Mission: The Fence Challenge — Level 5
Akuuu has 24 meters of fencing. She wants to build a rectangular garden for her vegetables.
Her brother says: “Make it long and skinny — you’ll get more space to plant!”
Her sister says: “Make it square — that’s always the biggest!”
👉 Who is right? Can you know without building it?
Think: Does the shape change how much fits inside, even with the same fence length?
✏️ Draw two different shapes with 24m of fence. Guess which has more space inside:
- 📏 Perimeter = total distance around the outside (your fence)
- ⬜ Area = space inside the shape (your growing space)
- 🔄 Same perimeter can give different areas depending on shape
Look at these two gardens, both using 24m of fence:
Garden A: 10m long × 2m wide
Garden B: 7m long × 5m wide
👉 Which garden has more growing space inside? Show your work.
👉 Why does the same fence length give different growing space?
You have 20m of fence. Find three different rectangles you could make.
👉 Which shape gives the MOST growing space? Prove it.
A child says: “A 8m × 4m garden has perimeter 32m and area 32m². So perimeter and area are always the same number!”
👉 What mistake are they making? Give a counter-example.
Akuuu builds an L-shaped garden. The outer edges measure 5m, 3m, 2m, 2m, 3m, and 5m.
👉 What is the perimeter? Is it still 24m? Explain.
🧠 Part A — Transfer
A farmer has 36m of fencing. She wants the biggest possible rectangular field for her cows.
👉 What dimensions should she choose? Prove this is the maximum.
Think: You found a pattern with 20m and 24m. Does the same rule work for 36m? What shape always wins?
🧠 Part B — Thinking Pause
- I explained why
- I found the mistake in the “same number” claim
- I showed another way to check my answer
⭐ Mission Reflection
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