Multiply and divide With Radicals

Can you make a multiple choice of test questions regarding this information given which is Curriculum from Different Points of View There are many definitions of curriculum. Because of this, the concept of curriculum is sometimes characterized as fragmentary, elusive and confusing. However, the numerous definitions indicate dynamism that connotes diverse interpretations of what curriculum is all about. The definitions are influenced by models of thought, pedagogies, political as well as cultural experiences. Let us study some of these definitions. 1. Traditional Points of View of Curriculum In early years of the 20th century, the traditional concepts held of the “curriculum is that it is a body of subjects or subject matter prepaid by the teachers for the student’s to learn”. It was synonymous to the “course of study” and “syllabus” Robert M. Hutchins views curriculum as “permanent studies” where the rules of grammar, reading, rhetoric and logic and mathematics for basic education are emphasized. Basic education should emphasize the 3 Rs and college education should be grounded on liberal education. On the other, Arthur Bestor as an essentialist, believes that the mission of the school should be intellectual training, hence curriculum should focus on the fundamental intellectual disciplines of grammar, literature and writing. It should also include mathematics, science, history and foreign language. The definition leads us to the view of Joseph Schwab that discipline is the sole source of curriculum. Thus in our education system, curriculum is divided into chunks of knowledge we call subject areas in basic education such as English, Mathematics, Science, Social Studies and others. In college, discipline may include humanities, sciences, language and many more. To Phoenix, curriculum should consist entirely of knowledge which comes from various disciplines. Academic discipline became the view of what curriculum is after the cold war and the race to space. Joseph Schwab, a leading curriculum theorist coined the term discipline as a ruling doctrine for curriculum development. Curriculum should consist only of knowledge which comes from disciplines which is the sole source. Thus curriculum can be viewed as a field of study. It is made up of its foundations (philosophical, historical, psychological and social foundations); domains of knowledge as well as its research theories and principles. Curriculum is taken as scholarly and theoretical. It is concerned with broad historical, philosophical and social issues and academics. Most of the traditional ideas view curriculum as written documents or a plan of action in accomplishing goals. 2. Progressive Points of View of Curriculum On the other hand, to a progressivist, a listing of school subjects, syllabi, course of study, and a list of courses or specific discipline do not make a curriculum. These can only be called curriculum if the written materials are actualized by the learner. Broadly speaking, curriculum is defined as the total learning experiences of the individual. This definition is anchored on John Dewey’s definition of experience and education. He believed that reflective thinking is a means that unifies curricular elements. Thought is not derived from action but tested by application. Caswell and Campbell viewed curriculum as “all experiences children have under the guidance of teachers”. This definition is shared by Smith, Stanley and Shores when they defined “curriculum as a sequence of potential experiences set up in the schools for the purpose of disciplining children and youth in group ways of thinking and acting”. Marsh and Willis on the other hand view curriculum as all the “experiences in the classroom which are planned and enacted by the teacher, and also learned by the students”. Points of View on Curriculum Development From the various definitions and concepts presented, it is clear that curriculum is a dynamic process. Development connotes changes which are systematic. A change for the better means any alteration, modification or improvement of existing condition. To produce positive changes, development should be purposeful, planned and progressive. This is how curriculum evolves. Let us look at the two models of curriculum development and concepts of Ralph Tyler and Hilda Taba. Ralph Tyler Model: Four Basic Principles. This is also popularly known as Tyler’s Rationale. He posited four fundamental questions or principles in examining any curriculum in schools. These four fundamental principles are as follows: 1. What educational purposes should the school seek to attain? 2. What educational experiences can be provided that are likely to attain these purposes? 3. How can these educational experiences be effectively organized? 