10 Logical Reasoning
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This document discusses logical reasoning and provides 3 examples of problems solved through logical reasoning. Logical reasoning involves breaking down problems into logical steps and using techniques like deduction and contradiction to arrive at solutions. The first example asks if 44 silver dollars can be distributed into 10 pockets with each pocket containing a different number of dollars. The second example asks if a notched checkerboard with squares removed can still be covered with the remaining dominoes. The third example asks if the equation x2 + y2 = 3(u2 + v2) has any integral solutions other than (0, 0, 0, 0). The document concludes by listing references on problem solving strategies and mathematical methods.
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忘盡背後 一世不離棄
對很多人來說，畢業是人生中一個很重要的里程碑。當子良老師提出要在畢業晚宴上演出時，我便著意將《忘盡背後》重新編曲，以鼓勵在場的每一位同學。盼望大家在畢業後能忘記背後，努力面前的，為著上主所賜的目標而努力。
在這首樂曲中，我刻意地引用了德伏扎克 E 小調第 9 交響曲的第 2 樂章，並重新譜上中文歌詞。這樣的編排有著雙重的意義：其一、這是敝校的校鐘，是多年來天天伴隨著我們成長的集體回憶；其二、喻意同學們畢業後將踏進「新的世界」，或是在本地升學，或是到外地進修，都不忘在這裡所學習到的一切。作為 12 年級的班主任，能看見同學們的成長、更新與改變，實在感恩。但願大家都能一生信靠主，一世不離棄。
Uiit itce portfolio submission sheet
1. This document is a portfolio submission sheet for an ITCE (Information Technology for Continuous Education) program submitted by Wong Hang Chi, a student in the PGDE(S) Mathematics program at HKIEd with a student number of 09451331 and expected graduation date of July 2010.
2. The sheet includes a declaration that the three required ITCE portfolio items have been completed at the Upper Intermediate Level, including a project-based learning proposal, reflection on changes to teaching philosophy/subject due to IT, and a conclusion on the pros and cons of integrating ICT in education in Hong Kong.
3. Wong Hang Chi signs the sheet to declare the work as his own and the instructor,
Uiit ai3
1) ICT tools can enhance the effectiveness of teaching by allowing teachers to demonstrate concepts like graphs and functions in new ways. However, it also increases the pressure on teachers who must acquire new skills and ensure appropriate use of technologies.
2) While ICT helps students learn independently, it risks exacerbating inequality if not all students have equal access. Weaker students especially benefit from tools like graphing calculators, but quality of access may differ by individual backgrounds.
3) Schools must be aware of both the advantages of ICT in modernizing education, as well as the disadvantages like potential increases in differences between strong and weak students due to unequal access, in order to develop policies that mitigate risks.
Uiit ai2
The document discusses two approaches to teaching students about the area of a circle - using ICT tools or a traditional non-ICT method. Using ICT tools like Mathematica Player allows the teacher to demonstrate incrementally increasing the number of sectors in a circle to show the limiting case of a rectangle, which helps students understand that the area is πr2. The traditional method involves students physically cutting a paper circle into sectors but is more time consuming and limited. While ICT tools save time and help demonstrate the limiting concept, the traditional approach allows students to physically manipulate the materials.
Uiit ai1
The document proposes a project-based learning activity to teach students about Fermat's problem for Torricelli. Students will form groups and use dynamic geometry software to investigate Viviani's theorem. They will then perform an experiment involving drilling holes in acrylic boards and attaching strings to masses to measure angles. Finally, students will research the Fermat point online and present their findings to the class. The teacher's role is to facilitate learning through questioning rather than simply providing answers. ICT tools like dynamic geometry software and videos are used to enhance collaboration and make the activities more interactive.
Pizza Problem
1. The document discusses the "pizza problem" of dividing a circle into slices using chords and determining if the black and white areas are equal.
2. It introduces the Tiffany Lemma, which shows that the sum of the squares of the lengths of four chords through a point is a constant equal to 4 times the radius squared.
3. By using polar coordinates and the Tiffany Lemma, the solution shows that the integral of the black and white areas over any interval of length π/2 is π/2, proving the areas are equal.
