Breaking Down the Scale Method for Weighted Averages

Before you dive into this post, make sure you are are familiar with  the Scale Method for weighted averages,  which we have discussed in previous posts.   We know that the scale formula of weighted averages is the following: w1/w2 = (A2 Aavg)/(Aavg A1) One point  of confusion for many test takers regarding this formula is  figuring out  what A1, A2, w1 and w2 actually are. Here is the simple answer: they can be anything. You can choose to set up the solution as you want. The only thing is that it  must be consistent across. A1 and w1 could be the parameters of either solution; A2 and w2 will be the parameters of the other solution. We could also work with the concentration of either ingredient of the solution. We will illustrate this point with an example GMAT question: A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume? (A) 4/3 (B) 5/3 (C) 7/3 (D) 8/3 (E) 10/3 Now, we have been given two solutions that we have to mix: A container holding 4 quarts of alcohol and 4 quarts of water Water (which means it has no alcohol in it) When these solutions are  mixed together, they give us a mixture that is 3 parts alcohol to 5 parts water by volume. So, what are A1, w1, A2, w2 and Aavg? We can work with the concentration of either alcohol or water. Let’s first see how we can work with the concentration of water: Method 1: A1 is the concentration of water in the solution of 4 quarts of alcohol and 4 quarts of water. So A1 = 4/8. w1 is the volume of this solution. A2 is the concentration of water in the solution of water only. So A2 = 8/8 (we want to write this in the same format that we write A1 in.) w2 is the volume of this solution. Aavg is the concentration of water in the final solution i.e. 5/8 w1/w2 = (A2 Aavg)/(Aavg A1) w1/w2 = (8/8 5/8)/(5/8 4/8) w1/w2 = 3/1 So 3 parts of the solution with alcohol and water should be mixed with 1 part of pure water. Method 2: A1 is the concentration of water in pure water. So A1 is 8/8 w1 is the volume of this solution. A2 is the concentration of water in the solution of 4 quarts alcohol and 4 quarts water. So A2 is 4/8 w2 is the volume of this solution. Aavg is the concentration of water in the final solution i.e. 5/8 w1/w2 = (A2 Aavg)/(Aavg A1) w1/w2 = (4/8 5/8)/(5/8 8/8) w1/w2 = 1/3 So 1 part of water should be mixed with 3 parts of the solution with alcohol and water (same result as above). Now we will see how to work with the concentration of alcohol. Of course the result will be the same. Method 3: A1 is the concentration of alcohol in the solution of 4 quarts alcohol and 4 quarts water. So A1 is 4/8. w1 is the volume of this solution. A2 is the concentration of alcohol in the solution of water only. So A2 is 0/8 (to write in the same way as above) w2 is the volume of this solution. Aavg is the concentration of alcohol in the final solution i.e. 3/8 w1/w2 = (A2 Aavg)/(Aavg A1) w1/w2 = (0/8 3/8)/(3/8 4/8) w1/w2 = 3/1 So 3 parts of the solution with alcohol and water should be mixed with 1 part of pure water (same as above). Method 4: A1 is the concentration of alcohol in pure water. So A1 is 0/8 w1 is the volume of this solution. A2 is the concentration of alcohol in the solution of 4 quarts alcohol and 4 quarts water. So A2 is 4/8. w2 is the volume of this solution. Aavg is the concentration of alcohol in the final solution i.e. 3/8 w1/w2 = (A2 Aavg)/(Aavg A1) w1/w2 = (4/8 3/8)/(3/8 0/8) w1/w2 = 1/3 So 1 part of pure water should be mixed with 3 parts of the solution with alcohol and water (same result as above). Hope there will be no confusion about this in future. Getting ready to take the GMAT? Check out one of our many  free GMAT resources  to get a jump start on your GMAT prep. And as always, be sure to follow us on  Facebook,  YouTube,  Google+, and  Twitter  for more helpful tips like this one! Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the  GMAT  for Veritas Prep and regularly participates in content development projects such as  this blog!

