FBA Reflection Essay Example

FBA Reflection Essay What are the strengths of using the ABA/PIP process for Improving behavior? This Is the first time I have ever used the ABA/PIP process. I found the structure and breakdown of the assessment categories very helpful for organizing data collected. Also this process can be extremely helpful for supplying information if needed to an PIPE for the future. B. Are there drawbacks to the system? If so, what are they and what could be done instead? I think there are two drawbacks with the ABA/PIP process. The first and most important in my opinion is the length of time that is needed to complete the process. The data collection is time consuming and requires lots of documentation. The second issue I have with this process is I believe it may draw focus away from the instruction a teacher Is giving. I think that If a teacher Is trying to chart behaviors correctly mentally, this Is distracting to the teaching process. Even though It may be minimal, this distraction still exists. C. Describe your own learning In completing the p recess. I learned a lot from this assignment; however I think two aspects were extremely important to the ABA/PIP process. I learned to be very specific when describing behaviors. Explain the behaviors in a way that another person can walk into your room and be able to identify that same behavior without question. Another important thing I learned from this assignment is to only record what you observe. I have to make a real effort to not draw conclusions. The ABA/PIP is about recording observed behaviors and conclusions are not facts. We will write a custom essay sample on FBA Reflection specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on FBA Reflection specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on FBA Reflection specifically for you FOR ONLY $16.38 $13.9/page Hire Writer D. How does the process support student behavioral learning? The ABA/PIP supports behavioral learning because it allows the teacher and support staff to come up with ways of dealing with the behavior problem. The staff can look at the data and find different interventions to help the student extinguish the unwanted behaviors. Some of these interventions can involve changing the seating arrangement, implementing a reward system, or moving a student to a different instructional area. E. Who should be involved in the process? There are a number of people that should be involved with the ABA/PIP process. Any teachers Involved with the students education should be there. Mainly the general education and special education teachers If applicable. At least one of the students parents should be Involved. Any professionals that work with the student can be Involved such as TO, Speech and Language Therapists, Psychologists, Guidance Councilor, and Social Worker. Basically, anyone who can be helpful in the ABA/PIP process if needed. F. How would this information impact student study team decisions? The ABA/PIP impacts the student study team by offering the data needed to implement different interventions. The team evaluates the information supplied and formulates intervention to discourage the behaviors in the least possible intrusive way possible for the student. G. How would this information impact student eligibility for special education services? If a student does not currently have an PIPE the ABA/PIP can provide excellent data to begin the process. If all interventions fail and the student continues to display the behaviors, the study team can requests the student move to the next step of being tested for an PIPE. The ABA/PIP shows the students progression with the behavior and provides a lot of background information to help the PIPE process along. H. How can information from an ABA/PIP be incorporated into an PIPE? The ABA/PIP can be incorporated into an PIPE by simply attaching it to the PIPE itself. Or the ABA/PIP information can be used to help diagnose an BED student which could be part of the PIPE.

I Pity the Full!

I Pity the Full! I Pity the Full! I Pity the Full! By Maeve Maddox Something strange has happened to the useful expression foolproof. Many writers are writing full proof to mean safe against misinterpretation, misuse, or failure: How to make a contract full-proof CREATING A FULL PROOF MARKETING CAMPAIGN Reduce Stretch Marks From Pregnancy Try These Full-proof Remedies Steps to a Full Proof Insect Free House 10 Full Proof Methods On How To Make Easy Income Online! The expression foolproof originated in 1902 as an Americanism meaning safe against the incompetence of a fool. It combines the words fool and proof. fool: a person lacking in judgment or prudence; a person who acts stupidly or recklessly proof: The evidence or argument that compels the mind to accept an assertion as true. Foolproof follows the pattern of such words as fireproof and waterproof and means that something has been tested and proved to withstand certain damaging agents. The growing use of the expression full proof in the sense of foolproof may stem from a reluctance to cause offense to the fool demographic. Yet the definition in Merriam-Webster Unabridged skillfully manages to define foolproof without the slightest mention of the wisdom-challenged portion of the population:    ï ¿ ¼ foolproof 1 : so simple, plain, or strong as not to be liable to be misunderstood, damaged, or misused 2 : guaranteed to operate without breakdown or failure under any conditions There probably are contexts in which the expression full proof can be justified. For example, one might demand full proof of identity. Although it seems to me that proof would suffice. The expression to make full proof occurs in the King James translation of the Bible: †¨But watch thou in all things, endure afflictions, do the work of an evangelist, make full proof of thy ministry. 2 Timothy 4:5 The expression and discussions of its meaning are to be found on many evangelical sites: What constitutes â€Å"full proof† in Paul’s advice to Timothy? I think make full proof of means to fulfill the ministry that God gives you to do. If you just cant bear to use an expression that you fear may suggest youre calling someone a fool, here are a few words you could substitute in certain contexts: infallible dependable reliable trustworthy certain sure guaranteed Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Expressions category, check our popular posts, or choose a related post below:70 Idioms with HeartHomonyms, Homophones, Homographs and HeteronymsHow Do You Fare?