4. How can we determine whether these purposes are being attained or not? In summary, Tyler’s Model show that in curriculum development, the following considerations should be made: (1) Purpose of the school, (2) Educational experiences related to the purposes, (3) Organization of the experiences, and (4) Evaluation of the experiences. On the other hand, Hilda Taba improved on Tyler’s Rationale by making a linear model. She believed that teachers who teach or implement the curriculum should participate in developing it. Her advocacy was commonly called the grassroots approach. She presented seven major steps to her model where teachers could have a major input. These steps are as follows: 1. Diagnosis of learner’s needs and expectations of the larger society. 2. Formulation of learning objectives. 3. Selection of learning content. 4. Organization of learning content. 5. Selection of learning experiences. 6. Organization of learning activities. 7. Determination of what to evaluate and the means of doing it. Thus as you look into curriculum models, the three interacting processes in curriculum development are planning, implementing and evaluating. Types of Curriculum Operating in Schools From the various concepts given, Allan Glatthorn(2000) describes seven types of curriculum operating in the schools. These are (1) Recommended curriculum- proposed by scholars and professional organizations. (2) Written Curriculum- appears in school, district, division or country documents. (3) Taught Curriculum- what teacher’s implement or deliver in the classrooms and schools. (4) Supported Curriculum- resources-textbooks, computers, audio- visual materials which support and help in the implementation of the curriculum. (5) Assessed Curriculum- that which is tested and evaluated. (6) Learned Curriculum- which the students actually learn and what is measured and (7) Hidden Curriculum- the unintended curriculum. 1. Recommended Curriculum- Most of the school curricula are recommended. The curriculum may come from a national agency like the Department of Education, Commission on Higher Education (CHED), Department of Science and Technology (DOST) or any professional organization who has stake in education. For example the Philippine Association for Teacher Education (PAFTE) or the Biology Teacher Association (BIOTA) may recommend a curriculum to be implemented in the elementary or secondary education. 2. Written Curriculum- This includes documents, course of study or syllabi handed down to the schools, districts, division, departments or colleges for implementation. Most of the written curricula are made by curriculum experts with participation of teachers. These were pilot-tested or tried out in sample schools or population. Example of this is the Basic Education Curriculum (BEC). Another example is the written lesson plan of each classroom teacher made up of objectives and planned activities of the teacher. 3. Taught Curriculum- The different planned activities which are put into action in the classroom compose the taught curriculum. These are varied activities that are implemented in order to arrive at the objectives or purposes of the written curriculum. These are used by the learners with the guidance of teachers. Taught curriculum varies according to the learning styles of students and the teaching styles of teachers. 4. Supported Curriculum- In order to have a successful teaching, other than the teacher, there must be materials which should support or help in the implementation of a written curriculum. These refer to the support curriculum that includes material resources such as textbooks, computers, audio-visual materials, laboratory equipment, playgrounds, zoos and other facilities. Support curriculum should enable each learner to achieve real and lifelong learning. 5. Assessed Curriculum- This refers to a tested or evaluated curriculum. At the duration and end of the teaching episodes, series of evaluations are being done by the teachers to determine the extent of teaching or to tell if the students are progressing. This refers to the assessed curriculum. Assessment tools like pencil-and-paper tests, authentic instruments like portfolio are being utilized. 6. Learned Curriculum- This refers the learning outcomes achieved by the students. Learning outcomes are indicated by the results of the tests and changes in behavior which can either be cognitive, affective or psychomotor. 7. Hidden Curriculum- This is the unintended curriculum which is not deliberately planned but may modify behavior or influenced learning outcomes. There are lots of hidden curricula that transpire in the schools. Peer influence, school environment, physical condition, teacher-learner interaction, mood of the teachers and many other factors made up the hidden curriculum.

