From this knowledge strategies can be developed to ensure your child will learn more effectively.

Our dominant, innate, basal patterns are especially valuable for understanding children in school. Yet they are also helpful to understand the behavior of adults when they are under stress. Knowing about and developing new strategies for learning enables a person to broaden and break free of the restrictions of their innate profile. Our dominance profile is based on our dominant brain hemisphere, eye, ear, hand and foot. This profile determines how we prefer to learn, perceive, and respond to the environment. As we take in new information especially when we are under stress, we access the senses which are ideally linked to our dominant brain hemisphere. This direct link is formed when our dominant eye, ear, hand, and foot is opposite our dominant brain hemisphere. When our dominant brain hemisphere is not opposite our dominant senses (as is true for many people) then learning is more difficult if different strategies are not used.

Learn how you can test your child for their Dominance Profile

Why Schools and Parents Need to Know About Dominance Profiles

Research shows that there is a huge and disheartening incongruity between unfavorable school instructional methods and the learning profiles of the majority of students. Schools have certain expectations about the ways students should learn. Student's who fail to fit this profile are seen as inferior rather than viewed as learning differently.

Labels that are used in school systems like "Gifted and Talented" or "Special Education", have a direct correlation to a child's inherent dominance profiles. This incongruity is a major contributing factor in higher numbers of students with dominance profiles that don't fit teaching methods being identified as ADD/ADHD, Dyslexic, and Emotional Behavioral challenges and other limiting labels. With no considerations or adjustments made to address normal differing profiles, children whose profiles don't fit the set teaching methods will continue to appear less capable. The sad truth is however that only about 15% to 20% of the population ideally fit the typical teaching practices used in schools today.

MaryEllen Jirak MS. Ed is a long time educator with a master degree in Special Education.

She is also the author of several books for parents of ADD children, including of The Gift of ADD Secrets For Transforming Liabilities Into Possibilities and a new book called Cracking The ADD Code: Why Outcomes Haven't changed and How They Can, Success in High School and Beyond and Creating Your Life, While Loving What Is: The ADD Self Care Manual

Get more natural treatments for attention deficit disorder

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Explaining the Links Between Pascal's Triangle and Sierpinski's Triangle

Explaining the Links Between Pascal's Triangle and Sierpinski's Triangle
By Alec L Shute

By assigning different colours to the odd and even numbers in Pascal's triangle, Sierpinski's triangle can be generated, as I have explained in my previous post entitled "Pascal's Triangle and Sierpinski's triangle". In this post, however, I attempt to explain why this interesting link arises between these two seemingly unrelated triangles, and how we can be sure that this pattern will always continue.

To begin with, as Pascal's triangle is a series of additions and we are colouring each number by whether it is odd or even, it seems sensible to look at some basic rules of adding odd and even numbers:

Rule 1: odd + odd = even,

Rule 2: 0dd + even or even + odd = odd

Rule 3: even + even = even

So, now to the main stage of the proof. Assume that a finite number of rows of Pascal's triangle did correspond to Sierpinski's triangle after a finite number of iterations. The bottom of Sierpinski's triangle is always a row of triangles all the same colour which correspond to odd numbers in Pascal's triangle. By rule number 1, the next row of Pascal's triangle will be all even (except outer 1s which are of course odd).

From the third rule, we can see that a row such as row eight, 1,8,28,56,70,56,28,1, which has many even numbers in a row will create an upside down triangle of even numbers below it - here, we have 6 even numbers in a row, and the 5 numbers in between them in the row below will be even, by rule 3, and the 4 in between those in the row below will be even and so on. So after our row of all odd numbers, we get a triangle of even numbers.

If you try this out, you should notice that the new triangle we just created is the same size as the section of Sierpinski's triangle we were just dealing with.

We now must look at what is going to happen due to those 1s on the edge of our otherwise even row. Will they not change what goes on in the rows below them? Yes, but the fact is that the very first number in Pascal's triangle is a 1, so why would the pattern below these 1s be any different to that first section of Sierpinski's triangle we had? Sure, the actual numbers will be different, but the parity (oddness/evenness) will be identical to before, as from rule 2, the parity of a number does not change by adding an even number to it.