Strategic Marketing Essay Example | Topics and Well Written Essays - 1500 words - 1

Strategic Marketing - Essay Example Strategies can be applied to any functional areas such as finance, marketing, production, human resource (Proctor, 2000). Organizations always try to gain competitive advantages by adopting various strategies for their functional areas. Marketing, when done with the objective of gaining strategic competitive advantages, is called strategic marketing. Generally marketing strategies are adopted for product, price, promotion, distribution, merchandise, market research in order to gain competitive advantages in the long run. All these concepts of strategic marketing are developed keeping in mind the aim of the business. Moreover each and every concept thus developed is directly or indirectly involved with the people because people and business inextricably linked. Leo Burnett, well known for his memorable quotations is one of the most renowned personalities in the world of advertising. He took advertising to a different height by creating icons such as Tony the Tiger and Jolly Green Giant. One of those quotes made by Leo Burnett is â€Å"What helps people, helps business’’. This report attempts to analyze the significance of this famous statement in the context of strategic marketing. Earlier business organizations were known only as profit making units. People then were not treated as the principle contributing factor in the process of making profit. They were treated as a means for achieving business objectives. This concept of business has changed significantly over the years. Today’s business leaders have realized that in order to achieve the desired objective, organizations must give enough importance to the people who are associated with the business. It is the people who make business and it is the people who run business. Nowadays while making any strategic decision, the primary focus is kept on the people who are associated with that decision. Organizations, before taking any decision try to have a clear

Marketing Planning and Strategy (Ethical Challenge) 1 Assignment

Marketing Planning and Strategy (Ethical Challenge) 1 - Assignment Example ntation may however target physically disabled people and people with health problems in order to determine involved costs and risk in product delivery for determining prices. This may harm members of the target population by subjecting them to higher prices based on their special needs. Raju (2009) argues that segmentation helps to meet needs of special groups but the associated disadvantage of cost may lead to greater harm than if products were offered without segmentation and prices remained uniform. In addition, such segmentation may for a basis for identification of the challenges facing the groups and therefore expose them to stigma. Consequently, targeting the physically disabled or people with help problems, with the aim of meeting their special needs at higher costs, are a violation of ethical practices. Targeting the segments in insurance coverage is an example. The segmentation may induce higher cover cost and limit the group’s ability to afford cover and access car e. In addition, the segmentation may create the impression that the segment have poor health and induce stigma against members of the segment to worsen their welfare through induced emotional instability (Brenkert and Beauchamp,

Determine the value of knowledge as a competitive weapon to modern Essay

Determine the value of knowledge as a competitive weapon to modern organisations - Essay Example nt position in this as they are the real â€Å"knowledge producers† and hence any new knowledge that a company looks for is produced courtesy through these people. (Rocca, 1992) Competitive success is basically commanded by the companys capability to harness and indeed develop new forms of knowledge, gained either by observation or by experience attained, which can be called as assets that in turn create the required â€Å"core competencies† of the said organization. While these competencies do exist in many forms, learning on the part of a particular company plays a pivotal role, which eventually ventures into other resources of knowledge to generate high-class and exceptional showing from the company’s employees. (Dunn, 2001) Core competencies, which usually flow out of a company, provide characteristic benefits to both the customers as well as any other individuals attached with it. These are generally espied as being the foundation of forming a competitive advantage within the said company. It is quite true that there is a host of ways in which new knowledge within a company is facilitated within its ranks. The need here is to classify the m with respect to their importance, which include the cultural infrastructure can be changed within a company so as to gather some proportion to the fact of the actual remains that have to be taken care of in the company and in its employees’ minds. It demands idealization and disclosure of everlasting knowledge that is created over a certain period of time. This usually requires basic changes to already set cultural notions in companies and more so in the minds of their employees. (Fahy, 1996) Also operational infrastructure is changed through human resources organizational practices that are managed and received by the employees and other people in a different way altogether. A basic revamp of a knowledge-centered company is required here, which would involve the job ladders, compensations, work locales and command and

