Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ST. FRANCIS’ CANOSSIAN COLLEGE MATHEMATICS DEPARTMENT CURRICULUM PLANNING 07-08 Subject : Class: Mathematics Textbook: Exploring Mathematics Book 2 (Oxford). Form 2 Subject Teachers: Mrs. E. Fu, Ms. W.K. Chan, Ms. S. Tsoi Chapter Date Cycle 1 4/9-13/9 1 2 17/9-11/10 Detailed Content N.P. Introduction Approximation and Errors 1.1 Significant Figures 1.2 Approximation and Errors in Measurement • Ask students to find some information from the internet and then estimate certain values. 2-4 Introduction to Polynomials 2.1 Index Notation 2.2 Laws of Indices • Abler students may try to simplify expressions like [(a2)3]4. • Use the following example to illustrate that two different methods can be used to solve the same question: 3 12/10-24/10 2 3 IT station (P.9) 1 2.5 3 3 a2 a2 a6 ( ) (a 21) a3 or ( ) 3 a3 a a a Discuss with students whether xn∙xn is equal to (x + x)n . . 2.3 Polynomials 2.4 Addition and Subtraction of Polynomials 2.5 Multiplication of Polynomials 2.6 Simple Factorization of Polynomials 3 Suggested Activities 4-6 Identities 3.1 Meaning of Identities 3.2 The Difference of Two Squares 3.3 The Perfect Square Identities • Ask students to prove (a − b)2 = (b − a)2. • Ask students to deduce the identity related to (a − b)2 by using the identity related to (a + b)2. 2 3 3 4.5 2 2 4 Powerpoint “Concept of Identity” 4 5 6 8 25/10-12/11 13/11-5/12 6/12-19/12 21/12-1/1 2/1-14/1 16/1-31/1 6-8 Formulas 4.1 Simple Algebraic Fractions 4.2 Formulas and Substitution 4.3 Change of Subject of a Formula 4 4 4 8-10 Linear Equations in Two Unknowns 5.1 Basic Knowledge of Linear Equations in Two Unknowns • Teach students to use softwares such as Winplot to draw the graph of a linear equation in two unknowns. 5.2 Solving Simultaneous Linear Equations in Two Unknowns by Graphical Method 5.3 Solving Simultaneous Linear Equations in Two Unknowns by Algebraic Method 5.4 Applications of Simultaneous Linear Equations in Two Unknowns Discuss two special cases of simultaneous equations: (1) The graphs of two equations are two parallel lines. (2) The graphs of two equations are two coincident straight lines . 10-12 Rate and Ratio 6.1 Rate • Discuss with students that apart from the comparison of two different kinds of quantities, a rate can also be used to compare two quantities of the same kind, e.g. exchange rate of different currencies. 6.2 Ratio 6.3 Applications of Ratio • Introduce that the scale on a map is usually expressed as 1 : n. In Geography, it is called representative fraction (R.F. in short form). • Use examples to illustrate how to find the actual distance from map or actual length of an object from plan by using R.F. Ask students to find some scale drawings from books, newspapers or internet, and then calculate the actual length of the object from the scale drawing. 1.5 X’mas Holiday Mid-Term Examination & Paper Correction 12-15 Angles in Triangles and Polygons 8.1 Angles and Sides of a Triangle 8.2 Angles of a Polygon 8.3 Basic Constructions • Introduce some websites about tessellated figures and let students appreciate the beauty of these figures. • Illustrate that tessellations can be created using two or more different kinds of regular polygons. 4 3.5 4.5 5 IT station (P.133) 3 5 4 3.5 3 Powerpoint “Tessellation” 9 1/2-5/2 6/2-17/2 18/2-26/2 10 11 3/3-17/3 18/3-19/3 20/3-30/3 31/3-14/4 12 15/4-28/4 15-17 Introduction to Deductive Geometry 9.1 Intuitive and Deductive Approaches in Studying Geometry • Explain the terms ‘axioms’, ‘definitions’ and ‘theorems’. Lunar New Year Holidays 9.2 Deductive Approach to Properties of Geometric Figures 17-19 Pythagoras’ Theorem 10.1 Square Roots 10.2 Pythagoras’ Theorem • Suggest students to find some proofs of Pythagoras’ theorem on the internet. 10.3 Application of Pythagoras’ Theorem 10.4 Converse of Pythagoras’ Theorem 10.5 Irrational Numbers 19-21 Trigonometric Ratios 11.1 Introduction to Trigonometric Ratios Easter Holiday 11.1 Introduction to Trigonometric Ratios • Ask students to learn from the internet that the sine ratio can also be defined by the coordinates of a point on the unit circle on a rectangular coordinate plane. The teacher may explain that we can then define the sine ratio for angles not only less than 90°, but also for any angles like 150°, 240°, etc, and this will be discussed in detail in senior levels. 11.2 Applications of Trigonometric Ratios 21-22 Trigonometric Relations 12.1 Trigonometric Ratios of Some Special Angles 3 6 1.5 2.5 2 2 3 2 6 IT station (P.130) 3 1.5 NF • ‘Rationalization of denominators’ will be discussed in Book 3A. At this moment, the teacher can briefly mention 1 1 2 2 and 2 3 to students. 3 3 12.2 Finding Trigonometric Ratios Using Pythagoras’ Theorem 12.3 Introduction to Trigonometric Identities • Explain how to prove the identity sin2θ+ cos2θ=1 in right-angled triangles. 13 29/4-16/5 23-24 Area and Volume (II) 13.1 Circles “周髀算經” (Civic Education) IT station (P.90) 1 6.5 3 13.2 Arcs and Sectors 13.3 Cylinders • Ask students an interesting question on enclosing the largest area, then guide them step by step to deduce the formula for the area of an n-sided regular polygon with known perimeter. • Then use a Spreadsheet program to compute and draw the results. Hence understand that among all plane figures with the same perimeter, the circle has the largest area. 7 19/5-6/6 25-27 Handling Continuous Data 7.1 Organization of continuous Data 7.2 Presentation of Continuous Data 7.3 Cumulative Frequency 7.4 Misuses of Statistical Diagrams • Ask students to collect some statistical graphs from newspapers or magazines, and discuss whether they are conveying misleading messages. 5 3 Class Exploration (P.A13) 3 7.5 5.5 2 Powerpoint “Histogram” Powerpoint “Frequency polygon” Powerpoint “Cumulative frequency” Powerpoint “Percentile” Powerpoint “Abuses of Statistics” Project : Collect data from newspaper, magazines or internet about Environmental Pollution in Hong Kong (Civic Education) 5/6-18/6 Final Examination Note: (1) a) region are only suitable for students of general and higher abilities, b) region are only suitable for abler students. (2) Topics / Exercises for abler students: ‘Challenging Problems’ at the end of each chapter.