Let's take a step back and look at what we have achieved so far. we now have a much bigger Sierpinski's triangle which is made up of 4 parts:

1. the initial section of Sierpinski's triangle that we started with

2. the all-even upside-down triangle below it.

3. The left hand side equilateral triangle that is identical in colouring to that in 1.

4. The right hand side triangle, again identical to 1.

Therefore, we have made the next iteration of the rule generating Sierpinski's triangle! You can check it works for the first iteration, then we could do this again and again and again and create whatever iteration of Sierpinski's we wanted. Do it infinitely, and we will thus create an infinite Pascal's triangle that yields the actual infinite fractal of Sierpinski's triangle itself. We are done! We have explained the link between Pascal's triangle and Sierpinski's triangle!

I know that these kinds of proofs can sometimes be rather hard to visualise. Please visit my site shown in the resource box below, which contains three articles each (with lots of pretty pictures and diagrams) all about Sierpinski's triangle and other fractals and their link with Pascal's triangle:

http://pascalangle.com

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Protecting Your Voice - Advice For The Teacher

Protecting Your Voice - Advice For The Teacher
By Richard D Boyce

Losing your voice is one of the most challenging times in a teacher's career so it is important to look after it at all times.

One of the skills to learn is to project your voice well to reduce the strain on it. You may need to go to a Speech Therapist or an Art of Speech Teacher if you are unable to learn this skill.

When you have a sore throat or you are fearful of losing your voice, there are some ways in which you can protect your voice and still manage the class.

Below are a few ideas for you to consider:

• Give your class a written revision test. Make sure there are enough questions to keep most of the class occupied as well as some to stretch the more able. Have a reserve activity ready for those who finish early. As well, have copies of the answers at your desk available for students to check near your desk. This sort of activity allows you to have students 'one on one' at your desk to check progress and to give extra assistance.
• A reading exercise with a work sheet requiring answers to be written. Again this should be an exercise that all students can attempt with some challenges for the more able.
• A video or DVD lesson on your current topic with a work sheet.
• A student quiz. Here students are given time to make up questions on the topic being studied. They should go from easy to hard and the student must know the answer. You could appoint a chair person to oversee the quiz with you checking the questions before they are asked. Each child should get a chance to ask a question.
• A study lesson. Here you need to set guidelines on how the study is done; on references to use and questions to test the success of the study session.

These are just a few starting ideas. As you become more experienced, you will have further ideas in each subject for lessons that require you to speak much less than normal.

Long Term Protection:

Here are some other ideas to consider:

• Never speak to your class unless all are ready to listen.
• Never shout over a noisy class. Develop a signal that the class will recognise that you want to speak.
• Be careful in open air venues. You need to have the class gather around you sitting on the ground close to you. Speaking outside can strain your voice. A whistle is an excellent device for getting your class's attention.
• Create a number of physical cues designed to gain students' attention to improve their work ethic in class. A simple one is to stand beside the student who is not on task. You could create your own; use them often, not just when your voice is failing.
• Insist that no matter what the situation in the class is or with you, that class and self-discipline must be maintained.
• Always reward your class for good discipline in difficult situations for them and for you.
• Where possible, have students talk for you. One way is for a student to answer a question that has been asked of the teacher by another student.

Remember your voice is your greatest teaching asset. Without it, you cannot impart your knowledge to those in your charge. Look after it and you can have a long and successful career in the class room.

Our author has written an eBook, "Speaking and Listening for the Teacher and the Student". You will find this on the website http://www.realteachingsolutions.com In it he shares his experience gained in the classroom and in public speaking on a large number of topics including the one in this article. The eBook will help the new teacher develop a successful presentation persona in the classroom. Search EzineArticles for others on speaking.