Policing Of Gangs In Rural And Urban Areas Criminology Essay

Policing Of Gangs In Rural And Urban Areas Criminology Essay Gang related crimes and activities are being exported to rural communities and gangs are migrating to more rural areas. Social reasons and drug trafficking are the primary reasons for the spread of drug use and why gangs are developing in rural areas. When concerning the exporting or spreading of urban crimes to rural areas, the migration of gangs and their criminal activities plays a large role. Police strategies make it hard for gangs to stay inside of the metropolitan areas, so gangs are moving their operations to places less known to the police. Gang members find a base for their operations and seek out troubled or lost youth to join their gang. When concerning the methods of policing, policing strategies, and crime, there is a big difference between rural environments and urban environments. Gang Identification There are significant indications which identity gang members in a particular group or gang. These indications are specific tattoos, graffiti tags, gang colors, and self identification by youths (Weisheit Wells, 2001). Law enforcement officials rely on visual impressions when determining whether or not a youth, or any individual is in a gang. When gang members try to keep a low profile, this can make it especially hard for law enforcement to identify them individually or as a group. Gang members keep low profiles by not getting tattoos that signify their gang, by not wearing any specific color in their dress, and by withholding the use of gang signs. Many suburban and rural communities are experiencing rises in gang related crimes and violence. However, the impact of gangs is worse the mores densely populated areas, especially areas with populations of 50,000 people or more (Howell, 2006). However, gangs are attracted to rural communities because this way they can grow their drug distribution areas, they can hide from or escape from police, and recruit new members into their gangs. Relocation of Gangs Gangs use tools to recruit new gang members and one of these tools is the Internet. The Internet makes communication between them and other gang members in other parts of the country or even in other foreign countries possible. These gangs commit about 80% of the crime in many communities (National Gang Intelligence Center, 2009). Reports of gang related homicides are mainly concentrated in the largest cities in the United States, because gangs are more persistent in these large cities. Youth gangs are also responsible for a disproportionate number of homicides (Howell, 2006). Some of the more common kinds of gang related crimes are smuggling aliens, armed robbery, assault, auto theft, trafficking drugs, fraud, identity theft, home invasions, and murder (National Gang Intelligence Center, 2009). Gangs deal with the trafficking of illicit drugs such as marijuana and cocaine in most suburban communities. The impact of gang migration on local gangs is not as large as once thought, but it is still an issue. According to a 2004 National Gang Youth Survey study, which involved information they received from law enforcement of gang member migration, the results showed that a small number of agencies had reported that more than half of the documented gang members had migrated from other areas (Howell, 2006). Of the agencies that experience a larger percentage of gang migration, 45% reported the reason behind the migration was due to social reasons, such as family. They also reported that 23% was due to the drug market, 21% was due to evading law enforcement, and 18% was because of other illegal ventures (Howell, 2006). Social reasons or issues are the driving force behind gang migration. Gangs spread out into smaller regions or towns because the access to transportation is easy to obtain. The easy access to transportation makes it easier to traffic drugs. Gangs are attracted to trafficking drugs out from small rural areas because of the large profits they can make off of drugs in smaller towns. The street value of drugs in smaller towns is two to three times higher than the value in metropolitan areas (Donnermeyer, 1995). These gang members establish or set up drug dealing businesses or franchises in these rural communities because they can move drugs more securely and safely and because the latest and most popular drugs are available more speedily (Donnermeyer, 2005). Even though there is a focus on urban street gangs in rural areas, biker gangs have a history of criminal activity in rural settings (Muhammad, 2002). It is also easier in rural areas for gang members to get the local drug dealer(s) to cooperate with them in drug transactions. Gangs not only migrate from urban settings or regions to rural areas, they also migrate from rural regions to urban areas. These types of gangs are generally known as hate groups. These hate groups include white supremacist groups. There are many members of these white supremacist groups such as Members of the Aryan Nation and Skinheads that are born and raised in rural areas (Donnermeyer, 2005). Since these white supremacist gang members are born and raised in rural areas, they are more likely to first establish gang operations in these rural areas. Once they have their drug franchises established in rural areas, they then reach out and get connected with gang members in the larger cities and then are able to move and set up their operations in the larger metropolitan areas (Donnermeyer, 2005). Once they are settled into the urban area, they have easier access to and can target minority groups. Urban Gangs and Rural Gangs There are many similarities between metropolitan and rural gangs. Metropolitan and rural gangs both are strongly connected with social stability and they both are molded by characteristics of the population (Weisheit Wells, 2001). According to a study or survey based on police reports on gangs between the years of 1996 and 1998, among the agencies in nonmetropolitan areas; 22.6 percent reported persistent gang problems, 57 percent reported a persistent absence of gangs, and 20.4 percent reported transitory gang problems (Weisheit Wells, 2001). The biggest difference in urban and rural gangs is the role economic issues have on these groups. Economic factors are more important to gangs in urban areas than gangs in rural areas. Gang activity in metropolitan areas has a different relationship to poverty as compared to gang activity in rural areas (Weisheit Wells, 2001). Gangs are more likely to be reported in nonmetropolitan areas that are growing economically. Police Response to Gangs The practices of policing are different from one jurisdiction to another and being able to gain information on the different styles of police behavior can bring about a detailed look into the role of the police in urban and rural communities. There are various types of policing styles when it comes to different rural regions. These differences change from region to region and from one jurisdiction to the next. In one region police may be more involved dealing with illegal immigration and in another region police may be more involved with drug trafficking and/or illegal crops. There are specific issues that influence law enforcement operations in rural communities. These aspects are the informal social control among individuals in the rural community, rural citizens not trusting the government, and keeping their inside problems to themselves (Falcone, Weisheit, Wells, 1994). Citizens in rural communities are less likely to report crimes and because of this, there is less information gathered on the precise number of crimes that happen in these rural communities. One way police deal with or respond to gangs in their jurisdiction is through gang training. Police have training on technical assistance thatà ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¾Ã‚ ¢s needed when dealing with gangs and when concerning forming task forces. The most frequent response to gang activity is suppression through strict enforcement, such as the zero tolerance policy, which is more associated with urban police (Weisheit Wells, 2001). It has been suggested that zero tolerance strategies are easier to implement in smaller communities where gang members were easier to identify. Police use the community and stress the importance of prevention when it comes to gangs and gang activity (Weisheit Wells, 2001). When it concerns youth in gangs and that have stronger bonds with the community, police tend to focus more on family pressure than on prevention. Conclusion There are differences in crimes and policing concerning gangs in rural regions and gangs in urban regions. It seems that the differences of gang related crimes and policing efforts in various jurisdictions and regions may be decreasing but the spread of gang related crimes is finding its way into rural regions. There needs to be more research on rural gangs so rural law enforcement can better understand, be better trained, and be better equipped to deal with these gang members and to be able to prevent and reduce gang related activities. Even though law enforcement agencies in rural areas may be lacking when it comes to tools and resources, rural police agencies seem to be more efficient and more respected by the public. .

