(6.1) Rational exponents and properties of exponents

Based on the PowerPoint you shared, here is a simple quiz focusing on vocabulary, exponent laws, and identifying function types. --- Quiz: Exponent Laws & Rational Exponents (3.1–3.3) Multiple Choice (5 questions) Choose the correct answer. 1. In the expression 5^3, the number 3 is called the a) base b) power c) exponent d) coefficient 2. Which law of exponents would you use to simplify (x^2)^3? a) Product rule b) Quotient rule c) Power of a power rule d) Zero exponent rule 3. According to the zero exponent law, 7^0 = a) 0 b) 1 c) 7 d) undefined 4. If the first differences in a table of values are constant, the function is a) linear b) quadratic c) exponential d) not a function 5. Which expression is equivalent to \frac{2^5}{2^3}? a) 2^2 b) 2^8 c) 2^{15} d) 2^{-2} True or False (5 questions) Write T for true or F for false. 1. When multiplying powers with the same base, you add the exponents. 2. A negative exponent means the answer will always be negative. 3. For an exponential function, the ratios of consecutive y-values are constant. 4. The power 16^{\frac{1}{2}} is equal to 8. 5. The quotient rule for exponents says \frac{x^a}{x^b} = x^{a-b}. Completion (2 questions) Fill in the blank with the correct term. 1. The _____________ rule states that when raising a power to another power, you multiply the exponents. 2. If the second differences in a table of values are constant, the function is ______________. --- Answer Key Multiple Choice 1. c) exponent 2. c) Power of a power rule 3. b) 1 4. a) linear 5. a) 2^2 True or False 6. T 7. F (a negative exponent indicates a reciprocal, not a negative value) 8. T 9. F (16^{\frac{1}{2}} = \sqrt{16} = 4) 10. T Completion 11. power of a power (or power rule) 12. quadratic

8.NSO.1.7 Solve multi-step problems involving the order of operations with rational numbers including integer exponents with: ➢ 2 to 4 steps, in a mathematical context (L2) ➢ 5 steps, in a mathematical context (L3) ➢ 6 steps, in a mathematical context (L4)

1. Absolute Value - The magnitude of a number or the distance from 0 on a real number line. 2. Addend - Any number or quantity being added. (addend + addend = sum) 3. Algorithm - Step-by-step process to accomplish a task. 4. Difference - The amount that remains after one quantity is subtracted from another. (The answer to a subtraction problem) 5. Dividend - A quantity or total to be divided. (dividend ÷ divisor = quotient) 6. Divisor - The number per group by which the dividend is to be divided. 7. Factor - A number that is multiplied by another number. 8. Integers - A set of numbers that includes natural numbers, their opposites, and zero. (… -3, -2, -1, 0, 1, 2, 3 …) 9. Product - The result of a multiplication expression (the answer to a multiplication problem) 10. Quotient - The result of the division of one quantity by another (the answer to a division problem) 11. Rational Numbers - Numbers that can be expressed

Use this to make a quiz: Excellent! Using an online game is a fantastic way to boost engagement. Here is a list of scenarios you can use. I've designed them to be clear and concise for a game format. I've also added a few "challenge" scenarios at the end that could fit more than one theory to really get your students thinking critically. You can copy and paste these right into platforms like Kahoot!, Blooket, or Gimkit. --- ### **Scenarios for Your Online Game** **Instructions for Students:** Read the scenario and choose the theory that BEST explains why the crime was committed. 1. **Scenario:** An accountant has been secretly stealing small amounts of money from his clients' accounts for years. He has a system that he believes is foolproof, and he has calculated that the potential reward is worth the small risk of being caught. * **Best Fit:** Choice Theory 2. **Scenario:** A high school student who lives in a neighborhood with high unemployment and rundown buildings begins to vandalize property with a group of friends who feel ignored by the city. * **Best Fit:** Social Disorganization Theory 3. **Scenario:** A young woman desperately wants the new smartphone and designer clothes she sees all over social media, but she has no way to afford them. She decides to start stealing packages from front porches to get what she wants. * **Best Fit:** Strain Theory 4. **Scenario:** A man is arrested for assault after getting into a fight at a restaurant. His family tells the police that he has always had a "short fuse" and has struggled with anger and aggression since he was a child, a trait that his father also had. * **Best Fit:** Biological/Psychological Theory 5. **Scenario:** The youngest child in a family of well-known burglars is caught breaking into a house. When questioned, he says he learned everything he knows from watching and helping his older siblings. * **Best Fit:** Learning Theory 6. **Scenario:** A corporate executive is caught illegally dumping toxic waste to save his company money. He decided that the cost of proper disposal was too high and the chance of being caught was low. * **Best Fit:** Choice Theory 7. **Scenario:** After her parents' messy divorce, a teenager starts skipping school and shoplifting. A counselor suggests her actions stem from untreated anxiety and depression. * **Best Fit:** Biological/Psychological Theory 8. **Scenario:** In a community where the local factory closed down and police presence is low, a group of residents forms a vigilante group to "patrol" the streets, often resorting to violence and intimidation. * **Best Fit:** Social Disorganization Theory --- ### **Challenge Scenarios (Could fit multiple theories)** 9. **Scenario:** A college student starts selling forged concert tickets to pay for their tuition. They learned how to make the fake tickets from a video online and felt it was the only way to stay in school. * **Possible Answers:** Strain Theory (can't afford tuition), Learning Theory (learned online), Choice Theory (weighed the risks). 10. **Scenario:** A person living on the streets with no job prospects is arrested for stealing a warm coat from a department store during a blizzard. * **Possible Answers:** Strain Theory (no means to achieve the goal of being warm), Choice Theory (made a rational decision to steal to survive). These scenarios should give you great content for your game. Have fun with it, and let me know if you need any more!

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.

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