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Polygon Law Of Vectors

Author: johnharmer

Introduction to polygon law of vectors:

A vector is characterised by an absolute value(magnitude) and a direction. The vector, as a mathematical object, is defined as a directed line segment. Displacement, velocity acceleration, force momentum, angular momentum are a few examples of vector quantities.      A vector is geometrically represented by an arrow. Length of the arrow is proportional to the magnitude of the vector; head of the arrow gives the sense of direction. A displacement vector is represented as an arrow.In print a vector is represented by a single bold type letter such as d . The bold type letter signifies the properties, viz magnitude and the direction of the vector. In hand writing, an arrow is placed above the letter symbol like `veca` . If only magnitude of the vector is to be specified one has to write either  | `veca` |  or a; in print it is indicated as a.

Polygon law of vectors

If a number of vectors are represented as the sides of a polygon taken in order, the resultant is represented by the closing side of the polygon taken in the reverse order. In the case where number of forces act simultaneously at a point and keep it in equilibrium, this law states that, these forces can be represented as a sides of a polygon taken in order.

Polygon Law of Vectors

Vectors a,b,c,d,e,f are taken as the adjacent sides of the polygon; the vector shown with dashed line is taken in the reverse order to  represent the direction of the resultant ; its length is the magnitude of the resultant.

Other laws of vectors:

Triangle law :  If two vectors are represented by the sides of a triangle taken in order, the resultant (sum) of the vectors is given by closing side of the triangle taken in the reverse order.

Parallelogram law of vectors :  It two vectors are drawn from a point so as to represent the adjacent sides of a parallelogram both in magnitude and direction, the diagonal of the parallelogram drawn from the same point represents the resultant of the two vectors both in magnitude and direction.


Introduction to Orion Constellation

Orion is one of the most famous constellations in the night sky. As it is located on the celestial equator, it can be seen from anywhere in the world. The ancient Greeks imagined the constellation Orion as a hunter. The constellation formed its present configuration around 1.5 million years ago. However, as constellations are not physical groupings, but just apparent positions of stars as seen from earth, the constellation may change its shape over time.

The Orion Nebula and Horseshoe Nebula

The Orion Nebula:

The Orion Nebula is a beautiful deep sea object. It can be observed through a pair of binoculars, and it is made of heavy clouds which contain nascent stars, dust, and luminous gases.

The Horsehead Nebula:

The Orion constellation also has another famous deep sky object – the Horsehead Nebula. It has a dark dust cloud which is in the form of a horse's head.

The Orion Constellation : Features

The image shows the position of Orion in the night sky.

Orion constellation

The most striking feature is the 'Belt of Orion' which has the three bright stars Mintaka, Alnilam, and Alnitak in a row, Around the belt, there are four other bright stars, which are

Betelguese: This star serves as the "right shoulder" of Orion. It is a massive red supergiant star which is close to ending its life in a supernova explosion. This star is the second brightest in the constellation.
Rigel: This star serves as the "left foot" of Orion, and is a blue supergiant. This star is also close to ending the fusion stage of its life. It is the brightest star in Orion, and the sixth brightest star in the whole sky.
Bellatrix: Bellatrix is the 'left shoulder" of Orion. It is known as the "Amazon Star"
Salph: This is the "right foot" of Orion. The star emits radiation in the ultraviolet range and is quite faint when compared to the other stars From the belt of Orion, you can also see three smaller stars forming a line. This is known as the sword of Orion. The middle star in this line is not a star, but the Orion Nebula.

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Algebra through the Ages

Author: Armando Townsend

By the moment of Plato, Greek math decide upon an extreme modify. The Greeks created a mathematical algebra exactly where conditions were displayed through sides of mathematical things, generally outlines, which in truth experienced words connected with each other. Diophantus (3rd hundred years AD), commonly known as since "the dad of algebra", had been an Alexandrian Ancient greek mathematics wizzard and the writer of a group of books called Arithmetica. These texts cope with correcting algebraic equations.

Although the word algebra comes from the Arabic terminology and of it's strategies from Arabic/Islamic mathematics, the origins could be watched to be able to before customs, the majority of especially ancient Indian mathematics, that in truth acquired an instant influence on Muhammad ibn Musa al-Khwarizmi (d. He or she resolved the linear indeterminate equations, quadratic equations, second buy indeterminate equations and equations together with several factors.