Essay --

The story of â€Å"Unwind† revolves around three main characters that are all scheduled to be sent to a harvest camp and unwound. Connor is a sixteen year whose family believes that he has caused too much trouble in society. Risa is a ward of the state, and due to budget cuts, is too expensive to be kept in the program. Lev is tithe, and individual that has been born with the purpose of being unwound. Connor one day discovers an unwind order in the house and decides to run away. With the help of an honest truck driver, Connor manages to slip away. However, Connor keeps his cell phone and the tracker inside gets him caught. The police attempt to arrest Connor but he resists arrest, runs through the traffic on the road, and grabs a tithed to use as a human shield. This event in turn causes a bus full of state home wards to spin out of control and overturn. Risa is one of the individual on that buss. Risa, Connor, and Lev all run into the woods. The next morning, while the thre e are gathering supplies such as food and clothes, they come across a storked baby on the door step. Due to past experiences, Connor decides to put all three of them in risk and decides to pick up the baby while a police car slowly passes nearby. Risa, Connor, Lev and the baby all get onto the school bus in hopes of not being suspected by the police car. Once they arrive at the school, they find the nearest bathroom and hide in it with the baby. Lev sees this as an opportunity to escape. As a tithe, he believes that it is an honor to live with the purpose of being unwound, so he finds his way to the school office and turns himself and Connor and Risa in. He then asks for a call, and calls his pastor, who to Lev’s surprise informs him that his face was purposely k... ... who explode inside of the unwinding facility. Lev wants to do the same, but changes his mind, saves Connor, and confesses to the police. Connor wakes up in a hospital and is informed that he was the unwilling recipient new eye and a hand that evidently belonged to Roland. The nurse also gives Connor a fake ID to save him from being unwound. Risa is left paralyzed from the waist down because her band was playing when the clappers exploded, but she refuses treatment because cripples cannot be unwound. Lev is also saved. The explosive liquid is being taken out from his blood stream and his uncle is applying for guardianship. Risa and Connor take over the admiral’s job because the admiral is too weak after his heart attack. Because the admiral did not want a heart of an unwound, his heart only function 25% of its full potential. However, he is still alive and well.

