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“ Success in math is considered a gateway to many educational and occupational opportunities ”.

“ Success in math is considered a gateway to many educational and occupational opportunities ”. (Jetter, 1993). GRANT UNION HIGH SCHOOL. Title I school 2,000 – 2,200 student population 90% of students have free lunch (low social economic status)

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“ Success in math is considered a gateway to many educational and occupational opportunities ”.

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  1. “Success in math is considered a gateway to many educational and occupational opportunities”. (Jetter, 1993)

  2. GRANT UNION HIGH SCHOOL • Title I school • 2,000 – 2,200 student population • 90% of students have free lunch (low social economic status) • 40% of student population are English Language Learners (Hispanic; Hmong and Lao refugees)are Special Education • At least 30% of students don’t live with parents (foster home, relatives) • Math skills of at least 50% of student population is 1 to 2 grade levels behind

  3. COLLABORATION GOALS • 70% of students in each class achieve in math • Weekly collaboration to discuss lesson delivery, teaching strategies, assessment results, and make revisions to plans as needed • Standards-driven reform is the primary approach • Activate student conceptual knowledge when presented with a real-life problem solving situation • Improve student motivation, participation, and generalization skills of students

  4. TEACHER COLLABORATION • Involves teachers of same subject matter • Weekly collaboration to discuss lesson delivery, teaching strategies, assessment results, and make revisions to plans as needed • Standards-driven reform is the primary approach • Planning for curriculum, pacing, common formative assessments, sharing of best practices during summer break

  5. RIGHT TRIANGLE TRIGONOMETRY GRANT PACERS REACH FOR THE STARS

  6. TRIGONOMETRY 三角法 TRIANGLE MEASURE 三角形计算 GREEK WORD MEANING: 在希腊的词汇中就是指：

  7. IN 140 B.C. HIPPARCHUS BEGAN TO USE AND WRITE TRIGONOMETRY 在公元前140年希帕庫斯 （Hipparchus）就已经开始使用三角法并撰写相关著作了。

  8. ANCIENT GREEKS USED TRIGONOMETRY TO MEASURE THE DISTANCE TO THE STARS 古希腊人曾使用三角法计算地球到恒星的距离。

  9. OBJECTIVES: • TO FIND TRIGOMETRIC RATIOS OF A RIGHT TRIANGLE. • TO FIND VALUES OF TRIGOMETRIC FUNCTIONS. • TO APPLY THE TRIGOMETRIC FUNCTIONS TO SOLVE RIGHT -TRIANGLE PROBLEMS.

  10. WE WILL DEAL ONLY WITH RIGHT TRIANGLES 我们将只对直角三角形进行说明 90 RIGHT TRIANGLES MUST HAVE A 90 DEGREE ANGLE 直角三角形必须有一个90度的角。

  11. HYPOTENUSE 斜边 LEG OPPOSITE TO B 角B的对边 B LEG ADJACENT TO ANGLE B 角B的邻边

  12. HYPOTENUSE LEG OPPOSITE TO B B LEG ADJACENT TO B SINE OF B = LENGTH OF LEG OPPOSITE B LENGTH OF HYPOTENUSE COSINE OF B = LENGTH OF LEG ADJACENT TO B LENGTH OF HYPOTENUSE TANGENT OF B = LENGTH OF LEG OPPOSITE B LENGTH OF LEG ADJACENT TO B

  13. 斜边 角B的对边 B 角B的邻边 sinB =角B对边长/斜边长 cosB = 角B邻边长/斜边长 tanB = 角B对边长/角B邻边长

  14. SAMPLE RIGHT TRIANGLE PROBLEMS 直角三角形例子 1.) x 20 c b 60 z 30 y Ø a Find the values to the nearest tenth of: b/c A.) sin Ø = _______ B.) cos Ø = _______ C.) tan Ø = _______ A.) XY = ________ B.) YZ = ________ 11.5 a/c 23.1 b/a

  15. APPLICATIONS: To avoid a steep descent, a plane flying at 30,000 ft. starts its descent 130 miles away from the airport. For the angle of descent Ø, to be constant, at what angle should the plane descend?

  16. 应用： 一个飞机在30,000英尺的高空飞行，为避免急剧下降，要从离机场130英里的时候开始降落。下降时与地面的角度 Ø一定, 求Ø?

  17. tan Ø = 30,000 5,280*130 Ø 30,000 ft. Ø 130 Miles

  18. An observer 5.2 km from a launch pad observes a rocket ascending. A. At a particular time the angle of elevation is 37 degrees. How high is the rocket? B. How far is the observer from the rocket? C. What will the angle of elevation be when the rocket reaches 30 km?

  19. b a 37 5.2 A. Tan 37 = a_ 5.2 B. Cos 37 = 5.2 b C. Tan = 30 Ø 5.2

  20. 一个观测员在离发射台5.2 km的地方观测火箭升空。 A. 在某一时刻，仰角是37度，这时火箭离地面多高？ B. 这一时刻观测员离火箭多远？ C. 当火箭到达 30 km 高空时，仰角是多少？

  21. A ship sails 340 kilometers on a bearing of 75 degrees. A. How far north of its original position is the ship? B. How far east of its original position is the ship?

  22. 一只船朝东北方向75度航行了340km. • 这只船距原来位置的北方多远？ • 这只船距原来位置的东方多远？

  23. b a A. Cos 75 = 340 a 340 B. Sin 75 = b 340 75

  24. BY THE STUDY OF TRIGONOMETRY---------- YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!! BE A ROCKET!!!!!!! REACH FOR THE STARS!

  25. BY THE STUDY OF TRIGONOMETRY---------- YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!! BE A ROCKET!!!!!!! REACH FOR THE STARS!

  26. APPLICATION ACTIVITY TRIGONOMETRY PROJECT with CLINOMETER WORKSHET

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