Math Facts Essay - 1881 Words

â€Å"Memorizing math facts is the most important step to understanding math. Math facts are the building blocks to all other math concepts and memorizing makes them readily available† (EHow Contributor, 2011). To clarify, a math fact is basic base-10 calculation of single digit numbers. Examples of basic math facts include addition and multiplication problems such as 1 + 1, 4 + 5, 3 x 5 and their opposites, 2 – 1, 9 – 4, 15/5(Marques, 2010 and Yermish, 2011). Typically, these facts are memorized at grade levels deemed appropriate to a student’s readiness – usually second or third grade for addition and subtraction and fourth grade for multiplication and division. If a child can say the answer to a math fact problem within a couple of†¦show more content†¦In the 1990’s, math curriculum reforms were introduced which replaced rote memorization with what is referred to as integrative math teaching. â€Å"This involves teaching many different concepts at the same time instead of sequentially, and using manipulatives in place of numbers to illustrate mathematical concepts long after number sense should have been mastered† (Groves, 2011). This switch in theory, caused serious controversy among mathematicians and math educators. If children have not yet mastered basic math facts, how can they be expected to master advanced concepts? Researchers believe that it is just too much too soon for young children (Groves, 2011). Tom Loveless says â€Å"Youngsters who have not mastered whole number arithmetic by the end of 4th grade are at risk of later becoming remedial students in mathematics.† Furthermore, he â€Å"urges that every student in the nation should receive a thorough grounding in arithmetic† (Loveless, 2011). The push to master facts by a certain age and prior to moving on to more complex math is most controversial with parents and teachers of gifted students. These students are often thought to be bored by simple, basic math concepts. Although â€Å"some of the very highest areas of math do not require automaticity of basic math facts, they do require automaticity of the skills that fall somewhere in between them and single-digit addition, and that those skills are very difficult to master and to automatize when theShow MoreRelatedBasic Math Facts On Math2643 Words   |  11 PagesMichalczuk‟s (2007) understood basic math facts to be an important skill for students to succeed in math. Michalczuk (2007) generalized students who could answer single-digit, 0 – 9, multiplication problems (2 times 3, or 5 times 7, etc.) â€Å"Within three seconds will do well at math and those that answer in less than one second will do excellent at math† (p. 1). Perso (2007) has defined the â€Å"looking back-to-basics† as a need to teach and focus on the basic arithmetic skills needed as a skill for higherRead MoreDifferences Between Facts And Theories Of Math And History Essay1074 Words   |  5 PagesDifferences in the Relationship between Facts and Theories: Math and History Theories have been defines as integrated set of concepts formed into propositions that explain different phenomena or events (Schneider 2), while facts as thing that is undisputed as the case or corresponds to the truth (Mellor 110). Both facts and theories are used to generate knowledge that can be applied in verse situations. However, the relationship between facts and theories differs between different areas of knowledgeRead MoreThe Golden Age Of Islamic Thought And Its Cultural Impact On Europe852 Words   |  4 Pageson Europe, Europeans denied this fact, their invents, thoughts, and ideas even being seemingly relevant all while their society was highly influenced by said denied facts. The historians and philosophers from Europe have denied Islam the credit that it really deserves for the development of modern culture. One thing that is stupidly ignored is their impact on mathematics. In today’s modern word there is more math than you could ever imagine, very difficult math at that. None of this would have trulyRead MoreHow Can Math Facts Help Solve Real World Word Problems? Essay993 Words   |  4 PagesTeacher: Loupe Title: I Can Add Doubles! 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Suicide Prevention Program Of The United States - 2160 Words

In the United States, suicide is the third leading cause of death for 10 to 14-year-olds (CDC, 2015) and for 15 to 19-year-olds (Friedman, 2008). In 2013, 17.0% of students grades 9 to 12 in the United States seriously thought about committing suicide, 13.6% made a suicide plan, 8.0% attempted suicide, and 2.7% attempted suicide in which required medical attention (CDC, 2015). These alarming statistics show that there is something wrong with the way mental illness is handled in today’s society. Also, approximately 21% of all teenagers have a treatable mental illness (Friedman, 2008), although 60% do not receive the help that they need (Horowitz, Ballard, Pao, 2009). To many people, these facts are certainly frightening because no one wants people to commit suicide, especially not children who have their entire lives ahead of them. 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It is the tenth leading cause of death among all age bracket in Maine. It is the second leading cause of death for ages 15 to 24; and the fourth leading cause in ages 10 to 14. (â€Å"Maine Suicide Prevention Program†) ThereRead MoreSuicide Can Be A Difficult Topic To Discuss. Especially1170 Words   |  5 PagesSuicide can be a difficult topic to discuss. Especially if one has known someone who has committed suicide. Suicide does not discriminate and happens anywhere that life exists. According to Rosenberg (1999),†Suicide is the 8th leading cause of death overall in the United States. For the elderly, it is the 13th, and for the young (15-24) it is it the 3rd leading cause of death† (pp. 83-87). The increasing rate of suicide has called implementations of suicide prevention plans. 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Assistive Technology

