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Stage 1: Find Original Spring Length
第一關：找出彈簧原長
Étape 1 : Trouver la Longueur Initiale
There is a spring and a ruler in the canvas above. Please observe the ruler and record the current length of the spring.
Stage 2: Stretch the Spring and Observe!
第二關：拉動彈簧，觀察變化！
請用滑鼠或手指拖曳下方彈簧尖端的紅色圓點，將彈簧拉長或壓縮。決定好後，點擊右上方鎖定按鈕。Drag the red dot at the tip of the spring to stretch or compress it. Click the Lock button when ready.Faites glisser le point rouge au bout du ressort pour l\'étirer ou le comprimer. Cliquez sur Verrouiller lorsque vous avez terminé.
| Unit 單位 Unité |
Before 變化前 Avant |
After 變化後 Après |
|---|---|---|
| 公分cmcm | ||
| 英吋inchpouce |
Stage 3: Calculate Percentage Change
第三關：計算變化量百分比
Étape 3 : Calculer le Pourcentage de Changement
Please calculate the percentage change based on your recorded values.
| Unit 單位 Unité |
Before 變化前 Avant |
After 變化後 Après |
變化量ChangeChangement | Percentage Change Calculation 變化量百分比計算 Calcul du Pourcentage
(Change ÷ Before)(變化量 ÷ 變化前) (Changement ÷ Avant) |
|---|---|---|---|---|
| 公分cmcm |
|
|||
| 英吋inchpouce |
|
External Reference (cm) vs Internal Reference (Original Length)
外部基準（以公分為基準）vs內部基準（以原長為基準）
Now drag the spring freely! The canvas will automatically display the "Absolute Length (cm)" and "Relative Length (%)".
💡 Focus:思考重點：Point de Réflexion : cm is a fixed "external measurement", while % is an "internal measurement" based on the spring itself.
Did you observe anything interesting?
你觀察到了什麼有趣的現象嗎？
Summary: Different Methods to Calculate Percentage Change
總結：計算變化量百分比的不同方法
There are two ways to calculate percentage change (relative change as translation):計算變化量百分比有兩種方式：Il y a deux façons de calculer le pourcentage de changement :
(1) Calculate change externally, then measure internally:
First, determine the change as a translation, and then calculate its relative measure.首先計算作為平移的變化量，然後計算它的相對比例。Déterminez d\'abord le changement comme une translation, puis calculez sa mesure relative.
(2) Measure states internally, then calculate change:
First, calculate the relative measures, and then determine the change as a translation.首先計算各自的相對比例，然後計算比例的變化差值。Calculez d\'abord les mesures relatives, puis déterminez le changement.
Note:註:Note : The beginning relative to itself is 1. The end relative to the beginning also represents the change as a dilation.
🎉 Experiment Successful! / 實驗大成功！ / Expérience Réussie !
📝 Teacher\'s Summary: / 老師的總結： / Résumé du Professeur :
Excellent! In this experiment, you learned two perspectives on measuring length:
- 外部絕對單位 (cm / inch)：External Absolute Unit (cm / inch): Unité Absolue Externe (cm / pouce) : 每個人量出來的結果都一樣，適合用來溝通和製作物品。Everyone\'s measurement is the same, suitable for communication and manufacturing.La mesure de chacun est la même, adaptée à la communication.
- 內部相對單位 (%)：Internal Relative Unit (%): Unité Relative Interne (%) : 用自己原本的狀態當作 100%。這能告訴我們彈簧「變形了多少比例」，這在物理學計算彈力，或是數學上討論成長率時，是非常重要的「相對量感」！Using its own original state as 100%. This tells us "what proportion the spring has deformed," which is a very important "relative sense of quantity" when calculating elastic force in physics or discussing growth rates in mathematics!
太棒了！你已經具備了科學家的觀察力與數學家的計算力！Great job! You now have the observation skills of a scientist and the calculation skills of a mathematician!
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