Generate all of these 25 questions Part A: Each correct answer is worth 5. 1. The regular pentagon shown has a side length of 2 cm. The perimeter of the pentagon is (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm (E) 10 cm 2 cm 2. The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots. Three of the faces are shown. What is the total number of dots on the other three faces? (A) 6 (B) 8 (C) 10 (D) 12 (E) 15 3. The equation that best represents \a number increased by _ve equals 15" is (A) n 􀀀 5 = 15 (B) n _ 5 = 15 (C) n + 5 = 15 (D) n + 15 = 5 (E) n _ 5 = 15 4. The line graph shows the number of bobbleheads sold at a store each year. The sale of bobbleheads increased the most between (A) 2016 and 2017 (B) 2017 and 2018 (C) 2018 and 2019 (D) 2019 and 2020 (E) 2020 and 2021 Number of 2016 2017 2018 2019 2020 Year Sale of Bobbleheads 2021 Bobbleheads 20 40 60 80 5. Starting at 72, Aryana counts down by 11s: 72; 61; 50; : : : . What is the last number greater than 0 that Aryana will count? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 6. In the diagram, \ABC = 90_. The value of x is (A) 68 (B) 23 (C) 56 (D) 28 (E) 26 Day of the Week 44° x° A B C x° 7. Which of the following values is closest to zero? (A) 􀀀1 (B) 5 4 (C) 12 (D) 􀀀4 5 (E) 0:9 Grade 8 8. A jar contains 267 quarters. One quarter is worth $0.25. How many quarters must be added to the jar so that the total value of the quarters is $100.00? (A) 33 (B) 53 (C) 103 (D) 133 (E) 153 9. A package of 8 greeting cards comes with 10 envelopes. Kirra has 7 cards but no envelopes. What is the smallest number of packages that Kirra needs to buy to have more envelopes than cards? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 10. For the points in the diagram, which statement is true? (A) e > c (B) b < d (C) f > b (D) a < e (E) a > c y x (e, f ) (a, b) (c, d ) Part B: Each correct answer is worth 6. 11. The 26 letters of the English alphabet are listed in an in_nite, repeating loop: ABCDEFGHIJKLMNOPQRSTUVWXY ZABC : : : What is the 258th letter in this sequence? (A) V (B) W (C) X (D) Y (E) Z 12. A public holiday is always celebrated on the third Wednesday of a certain month. In that month, the holiday cannot occur on which of the following days? (A) 16th (B) 22nd (C) 18th (D) 19th (E) 21st 13. A circular spinner is divided into three sections. An arrow is attached to the centre of the spinner. The arrow is spun once. The probability that the arrow stops on the largest section is 50%. The probability it stops on the next largest section is 1 in 3. The probability it stops on the smallest section is (A) 1 4 (B) 2 5 (C) 1 6 (D) 2 7 (E) 3 10 14. A positive number is divisible by both 3 and 4. The tens digit is greater than the ones digit. How many positive two-digit numbers have this property? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 15. A rectangular pool measures 20 m by 8 m. There is a 1 m wide walkway around the outside of the pool, as shown by the shaded region. The area of the walkway is (A) 56 m2 (B) 60 m2 (C) 29 m2 (D) 52 m2 (E) 50 m2 20 m 8 m 1 m Grade 8 16. The results of asking 50 students if they participate in music or sports are shown in the Venn diagram. What percentage of the 50 students do not participate in music and do not participate in sports? (A) 0% (B) 80% (C) 20% (D) 70% (E) 40% Music Sports 15 5 20 17. There are 2 3 as many golf balls in Bin F as in Bin G. If there are a total of 150 golf balls, how many fewer golf balls are in Bin F than in Bin G? (A) 15 (B) 30 (C) 50 (D) 60 (E) 90 18. In the sequence shown, Figure 1 is formed using 7 squares. Each _gure after Figure 1 has 5 more squares than the previous _gure. What _gure has 2022 squares? (A) Figure 400 (B) Figure 402 (C) Figure 404 (D) Figure 406 (E) Figure 408 Figure 1 Figure 2 Figure 3 19. Mateo's 300 km trip from Edmonton to Calgary passed through Red Deer. Mateo started in Edmonton at 7 a.m. and drove until stopping for a 40 minute break in Red Deer. Mateo arrived in Calgary at 11 a.m. Not including the break, what was his average speed for the trip? (A) 83 km/h (B) 94 km/h (C) 90 km/h (D) 95 km/h (E) 64 km/h 20. Equilateral triangle ABC has sides of length 4. The midpoint of BC is D, and the midpoint of AD is E. The value of EC2 is (A) 7 (B) 6 (C) 6:25 (D) 8 (E) 10 Part C: Each correct answer is worth 8. 21. The positive factors of 6 are 1, 2, 3, and 6. There are two perfect squares less than 100 that have exactly _ve positive factors. What is the sum of these two perfect squares? (A) 177 (B) 80 (C) 145 (D) 52 (E) 97 22. In the list p; q; r; s; t; u; v, each letter represents a positive integer. The sum of the values of each group of three consecutive letters in the list is 35. If q + u = 15, then p + q + r + s + t + u + v is (A) 85 (B) 70 (C) 80 (D) 90 (E) 75 Grade 8 23. The net shown is folded to form a cube. An ant walks from face to face on the cube, visiting each face exactly once. For example, ABCFED and ABCEFD are two possible orders of faces the ant visits. If the ant starts at A, how many possible orders are there? (A) 24 (B) 48 (C) 32 (D) 30 (E) 40 A D B C E F 24. The number 385 is an example of a three-digit number for which one of the digits is the sum of the other two digits. How many numbers between 100 and 999 have this property? (A) 144 (B) 126 (C) 108 (D) 234 (E) 64 25. Student A, Student B, and Student C have been hired to help scientists develop a new avour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below. Student A Student B Student C Percentage correct on samples 90% 98% (2m)% containing blueberry Percentage correct on samples 88% 86% (4m)% not containing blueberry Student B reports 315 more samples as containing blueberry than Student A. For some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. The sum of all such values of m is (A) 45 (B) 36 (C) 24 (D) 27 (E) 29

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