Grade 4 Geometry Worksheet on Tessellations - Identify which patterns show tessellations.

Problem Description:

The task is to identify which images in the worksheet represent tessellations. A tessellation is a pattern of shapes that covers a flat surface completely without any gaps or overlaps.

Solution Approach:

1. Definition Recap:
- A tessellation is a tiling of a plane using one or more geometric shapes (tiles) such that there are no gaps and no overlaps.
- The shapes must fit together perfectly to cover the entire surface.

2. Analysis of Each Image:
Let's analyze each image to determine if it meets the criteria for a tessellation.

#### Image 1:
- Description: Blue squares with green diamond patterns inside.
- Analysis: The blue squares are arranged in a grid pattern, and the green diamond patterns do not affect the overall tessellation. There are no gaps or overlaps.
- Conclusion: This is a tessellation.

#### Image 2:
- Description: Orange diamonds arranged in a repeating pattern.
- Analysis: The diamonds are arranged in a way that they fit together perfectly without any gaps or overlaps.
- Conclusion: This is a tessellation.

#### Image 3:
- Description: Hexagons with alternating colors (yellow and blue).
- Analysis: The hexagons are arranged in a honeycomb-like pattern, which is a classic example of a tessellation. There are no gaps or overlaps.
- Conclusion: This is a tessellation.

#### Image 4:
- Description: Triangles of various colors arranged in a complex pattern.
- Analysis: The triangles are arranged in a way that they fit together perfectly without any gaps or overlaps. Despite the complexity, the pattern is consistent.
- Conclusion: This is a tessellation.

#### Image 5:
- Description: Stars with overlapping points.
- Analysis: The stars overlap at their points, creating gaps between them. This violates the condition of no gaps or overlaps.
- Conclusion: This is not a tessellation.

#### Image 6:
- Description: Gray circles arranged in a grid pattern.
- Analysis: The circles do not touch each other; there are visible gaps between them. This violates the condition of no gaps.
- Conclusion: This is not a tessellation.

#### Image 7:
- Description: Yellow and blue shapes that appear to be irregular polygons.
- Analysis: The shapes fit together perfectly without any gaps or overlaps. Despite their irregularity, the arrangement satisfies the tessellation criteria.
- Conclusion: This is a tessellation.

#### Image 8:
- Description: Blue and red hexagons arranged in a repeating pattern.
- Analysis: The hexagons are arranged in a way that they fit together perfectly without any gaps or overlaps.
- Conclusion: This is a tessellation.

Final Answer:

The images that show tessellations are:
- Image 1
- Image 2
- Image 3
- Image 4
- Image 7
- Image 8

Thus, the boxes to check are: 1, 2, 3, 4, 7, 8.

\boxed{1, 2, 3, 4, 7, 8}