In 1545, the Italian math concepts wizzard Girolamo Cardano released Ars magna -The great artwork, any 40-chapter work of art in these people gave regarding the first-time a technique regarding fixing the common quartic equation.

The Ancient greek math wizzard Diophantus has generally already been recognized to as the "father of algebra" however in newer occasions there is significantly debate over whether or not al-Khwarizmi, who founded the self-discipline of al-jabr, court warrants in which title instead. People who help Diophantus indicate the indisputable fact that the algebra identified in Al-Jabr is a a bit more elementary as compared to the algebra discovered in Arithmetica which usually Arithmetica will be syncopated although Al-Jabr will be completely rhetorical. Individuals who assistance Al-Khwarizmi indicate the undeniable fact that he launched the strategies of "reduction" and also "balancing" (the transposition of deducted terms in order to the other area of a formula, that is, the termination of like conditions on reverse factors of the equation) that the expression al-jabr at first recognized to, which they gave an complete description of correcting quadratic equations, dependent on mathematical proofs, whilst managing algebra just as one self-sufficient self-control in it's own proper. His algebra appeared to become forget about worried "getting a group of problems being resolved, however a good exposition which starts with old fashioned terms in which the combos must offer all possible prototypes regarding equations, which henceforward obviously make up the correct item of research.Inch This individual also examined a formula simply because of the own benefit and "in a typical way, insofar because it will not basically emerge in the course of correcting an issue, however is especially referred to as on in order to define a good infinite course of difficulties."

The Local math wizzard Omar Khayyam will be credited together with determining the basic principles of algebraic geometry and located the general mathematical remedy of the cubic equation. Another Persian mathematics wizzard, Sharaf al-Din al-Tusi, identified algebraic and also report processes to numerous cases of cubic equations. He or she furthermore created the concept of a function. The Indian specialized specialist specialised mathematicians Mahavira and Bhaskara 2, the Local math concepts wizzard Al-Karaji, and the Chinese math wizzard Zhu Shijie, fixed numerous circumstances of cubic, quartic, quintic as well as greater-order polynomial equations utilizing record strategies. In the thirteenth century, the solution of a cubic formula by Fibonacci is rep of the start of the rebirth in Eu algebra. Because the Islamic planet had been reducing, the European globe was climbing. Which is right here which algebra was more produced.

François Viète's work on the close of the 16th hundred years represents the start of the classical discipline of algebra. In 1637, René Descartes introduced La Géométrie, creating analytic geometry and exhibiting modern day algebraic notation. Another crucial event in the more advancement of algebra has been the basic algebraic remedy of the cubic as well as quartic equations, created in the mid-16th hundred years. The idea of the determinant had been created by Western math concepts wizzard Kowa Seki in the Seventeenth century, implemented individually simply by Gottfried Leibniz a decade later on, for the goal of correcting techniques of synchronised linear equations making use of matrices. Gabriel Cramer furthermore do some perform on matrices and determinants in the 18th century.

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Informal And Formal Assessment With Multi Ability Classes

Informal And Formal Assessment With Multi Ability Classes
By Richard D Boyce

Formal assessment often creates fear within the student such that it prevents them from performing at their best. Therefore, it is important for the teacher to give students practice assessment items to allow them to gain experience in doing assessment under exam conditions to ease that fear. This informal assessment helps both the teacher and student gauge how they are progressing and what they need do to prepare for the real thing.

In classes with a wide range of ability, there are strategies you can use to help prepare all your students to do well in formal assessment by using your informal assessment as preparation.

Below are ideas to consider as part of your informal assessment:

1. It is important to find out what understanding of each new topic your class has as a starting point for your teaching.
2. Use frequent, quick, short tests to consolidate the basics.
3. Practice any new assessment task before you use it formally.
4. Make sure the format of your informal assessment reflects the formal assessment format.
5. If you divide your class into ability groups, set tests to reflect their progress.
6. You might read the questions aloud to the lower ability groups to help them understand what has to be done.
7. If you set a common test for the class, you could set different starting points for each ability group. This would allow all students to gain some success and the more able to progress to the more challenging questions.
8. Alternatively, consider testing each ability group separately with their own test or section of the main test.