The Bioethics Debate

Kristi Ellis Mrs. Scheidt English 1301. 174 11 October 2012 Paper #2 – The Bioethics Debate In â€Å"Patenting Life,† by Michael Crichton, and â€Å"Bioethics and the Stem Cell Research Debate,† by Robyn S. Shapiro, they discuss gene patenting, medicine, stem cell research, and the laws of bioethics. According to Crichton and Shapiro, humans are all born with genes, stem cells, and organs that are part of our natural world, yet when the law tries to put limits on these rights it becomes unethical. Crichton and Shapiro both agree about the controversial issues surrounding science and medicine.They both point out the unethical issues, the innovation in medicine, and the impact on science and medicine in relation to the law. In both essays Crichton and Shapiro list many immoralities that arise out of bioethical issues. For instance, Crichton refers to an example of the Canavan disease in which the process to find a cure was halted due to gene patenting. It was a pri me example of an issue that was unethical because the owner of the gene for the disease could choose whether or not to charge for a test and choose how much to charge for it, which blocks medical innovations.Crichton states, â€Å"There is no clearer indication that gene patents block innovation, inhibit research and put us all at risk† (432). Crichton goes on to say that genes are part of humans naturally and should not be privately owned (431). In comparison, Shapiro explains although embryonic stem cells give promise to the medical field, many ethical issues surround it such as the destruction of the embryo. Shapiro also writes that those who denounce embryonic stem cell research believe the embryo is already a human being with rights from conception, while others believe that human rights do not exist prior to birth (435).Additionally, medical advancement is critical for innovation in both essays. Crichton states that gene patenting prevents medical testing and slows medi cal advancement. Not only does it halt research, but it causes the costs of medical testing to rise because the owner can charge whatever he wants (431). He mentions doctors cannot get information on if a medication will or will not work on someone because the lack of quality tests. Crichton says â€Å"For years we’ve been promised the coming era of personalized medicine – medicine suited to our particular body makeup.Gene patents destroy that dream† (432). In contrast, Shapiro states that stem cells are important to the medical field because they can turn into a wide array of cell types that can help people with diseases such as diabetes, nervous system diseases, and Parkinson’s disease (434-35). In addition, he says stem cell research could provide important information on how human organs and tissues develop, which could lead to development of new medications (435). In both sources, the law plays a significant role in the unethical issues surrounding s cience and medicine.Crichton mentions how the United States Patent Office issued gene patents by mistake because of misinterpreted Supreme Court rulings. The issue of gene patents make it hard for people to donate their genes because most of the genes are privately owned (431). Crichton states that two congressman sponsored the genomic research and Accessibility Act, a bill that would ban patenting genes in nature (432). Shapiro denotes the growing importance of the law surrounding bioethical issues. He cites the United States Supreme Court cases of Roe v.Wade and Stenberg v. Carkart which dealt with a partial birth abortion law. Shapiro states, â€Å"In state courts, bioethical considerations inform judges’ balancing of patient healthcare confidentiality with a â€Å"duty to warn† of potentially dangerous patient behavior (433). The most significant law Shapiro cites is the Dickey Amendment which prohibits federal funding for embryo research (436). Shapiro mentions i n addition to federal funding restrictions, many states have laws that limit embryonic stem cell research.Lastly, he cites the eligibility of federal patent protections significantly, the Thomson Patents (437). In conclusion, both Crichton and Shapiro can conclude the topics of gene patenting and embryonic stem cell research are unethical in some way. Although gene patenting blocks innovation and embryonic stem cell research promotes it, they both have laws that limit the impact on the world of science and medicine. According to Shapiro, â€Å"As these issues have moved to the center of public debate, the law has assumed an increasingly important place in the discipline of bioethics† (433).Thus, when the law puts limits on human genetics it becomes unethical and immoral according to both essays in this bioethical debate. WORD COUNT: 740 Works Cited Crichton, Michael. â€Å"Patenting Life. † Perspectives on Contemporary Issues: Readings Across the Disciplines. 6th ed. E d. Katherine Anne Ackley. Boston: Wadsworth/Cengage Learning, 2012. 431-432. Print. Shapiro, S. Robyn. â€Å"Bioethics and the Stem Cell Research Debate. † Perspectives on Contemporary Issues: Readings Across the Disciplines. 6th ed. Ed. Katherine Anne Ackley. Boston: Wadsworth/Cengage Learning, 2012. 433-438. Print.

The Five Different Approaches to Motivation

The first being instincts which are the patterns of behavior that are biologically determined rather than learned. Fact: people and animals are born preprogrammed with sets of behavior's essential to survive. The second being the drive-reduction approach. It suggests that a lack of some basic biological requirement such as water produces the drive to obtain the water. The third being the arousal approach in which each person tries to maintain a certain level of stimulation and activity. The forth would be the incentive approach which it suggests that motivation stems from the desire to obtain valued external goals, or incentive. The fifth would be the cognitive approach and it suggests that motivation is a product of a person's thoughts, expectations, and goals-their cognitions. The one approach i chose would be the incentive approach. I feel that i am more motivated when there is some incentive involved because i know at the end of the day i am going to be rewarded for my assistance. For example: My boss wants me to do some work for him that might take two hours. The two hours would be over-time at twenty for dollars an hour. Fortunetly he say for the work, off the clock he would give me two sixty-five dollar tickets to the season opener for The Pistons at The Palace of Auburn Hills. The offer of the tickets gave me incentive to do the work and it only took me an hour and fifteen minutes to finish it.

