📏 觀測與描述變化量Observation and Description of Change
Created by fj , inspired by tiger

Stage 1: Find Original Spring Length
第一關：找出彈簧原長

There is a spring and a ruler in the canvas above. Please observe the ruler and record the current length of the spring.

上方的畫布中有一條彈簧和一把尺。請觀察尺規的刻度，並記錄彈簧目前的長度。

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.

Unit
單位
 Before
變化前
 After
變化後
公分cm
英吋inch

Stage 3: Calculate Percentage Change
第三關：計算變化量百分比

Please calculate the percentage change based on your recorded values.

請根據剛剛記錄的變化量，計算出形變的百分比。

Unit
單位
 Before
變化前
 After
變化後
 變化量Change Percentage Change Calculation
變化量百分比計算
(Change ÷ Before)
(變化量 ÷ 變化前)
公分cm
= %
英吋inch
= %

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 (%)".

現在請隨意拉動彈簧！畫布會自動顯示「絕對長度(公分)」與「相對原長(百分比)」。

💡 Focus:思考重點： cm is a fixed "external measurement", while % is an "internal measurement" based on the spring itself.

公分是尺規上固定的「外部測量」，而百分比是以彈簧自己為基準的「內部測量」。

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：

(1) Calculate change externally, then measure internally:

(1) 先用外部基準計算變化量, 再用內部基準測量此變化量：

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。

-

(2) Measure states internally, then calculate change:

(2) 先用內部基準分別測量終了值與初始值, 再計算變化量：

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。

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Note:註: The beginning relative to itself is 1. The end relative to the beginning also represents the change as a dilation.

變化前相對於自己是 1。變化後相對於變化前的比例，也代表了伸縮的倍率。

🎉 Experiment Successful! / 實驗大成功！

📝 Teacher's Summary: / 老師的總結：

Excellent! In this experiment, you learned two perspectives on measuring length:

非常好！在這次的實驗中，你學到了測量長度的兩種觀點：

  • 外部絕對單位 (cm / inch)：External Absolute Unit (cm / inch): 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.
  • 內部相對單位 (%)：Internal Relative Unit (%): 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!

Created by fj , inspired by tiger