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這教材可讓學生直觀理解快慢的比較,從而認識速率的概念。五場賽事分別展示不同距離與時間的關係。最後一個"特訓"的活動可讓學生詳細分析距離和時間的關係,甚至速率、距離和時間的計算。教師可考慮先進行下半部簡單的行程圖活動,之後才利用這"特訓"活動作進一步的探討。
This set of materials is designed for developing concept of speed and techniques of calculation or estimation. It can be used for discussion in class. There are 5 recorded races at the beginning, representing different situations where distance and time vary. The final applet of 'training' allows more detailed exploration by adjusting relevant quantities.
五場賽事的情景如下(details of first 5 races):
1. 距離相同但時間不同 (same distance; different time)
2. 距離不同但時間相同 (different distance; same time)
3. 距離與時間都不同,速率相同:2格每秒 (different distance, time; same speed)
4. 距離與時間都不同,速率亦不同:2·5格和3格每秒 (different distance, time, speed)
5. 距離與時間都不同,速率亦不同:2格和1·5格每秒 (different distance, time, speed)
賽事3至5都需要格線和仔細的時間記錄作分析,跟賽事1和2不同。建議使用賽事1,2再加上3至5之中的一至兩項作課堂討論。
Races 3 to 5 may require more detailed analysis. It leads to more precise description of speed.
特訓專區 (training area):
你可以設定跑道和完成時間,從而分析蝸牛的快慢。You may set your own track length and finishing time in order to explore relation among those quantities.
有關速率,時間和距離的提問,可參考以下例子(3 main ways to ask):
1. [url=https://docs.google.com/presentation/d/13L49RsvA46JyQCiK99sCpmFS5BE_qzsZMJ3AkS_Gtok/edit?usp=sharing]找速率 find the speed[/url]
2. [url=https://docs.google.com/presentation/d/1sJxfWXaLR__X2YJvsGwU6FzTlRu3nksuylxILUmJ52Y/edit?usp=sharing]找時間 find the time[/url]
3. [url=https://docs.google.com/presentation/d/1uKMAc6IeR7wvDY30JWH6v1PTJWEGFB1_andYgJsv4FA/edit?usp=sharing]找距離 find the distance[/url]
The following activities were adapted from the DfE Standards Unit resource: Interpreting Distance-Time Graphs with a computer (https://www.stem.org.uk/rxucg).
This GeoGebra version is adapted from the work of Dan Cooper, Tom Button and Tim Brzezinski. Please see https://ggbm.at/FYdzG77h
More resources related to this activity:
Language of Functions and Graphs (from Shell Centre) https://www.mathshell.com/materials.php?item=lfg&series=tss
有關"行程1":
本課業可介紹基本行程圖的製作和閲讀。它亦可讓學生集中討論均速運動中距離和時間的正比關係。
圖中一段"短片"顯示一輛汔車在公路上行走十秒的情況。另外,我們亦可顯示每秒航拍的照片,並列在圖表上。
進一步提問讓學生觀察和思考距離和時間的關係。例如:
隱藏所有照片後,點擊A顯示某一秒的照片。(移動時間軸上的綠點可揀選任何一秒。)
第6秒的照片顯示那一刻車已行走120米。那麼,如果車速不變,學生能計算(或估計)任何一秒車行的距離嗎?
點擊B可顯示另一秒的路面照片,但車的位置暫時隱藏。這照片亦可移動,以方便討論任何一秒車的位置。
學生可嘗試描述3秒、2秒或1秒的情況,並解釋如何得知。最後點擊顯示車的位置作比較。
如有需要,重複以上討論或是轉看行程2,讓學生認識均速情況下距離和時間的正比關係。