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Geometric Patterns in Nature
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Geometric Patterns in Nature
📚 Part 1: Multiple Choice
1. Which type of symmetry does a typical maple leaf most often display?
Reflectional (line of symmetry)
Rotational
Translational
No symmetry
2. Many seed heads and pinecones show spiral patterns that are modeled well by which sequence?
Fibonacci sequence
Arithmetic sequence
Geometric sequence
Prime numbers
3. If one leaf is a dilation of another with scale factor 3, which statement is true?
All corresponding lengths are 3 times larger and areas are 9 times larger
All lengths are 3 times larger and areas are 3 times larger
Angles change by a factor of 3
The perimeter stays the same
4. Check all observations that indicate congruent parts in a natural object (e.g., petals, leaflets):
Equal length segments measured across parts
Identical angles between corresponding edges
Same color pattern
One part is a scaled enlargement of the other
✏️ Part 2: Short Answers & Analysis
5. Sketch one natural object you collected. Mark any line(s) of symmetry or center of rotation you observe.
6. Use measurements from your sketch: original leaf length = 4 in, a similar enlarged leaf = 10 in. Calculate the scale factor from original to enlarged. Show work.
7. A flower has 5 identical petals arranged around its center. What is the smallest angle of rotation (in degrees) that maps the flower onto itself? Explain in one sentence.
8. In 2–3 sentences, describe one proportional relationship you observed in your object and explain how that relates to a geometric transformation (dilation, reflection, or rotation).
🧩 Part 3: Collaborative Planning
9. Planning the giant visual: List two clear ways your group will show symmetry and two ways you will show proportional relationships on the chart paper (use brief phrases).
10. Presentation note (one short sentence): Write a single sentence your pair can use to explain the main mathematical idea you discovered.
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