中二数学教学笔记.pdf

中二數學教學筆記 Chapter 06 Square Roots and Pythagoras Theorem 平方根及畢氏定理 勾股定理 數學新里程 第二版 Section Topic Teaching Notes Classwork or Homework 6 1 Squares and Square Roots Students should be able to recall the definition of square and square root Students should be able to write down the values of the following x x where x is a perfect square 平方數 Ex 6A Q 1 4 6 2 The Values of Square Roots Students should be able to estimate the values of square roots Students should be able to obtain the values of square roots using calculator and rounding off in the stated conditions Ex 6A Q 2 Ex 6A Q 3 6 6 6 Irrational Numbers 無理數 Students should be able to identify real numbers 實數 under rational numbers 有理數 and irrational numbers 無理數 Students should be able to express numbers in surd form 根式 Students should be able to carry out 4 arithmetic operations of surds Students should be able to rationalize fractions Students are appreciated to explore transcendental number 超越數 on their own Ex 6E Q 1 5 Ex 6F Q 1 7 6 3 Pythagoras Theorem 500 600 B C 畢達哥拉斯定理 畢氏定理 百牛定理 Hecatomb Proposition 木匠定理 Carpenter s Theorem 新娘之椅 Bride s Chair 驢橋定理 法國和比利時等國 商高定理 商高時代 1100 B C 陳子定理 由陳子才提出 勾股定理 勾股弦定理 周脾算經 Students should be able to state the necessary condition in using Pythagoras Theorem Students should be able to apply Pythagoras Theorem to solve problems Students should be able to solve the special problems Ex 6B Q 1 9 Ex 6B Q 12 14 16 6 4 Proof of Pythagoras Theorem and its Converse Students should be able to give some examples of the proof of Pythagoras Theorem Students should be able to use the Converse of Pyth Th 畢氏定理的逆 定理 to identify whether a triangle is a right angled triangle Ex 6C Q 1 2 6 5 Applications of Pythagoras Theorem Students should be able to draw the right angled triangle for the given problems Students should be able to apply Pythagoras Theorem to solve the problem Ex 6D Q 2 7 參考書籍 1 數學拾趣 梁易天 劉應泉編