Problem: Identifying Tessellations
#### Task:
1. Determine whether each of the given tiling patterns is a tessellation.
2. Write "Yes" or "No" in the blanks provided for each pattern.
3. Provide reasons for your answers.
#### Definitions:
- A
tessellation is a pattern of shapes covering a plane without any gaps or overlaps.
- The shapes must fit together perfectly, and the pattern should be able to extend infinitely in all directions.
#### Analysis of Each Pattern:
---
(i)
-
Observation: This pattern consists of identical parallelograms arranged in a grid-like structure.
-
Reasoning:
- The parallelograms fit together perfectly without any gaps or overlaps.
- The pattern can be extended infinitely in all directions.
-
Conclusion: This is a tessellation.
Answer: Yes
---
(ii)
-
Observation: This pattern consists of irregular, interlocking shapes that appear to form a continuous surface.
-
Reasoning:
- The shapes fit together without gaps or overlaps.
- The pattern appears to be able to extend infinitely in all directions.
-
Conclusion: This is a tessellation.
Answer: Yes
---
(iii)
-
Observation: This pattern consists of hexagons arranged in a honeycomb-like structure.
-
Reasoning:
- The hexagons fit together perfectly without any gaps or overlaps.
- The pattern can be extended infinitely in all directions.
-
Conclusion: This is a tessellation.
Answer: Yes
---
(iv)
-
Observation: This pattern consists of circles arranged in a grid-like structure.
-
Reasoning:
- There are noticeable gaps between the circles.
- The spaces between the circles cannot be filled by the same shape, meaning the pattern does not cover the plane completely.
-
Conclusion: This is
not a tessellation.
Answer: No
---
Reasons for Answers:
1.
Pattern (i): The parallelograms fit together perfectly without gaps or overlaps, and the pattern can extend infinitely. Therefore, it is a tessellation.
2.
Pattern (ii): The irregular shapes fit together seamlessly without gaps or overlaps, and the pattern can extend infinitely. Therefore, it is a tessellation.
3.
Pattern (iii): The hexagons fit together perfectly without gaps or overlaps, and the pattern can extend infinitely. Therefore, it is a tessellation.
4.
Pattern (iv): The circles do not fit together without gaps; there are visible spaces between them that cannot be filled by the same shape. Therefore, it is
not a tessellation.
---
Final Answer:
\[
\boxed{
\text{(i) Yes, (ii) Yes, (iii) Yes, (iv) No}
}
\]
Parent Tip: Review the logic above to help your child master the concept of tessellations worksheet.