Question: Discuss the importance of AT Devices.Use of AT Devices.Selection and Decision Making Process in Assistive Technology.Assistive technology performance over their working principals.Scope of Improvement. Answer: Importance of AT Devices The over growing technological enhancement brings many features towards the modern age people, but this technological improvement is not compatible for people with disability. To make a suitable platform in between the new technology and the physically challenged people Assistive Technology or AT is introduced. Assistive technology act as conversion buffer so that the newly introduced technology can be converted for the person with a disability. Knowing the range of matching ratio of AT devices - Assistive technology based devices are designed from the user perspective ("Assistive Technology Assessment - Find the Right Tools", 2016). So it can create an influential impact over its user because the type of disability and percentage of disability are differed from time to time and person to person. If the usability ratio varied from one end to another end, so it is oblivious the AT device users need to check their device range or description before using it on their purpose. Use of AT Devices If I use the Assistive technology in my classroom to overcome my disability factor with the layer of new technological development, then I should follow some precaution before using it. Before adopting of new assistive technology, first I will make an analysis to check the compatibility of the device with my disability ("Consumer Guides for Buying and Marketing Assistive and Learning Technologies", 2016). If the compatibility ratio turns a green signal about confirming the maximum compatibility factor, then I go for the next level checking. After satisfying with the compatibility ratio, I will check for its quality standard because low or wrong quality standard can harm my physical condition. Now I should check the AT devices user instruction manual for creating a proper and convenient communication channel among the device and technological approach. Selection and Decision Making Process in Assistive Technology Assistive technology is born by helping the physically challenged person so that they can also take the advantage of new edge technological development. In the era of utilizing Assistive technology, it is the best way to integrate this technology in the root level of disability ("assistive-technology-resources", 2016). Peoples can suffer from their disability from the birth or the disability developed over the years. It is easy to select those people who are disabled by their birth and in this scenario school children are the top most area where AT can totally change their view towards technology uses. The using of assistive technology over the child education or assistance it is necessary to take some measurements over its uses. These proactive measurements will help for a successive decision making AT services. Assistive technology performance over their working principals For creating a performance evaluation, it is necessary to check the workability of AT devices in regular interval. First of all users' needs to check their AT device services are goes on the predefined context of materials which is set by the manufacturer ("assistive-technology-resources", 2016). The Next thing is to collaborate all the functionality over application uses. If the functionality of the AT device met all the requirements, then it can say that the AT device is well formatted. Scope of Improvement The functionality of an Assistive technological device differs by its type of uses and type of user. There are no one AT device is present in the market which can directly improvise the content of AT module along with the user needs (Gilman, 2016). Users are trained on AT devices services for making it more useful but now day's artificial knowledge learning system make it simpler with the help adaptive knowledge base. So it oblivious the rapid technological growth in the area of artificial programming or algorithm can make life easier for the person with a disability. References Assistive Technology Assessment - Find the Right Tools. (2016).Techpotential.net. Retrieved 19 August 2016, from https://www.techpotential.net/assessment assistive-technology-resources. (2016).Edutopia.org. Retrieved 19 August 2016, from https://www.edutopia.org/article/assistive-technology-resources#graph2 Consumer Guides for Buying and Marketing Assistive and Learning Technologies. (2016).https://techmatrix.org/. Retrieved 19 August 2016, from https://techmatrix.org/sites/all/themes/TechMatrix/images/consumerguide.pdf Gilman, d. (2016).cognitive disabilities reminders, prompts and cues at specified times or under specified conditions.Abilityhub.com. Retrieved 19 August 2016, from https://www.abilityhub.com/cognitive/index.htm