Circles on ACT Math Geometry Formulas and Strategies

Circles on ACT Math Geometry Formulas and Strategies SAT / ACT Prep Online Guides and Tips One of the ACT’s absolute favorite shapes is the circle (or at least we assume so, given how often circles show up on the test). You will not be given any formulas on the ACT, so you’ll have to know and memorize the ins and outs of how circles work before test day. And, considering how often circles show up, mastering circle problems is definitely in your best interest. This will be your complete guide to ACT circles, including areas, circumferences, degrees, arcs, and points on a circle. We’ll take you through what these terms mean, how to manipulate and solve for various aspects of a circle, and how to tackle the most difficult ACT circle questions you may see on test day. What Are Circles? A circle is formed from the infinite number of points equidistant (the same distance) from a single pointthe center of the circle. A circle is also a two dimensional shape, which means it is completely flat. So any and all straight lines drawn from the center will exactly hit the edge of the circle as long as all the lines are of equal length. Degrees and Radians A circle is measured in either degrees or radians. Both are ways to express either the whole circle or pieces of the circle. A full circle has 360 degrees. A semicircle (half a circle) has $360/2 = 180$ degrees, which is why a straight line equals 180 degrees. To find a piece of a circle, you must find it in relation to 360 degrees. So an eighth of a circle is $360(1/8) = 45$ degrees, and a third of a circle is $360(1/3) = 120$, etc. Just as a circle has 360 degrees, you could also say that it has $2Ï€$ radians. You find the radian measure of pieces of a circle the exact same way that you found pieces of a circle using degrees. So an eighth of a circle in radians is $2Ï€(1/8) = Ï€/4$ radians and a third of a circle in radians is $2Ï€(1/3) = {2Ï€}/3$ radians, etc. (For more information on radians, check out our guide to ACT trigonometry.) Circumference The circumference is the edge of the circle. It is made from the infinite points equidistant from the center. Diameter A diameter is any straight line drawn through the center of the circle which connects two opposite points on the circle’s circumference. Radius The radius of a circle is a straight line drawn from the center to any point on the circle’s circumference. It is always half the diameter. Tangency Circles are often described as â€Å"tangent† with one another. This means that they touch at exactly one point on each circumference. They might be inside one another (as in this picture), or they may touch "externally" at a single point. p p="" Ï€ (pi) If you’ve taken a geometry class, then you are also probably familiar with Ï€ (pi). Ï€ is the mathematical symbol that represents the ratio of any circle’s circumference to its diameter. It is usually expressed as 3.14(159), but its digits go on infinitely. (For more information on ratios, check out our guide to ACT ratios.) Let's say we have a circle with a particular diameter (any diameter will do). Now let's line up this same circle so that we have a series of the same diameter measurement all in a row. Now, if we pick a point on the circumference of the circle and line it up at the beginning of the line, we can then "unroll" the circumference to see how long it is. Once we unroll the circumference and lay it out flat, we can see that it measures a little over 3 times the diamter of the circle (specifically, 3.14159, or Ï€, times the diameter). No matter what the diameter of the circle, the circumference will always be Ï€ times that diameter. So, if a circle’s diameter is 1, then its circumference is Ï€. And if its diameter is 2, then its circumference is 2Ï€, etc. You know all your definitions (whoo!), so now what? Well it's time to put the pieces together into our trusty circle formulas! Circle Formulas You will not be given any formulas on the test, so you will need to know these ACT circle formulas by heart in order to solve your circle problems. Let's look at all the formulas you'll need. Circumference $$c = Ï€d$$ Because Ï€ is the relationship between a circle’s diameter and its circumference, you can always find a circle’s circumference as long as you know its diameter (or its radius) with the formulas: $c = Ï€d$ or $c = Ï€2r$ Because the contestant must run around the course, she is running the circumference of the circle. And we are told that she will do so 3 times in order to complete her race. So a 1-track loop would be: $c_{1 \loop} = Ï€2r$ (We are told that the radius is â€Å"$R$† so we can leave it as is.) And a 3-track loop would be: $c_{3 \loop} = (Ï€2r) * 3$ $Ï€6r$ So our final answer is K, $6Ï€r$ Area $$a = Ï€r^2$$ You can also use Ï€ to find the area of a circle as well, since a circle’s area is closely related to its circumference. (Why? Because a circle is made of infinite points, and so it is essentially made up of infinite triangular wedgesbasically a pie with an infinite number of slices. The height of each of these wedges would be the circle’s radius and the cumulative bases would be the circle’s circumference.) So you would be able to find a circle’s area using the formula: $a = Ï€r^2$ The dog’s leash represents the radius of the circle, because the dog can run 9 feet in any straight line from the center of the stake in the ground. So we must find the area of the circle using 3.14 for $Ï€$ and 9 for the radius. $a = Ï€r^2$ $a = (3.14)(9^2)$ $a = (3.14)(81)$ $a = 254.34$ So our final answer is D, 254. Arcs $$c_\arc = Ï€d({\arc \degree}/360 °)$$ $$a_{\arc \sector} = Ï€r^2({\arc \degree}/360 °)$$ In order to find the circumference of a circle’s arc (or the area of a wedge made from a particular arc), you must multiply your