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【教学课件】《1.1 锐角三角函数(1)》

  • 2026-03-29 13:24:12
【教学课件】《1.1 锐角三角函数(1)》

《1.1 锐角三角函数（1）》

左立元（赵桂芳名师工作室A组）

作者简介

左立元，沈阳市第四十五中学数学教师，赵桂芳名师工作室A组成员。曾获得辽宁省教育教学课件三等奖、沈阳市优课一等奖、沈阳市中小学校本课程特等奖、沈阳市工会暨青年教师比赛中学数学组第4名、“一师一优课”市级优课和区微课大赛特等奖等奖项，多次参与市规划办、主持区规划办和学会课题研究。

作品简介

本节课，选自北师大版教材九年级下册第一章第1节《锐角三角函数》第1课时，既是对初中直角三角形的边角关系探究的延伸与升华，也是高中三角函数体系构建的认知基础，为学生实现从几何直观到代数抽象的思维跨越搭建关键桥梁。
章前引言以小明测塔高的实践经历导入，使学生直观感受到本章知识在现实生活的广泛应用价值，进而认识到开展相关内容学习与探究的必要性。继而，新授课以“哪个梯子更陡”的生活实际问题作为探究起点，引导学生将实际问题抽象为数学问题，启发学生思考在实际测量或工具受限的情况下如何科学描述“陡”的程度。多层次的数学探究活动，充分发挥学生的主体性。从动手操作测量、猜想比值规律，到几何画板交互式体验，再到相似三角形原理的严谨证明与数学抽象，层层递进，学生自然生成并建构了正切概念。从特殊角的正切值的计算到非特殊角的正切值的几何画板动态演示，让学生直观感受到正切值随着锐角大小的变化而变化，感受函数思想。后续通过多元例题辨析、变式练习深化、结合坡度概念的实际应用，进一步促进了学生知识的迁移与能力的培养。课堂小结融入结构框图的设计，既与章前引言形成有效呼应，同时又为学生系统学习三角函数夯实了认知基础。最后，希望这一教学课件能够成为和教师共同研讨教学的媒介，也能如一缕引路微光，帮助更多的学生拨开认知的迷雾，奔向更开阔的数学远方。

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  1. CONNECT:[ UseTime:0.000957s ] mysql:host=127.0.0.1;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.001654s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000739s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000708s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.001408s ]
  6. SELECT * FROM `set` [ RunTime:0.000608s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.001498s ]
  8. SELECT * FROM `article` WHERE `id` = 466607 LIMIT 1 [ RunTime:0.001214s ]
  9. UPDATE `article` SET `lasttime` = 1775612057 WHERE `id` = 466607 [ RunTime:0.019272s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 66 LIMIT 1 [ RunTime:0.003275s ]
  11. SELECT * FROM `article` WHERE `id` < 466607 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.001383s ]
  12. SELECT * FROM `article` WHERE `id` > 466607 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.001119s ]
  13. SELECT * FROM `article` WHERE `id` < 466607 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.002430s ]
  14. SELECT * FROM `article` WHERE `id` < 466607 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.002163s ]
  15. SELECT * FROM `article` WHERE `id` < 466607 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.014117s ]
0.153635s