When it comes to formal testing, consider the following. If you are responsible for your class's total assessment program, then some of the ideas below will give you more flexibility than you would have if the assessment program incorporated many classes.

1. In formal testing, separate the testing of the basics from problem solving. This reduces stress on students allowing them to perform at a higher level more confidently.
2. Make sure each unit of the test begins with an easy example and progress through a range of difficulties. This means most students will get a start.
3. If you are prepared to be adventurous, you might set a test, graded in difficulty, to allow the students to choose where they start and finish.
4. With some less able students in your class, you might decide to give them a clue to get them started. You should record this on their paper and make adjustments to the marking scheme.
5. All of the above may need to be tempered to the rules set up by the formal testing procedures mandated by outside authorities in upper high school year levels.
6. Give separate skills and problem solving tests. The skills test would have a set time while the problem solving test might be more time flexible.
7. Remind students that the basic skills are paramount to gaining a pass mark and are the essential basis for problem solving.
8. Your assessment tasks should always reflect your teaching pedagogue.

Overarching these ideas are two important strategies that the teacher must engage in with their classes.

No student will do well in any assessment program, no matter how hard they work, unless they have an effective examination technique. Teachers need to teach their students how to do an examination and constantly review those techniques before each assessment task. In addition, when reviewing the assessment task with their students, they must point out where students have made errors due to poor examination technique.

Finally, it is important for the teacher to model for students how to actually do each different type of assessment by using one of each and discussing how they would go about doing that type of assessment task. This should not be a one-off.

This article is one of many written by our author who had over 40 years' experience in the classroom. In his final years of permanent teaching, as Head of Mathematics, he was responsible for the total assessment program in his school. All of his experience on many examination and assessment topics can be found in his eBook, "The Exam Book" on the website http://www.realteachingsolutions.com

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Understanding the Dyslexic Learner's Weaknesses

Understanding the Dyslexic Learner's Weaknesses
By Candace Mondello

Dyslexic learners, or students, have many strengths, but for some reason the focus in the classroom seems to remain attuned on their weaknesses. Perhaps this is because dyslexic learners weaknesses frustrate educators who don't understand how to address the situation effectively. Also, it can appear to outsiders, that dyslexic learners as a group aren't trying their best, give up too easily, don't care about academics, or even purposely sabotaging their learning.

How Can this Group Be So Misunderstood?

Let's look closely at the specific weaknesses that plague dyslexic learners and discuss why these behaviors and practices can be misunderstood by educators and frustrating to the learner.

• Auditory Processing: The misconception is that these learners aren't listening. They tend to be the students who constantly say, "What did you say?" or "What are we supposed to do?" Although this can be aggravating when trying to motivate a classroom full of students, it's not the dyslexic learners fault. As the teacher speaks, most students process the information immediately and are already taking action before the teacher has completed the instructions. The dyslexic student is generally five words behind in short sentences, ten or more words behind in long instructions. It's not uncommon for a dyslexic learner to still be contemplating the first few words of the teacher's instructions while the rest of the class has moved on. The best way to describe it is if you're in a foreign language class and the teacher is speaking exclusively in the foreign language. If you aren't fluent, you're only catching words here and there and trying to piece together the gist of the conversation.


• Phonemic Awareness: Related to auditory processing, some, but not all, these students have difficulty differentiating the distinct sounds made by each letter. It's not automatic for them; they need to consciously remind themselves of each sound as they go.


• Auditory Discrimination: Also related to auditory processing, some, but not all, dyslexic learners have difficulty hearing words in sentences correctly. Think of the comedians who replace negative phrases with another phrase: For example, the person says, "Mind your business." The other character says, "What did you say?" The comedian replies, "I said, I'd do the dishes." It's very typical for dyslexic learners to mishear instructions.


• Memorizing: Dyslexics severely struggle with all memorizing: sequences (alphabet, numbers, lists), visual memory (like the memory game), and in math, multiplication tables. These students may be able to play instruments, but they will have trouble reading music.