Epa5075
The document discusses the trial scheme on school drug testing in Tai Po District from three sociological perspectives - structural functionalism, social conflict theory, and symbolic interactionism. From the structural functionalist view, the scheme aims to fulfill the social functions of the education system and narcotics division by deterring drug use and motivating abusers to seek help. However, it also creates social dysfunctions like increased public tension and labeling effects. The social conflict perspective sees the scheme as imposing government authority and creating social inequality between authorities and students. Finally, the symbolic interactionism perspective analyzes how the government constructs positive perceptions of the scheme through explanations, media coverage, and protecting students' self-concepts and esteem.
教大理想
This document is a 3-part choral work titled "Hong Kong Youth" arranged for SATB voices with piano accompaniment. It was written by Chong Wing Fat, Kai Yi Ni, and Chan King Ho, and arranged by Wong Hang Chi. The choral work has an allegro tempo of 120 beats per minute and is in 3/4 time. It features the soprano, alto, tenor and bass vocal parts, with the piano providing harmonic and rhythmic support.
複習（二元一次方程及百分法）
The document contains several math equations, including two systems of linear equations and two other equations involving variables a and x and y. It also includes some music and financial examples, such as discussing the Well Tempered Clavier, frequency of notes, interest rates calculations on $4000 and $68,000 amounts. Overall it seems to be presenting various examples from math, music and finance to illustrate concepts.
複習（特殊四邊形）
This document discusses a proof in geometry about angles in a triangle. It shows that the angle between a line parallel to one side of a triangle and another side is equal to the opposite angle in the triangle. It provides two steps to prove this using properties of parallel lines and the angle sum of a triangle being 180 degrees.
與平行四邊形有關的簡單證明
El documento presenta una demostración geométrica de que si AB = CD y AD//BC, entonces BD = CA. Primero establece que si AB = CD y AD//BC, entonces EBC ~ EAD y BE = CE. Luego, usando propiedades de triángulos similares y congruentes, deduce que BD = CA.
平行四邊形的判定條件
El documento describe un triángulo ABCD donde se dan los ángulos A = 63° y D = 117° y las longitudes BC = AD. Se deduce que la suma de los ángulos internos es 180° y que los lados AB y CD son paralelos, por lo que ABCD es un paralelogramo.
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10 Logical Reasoning
- 1. Logical Reasoning Tsang Yiu Ping (09451745) Wong Hang Chi (09451331) Logical Reasoning – p.
- 2. Problem-solving by Logical Reasoning Discussion with friends/plan a strategy for a work plan → Predict a conversation or a potential discussion/argument. A −→ B −→ C −→ D. Strength of an argument depends on the validity of the logical reasoning used. Logical Reasoning – p.
- 3. Logical Reasoning Proving by deduction Proving by contradiction Logical Reasoning – p.
- 4. Logical Reasoning - Example 1 Bob has 10 pockets and 44 silver dollars. He wants to put his dollars into his pockets so distributed that each pocket contains a different number of dollars. Can he do so? Logical Reasoning – p.
- 5. Logical Reasoning - Example 2 A domino can cover exactly 2 adjacent squares on a standard checkerboard. Thus, 32 dominoes will exactly cover the 64 squares on the checkerboard. Suppose we now remove one square from each of the two diagonally opposite corners of the checkerboard and remove one domino as well. Can you now cover this “notched” checkerboard with the 31 remaining dominoes? Why or why not? Logical Reasoning – p.
- 6. Logical Reasoning - Example 2 Logical Reasoning – p.
- 7. Logical Reasoning - Example 3 Show that the following equation has no integral solution except (x, y, u, v) = (0, 0, 0, 0). 2 2 2 2 x + y = 3(u + v ). Logical Reasoning – p.
- 8. References Posamentier, A. S. & S. Krulik. (1998). Problem solving strategies for efficient and elegant solutions : a resource for the mathematics teacher. Thousand Oaks, CA : Corwin Press. Pólya, George. (1990). How to solve it : a new aspect of mathematical method (2nd ed.). London : Penguin Books. 恩格爾著，舒五昌、馮志剛譯(2004)。《解決 問題的策略》上海，上海教育出版社。 Logical Reasoning – p.