✅ Figure it Out – Answers
1. Pattern in each sequence
🔷 (A) Regular Polygons
Pattern: The number of sides increases by 1 each time
👉 3, 4, 5, 6, 7, 8, 9, 10
✔ Next shape: 11-sided polygon (Undecagon)
🔷 (B) Complete Graphs (K₂, K₃, K₄, …)**
Pattern:
Number of vertices increases by 1
Each new vertex is connected to all other vertices
✔ Next shape: K₇ (7 vertices, all connected)
🔷 (C) Stacked Squares
Pattern: Squares form an n × n grid
👉 1, 4, 9, 16, 25
✔ Next: 6 × 6 = 36 small squares
🔷 (D) Stacked Triangles
Pattern: Triangular numbers
👉 1, 3, 6, 10, 15
✔ Next: 21 small triangles
🔷 (E) Koch Snowflake
Pattern:
At each step, every side is divided and a small triangle is added
✔ Next: A more complex snowflake shape
2. Try and redraw each sequence in Table 3 in your notebook.
Can you draw the next shape in each sequence? Why or why not?
After each sequence, describe in your own words what is the rule or pattern for forming the shapes in the sequence
✔ Yes, because each sequence follows a clear rule:
Polygons → add one side
Graphs → add one vertex and connect it to all others
Squares → follow n² pattern
Triangles → follow triangular numbers
Snowflake → follow repeating fractal rule
👉 So, the next shape can be predicted and drawn.
3. Rule in simple words
| Sequence | Rule |
|---|---|
| Polygons | Add one side each time |
| Graphs | Add one vertex and connect to all |
| Squares | Make n × n grid |
| Triangles | Add one more triangle in each row |
| Snowflake | Add small triangles on each side |
🔥 Final Conclusion
Every shape sequence follows a mathematical rule
These rules are often related to number sequences
So, shapes and numbers are closely connected
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