| Curriculum Map 2006-2007 | |||
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The Dwight School |
| Period | Content | Purpose/ Objectives | Activities & Resources | Areas of Interaction | Assessments | |
| TRIGONOMETRY : | Review of trigonometry of the right triangle The sine rule The cosine rule Area of triangles |
Review previous year's work. Be able to solve triangles using an appropriate method. Application of trigonometry to practical situations. Familiarity with special right triangles. |
In Central Park: finding the height of buildings and the distance of the observer from them. Finding the distance of the observer from a building. |
Environment: How does trigonometry enable us to measure and better understand the world? Homo Faber: how was trigonometry developed. Contributions of different cultures. ATL: Strategies for problem solving. |
Formative: Use of SOHCAHTOA. Application of algebraic techniques to trigonometry. Showing ability to choose the suitable method for solving a triangle. Summative: Quizzes. End of topic test. |
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| PSAT PREPARATION : | PSAT PREPARATION. Review of relevant arithmetic, algebra, and geometry topics. |
Preparation for the October PSAT. Awareness of relevant strategies in taking this test. |
Practice PSATs for classwork and homework. |
ATL: Tactics and techniques for raising PSAT scores |
Formative: practice test questions by topic Summative: Diagnostic and end of topic test. |
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| NUMBER SETS : | NUMBER SETS. Whole numbers, integers,rationals and irrational numbers |
Able to identify subsets of the real number set. Understand difference between rational and irrational numbers. Able to change fractions to decimals and vice versa (including non-terminatimg decimals) Able to simplify fractions and radical expressions. |
Problem sets involving these concepts. |
Homo Faber:how did the concept of number develop over the centuries? |
Formative: question sets and quizzes Summative: End of topic test |
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| ALGEBRA : | ALGEBRA Review of linear algebra Absolute value equations Inequalities including those involving absolute value Solving quadratics by factoring The quadratic formula The use of the discriminant Radical equations Recognition of polynomials. |
Understand the different techniques for solving equations. Awareness of need to check solutions for reasonableness and by substitution. |
Problem sets. Devising puzzles that can be solved algebraically |
Homo Faber, Social Education, Environment: What were the historical origins of algebra? Why is it such a powerful tool in mathematics. |
Formative: Homework,quizzes, oral and group work in class Summative: End of topic test |
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| ALGEBRA : | As November |
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| FUNCTIONS : | FUNCTIONS The concept of a function Composite functions Inverses of functions Logarithms Exponential and logarithmic functions Greatest integer function Review of rules of Indices. |
Able to recognize a function. Able to use function notation correctly. Able to find inverses of functions and composites of functions. Recognition of logarithm as inverse of exponential function. |
Problem sets. Worksheets |
Environment and Homo Faber: How are exponential functions used in the study of growth and decay? Why were logarithms developed? How are they of use nowadays? |
Formative: homeworks, and quizzes. Summative: end of topic test. |
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| CIRCLE GEOMETRY : | GEOMETRY OF CIRCLE Angles in same segment Angle in semi-circle Areas of sectors and segments Arc length Chords, secants and tangents |
Able to find unknown angles, areas and lengths using knowledge of circle geometry |
Problem sets Geometer's sketchpad |
ATL: how to develop proofs Strategies for finding unknown angles or areas Environment: geometric patterns in the universe |
Formative: homework, quizzes, class discussion Summative: end of topic test |
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| TRIGONOMETRY : | TRIGONOMETRY The unit circle The general angle Special right triangles Radian measure Reciprocal trigonometric functions Trigonometric identities and their proofs Solving trigonometric equations |
Understand the definition of trigonometric functions in terms of a unit circle. Understand radian measure as an alternative to degree measure |
Problem sets. |
Homo Faber: why does this definition represent a significant advance |
Formative: homework, quizzes, class discussion Summative: end of topic test |
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| STATISTICS : | STATISTICS Simple and compound probability Mean, median, mode, standard deviation |
How to solve problems involving probability Know how to use Pascal's Triangle Understand the uses of mean, median, mode and standard deviation |
Problem sets Coin and dice experiments |
Social education: how can statistics be used and abused? How did probability theory evolve from questions posed by gambling? ATL: what are the ways to tackle probability problems? |
Formative: homeworks and quizzes Summative: End of topic test |
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| SEQUENCES AND SERIES : | Sequences and patterns The Fibonacci Sequence Arithmetic sequences Geometric sequences  website about Fibonacci numbers |
Develop the ability to recognize patterns and sequences. The use of geometric and arithmetic sequences. The importance in nature of the Fibonacci sequence. |
Problem sets. Looking for examples of patterns and sequences in nature and art. |
Environment: What links the Fibonacci sequence to the Parthenon, and to sunflowers? How do these patterns enable us to make sense of our environment? Homo Faber: How did Gauss find the sum of an arithmetic sequence? Health and social education: How does the golden ratio relate to the human form? |
Formative: homework, quizzes, class discussion Summative: end of topic test |
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| COURSE REVIEW AND EXAMINATION : | A review of the entire year's work |
To remember the main ideas of this year's course and to deepen understanding of the essential concepts |
review worksheets, students teach topics to fellow students |
Why is the concept of a function so important ? |
End of year examination |
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