standard circle formulas by the fraction of the circle that the arc spans. To determine the fraction of the circle that the arc spans, you must have the degree measure of the arc and find its measure out of the circle’s full 360 degrees. So if you want to find the circumference of an arc that is 90 °, it would be $1/4$ the total area of the circle. Why? Because $360/90 = 4$ (in other words, $90/360 = 1/4$). In order to find the circumference measure of an arc, we must have both the degree measure and the circle’s radius or diameter. Luckily, we have all of these. The degree measure of the arc, we are told, is 45. The top diagram tells us that the diameter of the circle is 24 feet. So the circumference of our arc is: $c \arc = Ï€d({\arc \degree}/360 °)$ $c \arc = Ï€24(45/360)$ $c = 3Ï€$ Because we can see that our answer does not use units of $Ï€$, let us convert our answer to digits by replacing $Ï€$ with 3.14. $3Ï€ = 3(3.14)$ $9.42$ We have successfully found the measurement of our arc, but we are not quite done. The question is asking us to find the full length of the zipper, which spans the length of the arc as well as the radius of the circle. This means we must find our radius and add it to our arc measurement. The radius of the circle is 12. Why 12? Because our diameter is 24 feet and a circle’s radius is always half the diameter. $24/2 = 12$ So when we add our arc measure and our radius together, we get: $9.42 + 12 = 21.42$ And the closest answer to match our measurement of 21.42 is answer choice G, 22. This means our final answer is G, 22. With a dash of formula knowledge (and, presumably, some eye of newt), you can solve any and all circle problems. Magic! Typical Circle Questions on the ACT Circle problems on the ACT will be one of two typesdiagram problem or word problem. Let us look at each type. Diagram Problem A diagram problem will give you a diagram from which to work. You must use the visual you are provided and either find a missing piece or find equivalent measurements or differences. Helpful hint: often (though not always), the trick to solving a circle problem is in finding and understanding the radius. All lines drawn from the center to the circumference are radii and are therefore equal, and this will often play a vital part to solving the whole problem. We are hoping to find the one statement that is NOT true, so let’s go through them and see which ones are accurate and inaccurate. Answer choice F says that angle TUM is 65 °. Well, we know that angle TMU must be 50 ° because it is opposite angle RMS and opposite angles are equal. (For more on this, check out our guide to ACT lines and angles.) We also know that lines TM and MU are equal. Why? Because they are both radii of the circle (lines from the center to the circumference of the circle) and so they must be equal. This means that the triangle TMU is an isosceles triangle, which means that angles MTU and TUM are equal. There are 180 ° in a triangle, so if we subtract 50 °, we get: $180 - 50 = 130$ This means that each of the angles MTU and TUM add up to equal 130. And, because they are equal, we can find their measure by dividing 130 ° in half. $130/2 = 65$ So F is correct, angle TUM is 65 °. Now let’s look at option G, which says that lines RS and TU are parallel. We know this to be true. Why? Because together, the triangles form two diameters of the circle. And so straight lines downwards from where those diameters touch the circumference of the circle will be parallel. H says that arc TXU measures 50 °. We already know this to be true, because angle RMS measures 50 ° and its opposite angle is TMU, which must also measure 50 °. Because the arc TXU contains and is made from angle TMU, its measurement must also be 50 °. Answer choice J says that line RM = line TM, which we also know is true. Why? Because they are both radii of the circle and so they must be equal. By process of elimination, this must mean that K is wrong (and thus our final choice), but let’s make sure. K says that lines RS and SM are equal, but we already know this cannot be true. Why? Because RM and MS are both radii and so they must be equal and angle RMS is 50 °, which means the triangle is not equilateral. Because it is not an equilateral triangle, lines RM and TM cannot be equal. (Note: if this question was at all confusing to you, check out our guide to ACT triangles) So our final answer is K. Word Problem Word problem questions about circles will describe a scene or situation that revolves around circles in some way. As you saw earlier in the section on areas and circumferences, word problem questions will often be a little more straightforward than a diagram question, as the picture is not given to you. When given a word problem question, it is a good idea to do your own quick sketch of the scene. This will help you keep all the details in order. Because this is a word problem, let us make our own picture of the scene. First, we know that we have a circular table. We are told that is is 3 feet in diameter (in other words, 36 inches), so let us draw it. Now, the tablecloth will be rectangular and will hang down at least 5 inches from any point on the circular table. Finally, we need 1 more inch of tablecloth on every side (to sew down as a finishing touch). Now, we can simply count our inches from top to bottom (or side to side) in a straight line. This will tell us the minimum length required for the fabric. If we go from top to bottom, we can see that we will need: $1 + 5 + 36 + 5 + 1$ $48$ inches of fabric. Our final answer is K, 48. Real life (and delicious) applications of circumferences and areas. How to Solve a Circle Problem When confronted with a circle problem, remember to employ these ACT math strategies: #1: Write down your formulas at the beginning of the math section As soon as