• Directionality: Most people think that people with dyslexia don't know their right from their left. It may appear that way, but that's not exactly the case; it more closely relates to their inability to memorize and interpret. For example, a dyslexic will have to concentrate hard to interpret mirror images. With their letters, like b, d, p, q, they forget which way they are supposed to go in the quick decision time they have. They will SEE the b just like everyone else, but when they go to write it down, they can't remember which way the stick and the round part go. They can confuse vertically or horizontally - so a b could be written as a "d," or a "p." A "d" might be written as a "b," or a "q." The dyslexic learner is constantly making decisions based on the mirror images of the letters. Can you imagine how frustrating and confusing this can be to a child?


• Rapid Naming: Students with dyslexia will never be quick to answer questions. The process that they brain goes through to catalogue and retrieve information prevents them from performing quickly. It's best to warn these students ahead of time that you'll be calling on them to answer a question (and be specific what the question will be so they have time to process and prepare an answer).


• Reading and Spelling: These are classic signs of dyslexia. The student who can't read or spell no matter how much an adult works with them. It isn't necessarily the inability to read, as it is the inability to perform quickly. A dyslexic learner will substitute similar words under pressure. For example, if the word in the story is pony, but this learner isn't familiar with the word pony, he or she may substitute "horse" because it fits in the context of the story. Dyslexic learners may also substitute a word that is shaped the same as the word they are trying to figure out - for example, if the word is "trait" they may say "treat" because that is a familiar word. Dyslexic learners focus on the appearance of words - meaning the overall shape of words than the actual letters (zeroing in on the above or below the line shape).


• Organization: Dyslexics will stand out as students who are disorganized. But it won't be in just one area of their life, it will present in many areas.

* Time: Dyslexic learners are not able to estimate the time it takes to complete a project. They are usually far behind, appear to have not planned at all, or will become so engrossed in the task that they have no concept that they've done a task for hours.

* Space: Dyslexic students are often incapable of keeping track of their possessions. They are the ones with messing lockers, binders, backpacks, bedrooms, and have pockets full of "stuff." They often lose things: keys, homework, books for class, pen or pencil, and their agenda book. It is beyond their grasp to keep track of these things.

* Planning and management: Dyslexic learners minds are working so hard on keeping up with instructions, knowing which class they are supposed to be in, or which book they are supposed to have with them. If they have to follow rotating schedules, it can put their mind in overload.

• Written Expression: Students with dyslexias have the bleakest writing in the class. They usually use short, choppy sentences with minimal descriptors; and even that minuscule offering took them forever to put on paper. But if an educator takes the time to talk with the dyslexic learner, they'll discover that this student fully grasps the concept, has a complete, fully developed response that he or she can convey with astounding accuracy. This practice alone causes educators to assume that they students are lazy. However, most often the dyslexic learners brain is moving way faster than their hand can document. So along the way, they edit their own explanations down to the most simplistic explanation - thus the short, choppy sentences.


• Dysgraphia (or handwriting): Dysgraphia is simply (dys - difficulty with and graphia - writing); so, difficulty with writing. Dyslexics grip pencils with a death grip, their hands hurt, educators will often see them shaking out their hand. Their writing is hardly legible - sometimes the letters are cramped way too close together, other times the letters are huge and spread far apart. They also have a tendency to write up or downhill.

With a set of weaknesses like these, it's a wonder that dyslexic learners have been able to adapt and survive in classrooms where students are pushed to perform quickly, in teams, and with increasing accuracy. It appears to the dyslexic learner that mistakes are bad, so they tend NOT to be risk-takers - opting to stay within their comfort zone. In fact, they may have learned the hard way (by being ridiculed in class) to play it safe.

If you think your child or a student in your class may be dealing with dyslexia, show them some sympathy and take steps to provide scaffolding support for them to be able to demonstrate their intelligence.

Have more questions about helping your child get the BEST education possible? If your child struggles in school - this blog is your resource for finding the answers and getting results. Candee has been an educator in the public system for a decade. She LOVES helping parents connect with their child's education. Go to her website Dyslexia Testing Online and talk with her!! http://www.dyslexiatestingonline.com

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