When Pearls Meet Seasonal Changes: Mathematical Thinking on a Variable Growth Model

Math in Biology: Quantity in Summer, Quality in Winter

There is a golden rule in pearl farming: in summer, the water temperature is high and metabolism is fast, so pearls grow quickly but have a loose luster; in winter, the water temperature is low and growth is slow but the layers are dense. This "variable growth" makes the calculation of the number of pearl layers very interesting.

🟢 Middle School Math Practice: Partial Mean

Let's assume we simplify a year into two seasons, each with 180 days:

1. Total quantity calculated in segments:

   • Summer (Fast): 6 floors per day -> 180 x 6 = 1,080 floors

   • Winter (slow): 3 floors per day -> 180 x 3 = 540 floors

   • Total for one year: 1,620 floors.

2. Strategy Comparison: If pursuing high quality, maintaining a steady, slow growth of 4 floors per day throughout the year would only result in a total of 1,440 floors per year. This helps students understand the concepts of **trade-off** and averages.

🔴 High School Math Challenge: Mr. Hui's Q&A Section

Real-world temperature changes are periodic functions, not simple piecewise constants. I'd like to discuss this with Dick Sir:

• Periodic modeling: If a more accurate model is to be built for this kind of seasonally fluctuating growth rate (e.g., combining trigonometric functions or piecewise exponential functions), how would students be advised to break down such complex problems within the scope of the DSE curriculum?

• Series and Accumulation: When faced with variable-speed accumulation in long-term farming (e.g., 3 years or more), how can we use the concept of **Series** to make efficient estimates instead of calculating them month by month?

We look forward to Mr. Hui@Mathmagic revealing the quick solutions to these advanced calculations from the perspective of a professional DSE instructor!