you open up your ACT math section, take 20 seconds and write down your formulas. This way, you’ll have them as a reference for the rest of your allotted time, and you won’t worry about forgetting them in the heat of the moment when you’ll need them later on. #2: Draw your own diagrams If you’re not given a diagram, draw one yourself! It doesn’t take long to make your own picture and doing so can save you a lot of grief and struggle as you go through your test. It can be all too easy to make an assumption or mix up your numbers when you try to perform math in your head, so don’t be afraid to take a moment to draw your own pictures. And if you are given a diagram, draw on it too! Mark down congruent lines and angles, write in your radius measurement or your given angles. Mark any and all pieces of information you need or are given. The reason not everything is marked in your diagrams is so that the question won’t be too easy, so always write in your information yourself. #3: Analyze what’s really being asked of you All the formulas in the world won’t help you if you think you’re supposed to find the area, but you’re really being asked to find the circumference. Always remember that standardized tests are trying to get you to solve questions in ways in which you’re likely unfamiliar, so read carefully and pay close attention to the question you’re actually being asked. #4: Use your formulas Once you’ve verified what you’re supposed to find, most circle questions are fairly straightforward. Plug your givens into your formulas, isolate your missing information, and solve. Voila! A tasty mathematical conspiracy? Test Your Knowledge Now let's put your circle knowledge to the test on these real ACT math problems. 1. 2. 3. Answers: B, B, H Answer Explanations: 1. In order to determine the degree measure of a section of a pie chart, we must determine the fraction (or percentage) of the sector we’re working with compared to the whole amount of the circle. In this case, we want to know what fraction of people total voted for Gomez in order to find how much of the pie chart the Gomez votes should be allotted. If 40 people out of 200 voted for Gomez, then the Gomez votes are: $40/200$ $1/5$ of all the votes total. Because Gomez votes are $1/5$ of the total votes, then they should take up $1/5$ of the pie chart. A circle is 360 degrees. So: $(360)(1/5) = 72$ The arc sector of the Gomez votes will be at a 72 degree angle in the pie chart. So our final answer is B. 2. We are given a diameter of 8 and we need to find the perimeter of the entire figure of two semicircles and a square. Together, the two semicircles make a full circle with a diameter of 8, and their circumference makes up part of the perimeter. This means we must find the circumference of the circle the two semicircles make when put together. $c = Ï€d$ $c = Ï€(8)$ So the circumference of the circle the two semicircles make is $8Ï€$. (Because we are dealing with semicircles, you could also find half of each of their circumferences by saying: ${1/2}c = 8Ï€$ = $4Ï€$. Each of their circumferences would be $4Ï€$, so together, they would make: $4Ï€ + 4Ï€ = 8Ï€$. Either way, the total circumference of the perimeter would be $8Ï€$.) Now we must add that to the rest of the perimeter, which is formed by part of the square. Two sides of the square (both measuring 8) make part of the perimeter, so we have: $p = 8 + 8 + 8Ï€$ $p = 16 + 8Ï€$ So our final answer is B. 3. Because we are working with circles, we know that lines PS and PT are radii. Why? P is the center of the circle and points T and S lie on the circumference, so we know that the lines connecting them are radii. Because PS and PT are equal and angle PST is 30 degrees, that means that angle PTS is also 30 degrees. Why? Angles opposite equal lines are equal (for more on this, check out our guide to ACT triangles). This means we can find angle TPS as the shape is a triangle (which has 180 degrees total). $180 - 30 - 30 = 120$ So angle TPS = 120 degrees. Now that we have found angle TPS, we can also find angle RPS. Together, the two angles make a straight line, which means that they must equal 180 degrees total. (Why? Because a circle is 360 degrees and a semicircle is 180 degrees. A straight line will therefore always measure 180 degrees.) $180 - 120 = 60$ This means that angle RPS = 60 degrees. And since angle RPS forms our arc, our arc measure it 60 degrees. So our final answer is H. Puppies cannot lie; it is scientific fact. You solved your ACT math problems and are, indeed, awesome. The Take-Aways Circle problems are quite common, but most of them are slight variations on the same themes of area and circumference. On the ACT, the most useful part of any circle is generally the radius and, once you’ve gotten used to thinking that all radii are equal, then you will often be able to breeze past even the trickiest of ACT circle problems. Remember your formulas and keep a clear head about what’s being asked of you and you will be able to take out a significant portion of the ACT geometry section with circles alone. What’s Next? Now that you know all there is to know about ACT circles, make sure you're up to speed on all the other math topics on the ACT. Whether you need to brush up on solid geometry, trigonometry, ratios, or integers, you'll find what you need in our ACT math guides. Running out of time on ACT math? We'll show you the tips and tricks you need in order to beat the clock. Looking for a math tutor? Check out our guides on how to find the perfect ACT tutor for your needs. Angling to get a perfect score? Our guide to an 800 on the math (written by a perfect-scorer) will tell you exactly how to reach those score goals by test day. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

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