Problem Analysis:
The task involves identifying a pattern or rule governing the shapes in the given images and determining which of the provided options (labeled A, B, C) fits the sequence. The images consist of geometric shapes with shaded regions, and we need to deduce the underlying logic.
#### Observations from the Images:
1.
Top Row:
- The first image shows a quarter-circle shaded in the top-left corner of a square.
- The second image shows a semicircle shaded in the top-right corner of a square.
- The third image shows a full circle shaded in the center of a rectangle.
2.
Bottom Row:
- The first image shows a half-circle shaded in the bottom-left corner of a square.
- The second image shows two overlapping circles shaded within a square.
- The third image shows four overlapping circles shaded within a square.
#### Key Patterns:
-
Shape Evolution: The shapes evolve from simpler forms (quarter-circle, semicircle) to more complex forms (full circle, overlapping circles).
-
Shading Placement: The shading moves systematically across the grid (top-left, top-right, center, bottom-left, etc.).
-
Increasing Complexity: The complexity of the shaded region increases as we move from left to right in each row.
Step-by-Step Reasoning:
1.
Identify the Sequence:
- The top row progresses from a quarter-circle to a semicircle to a full circle.
- The bottom row starts with a half-circle and then shows overlapping circles.
2.
Determine the Next Shape:
- The top row ends with a full circle in the center.
- The bottom row starts with a half-circle and then shows two overlapping circles.
- Following this pattern, the next shape should involve an increase in complexity, likely involving more overlapping circles.
3.
Evaluate the Options:
-
Option A: Shows a single circle shaded in the center of a square. This does not fit the increasing complexity pattern.
-
Option B: Shows three overlapping circles shaded within a square. This fits the pattern of increasing complexity.
-
Option C: Shows four overlapping circles shaded within a square. While this is complex, it does not logically follow the sequence as closely as Option B.
4.
Conclusion:
- The sequence suggests that the next shape should have three overlapping circles, as it maintains the increasing complexity while fitting the observed pattern.
Final Answer:
$$
\boxed{B}
$$
Parent Tip: Review the logic above to help your child master the concept of circle area and perimeter worksheet.
