Growing Pattern Worksheet - Draw the next picture in each sequence.

Problem: Growing Pattern

The task is to identify the growing pattern in each sequence and draw the next figure in the series. Let's analyze each pattern step by step.

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#### Pattern 1: Triangles
- Sequence:
- First figure: 1 triangle
- Second figure: 3 triangles
- Third figure: 6 triangles

- Observation:
- The number of triangles increases in a specific pattern.
- The first figure has 1 triangle.
- The second figure adds 2 more triangles (total = 3).
- The third figure adds 3 more triangles (total = 6).
- The pattern suggests that the number of triangles added increases by 1 each time.

- Next Figure:
- The fourth figure should add 4 more triangles to the previous total (6 + 4 = 10).
- Therefore, the fourth figure will have 10 triangles.

- Drawing:
- Draw 10 triangles arranged in a triangular pattern.

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#### Pattern 2: Squares
- Sequence:
- First figure: 2 squares
- Second figure: 4 squares
- Third figure: 6 squares

- Observation:
- The number of squares increases by 2 each time.
- First figure: 2 squares
- Second figure: 2 + 2 = 4 squares
- Third figure: 4 + 2 = 6 squares

- Next Figure:
- The fourth figure will have 6 + 2 = 8 squares.

- Drawing:
- Draw 8 squares arranged in a rectangular pattern (e.g., 2 rows of 4 squares).

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#### Pattern 3: Blue Circles
- Sequence:
- First figure: 1 blue circle
- Second figure: 1 blue circle + 2 smaller circles
- Third figure: 1 blue circle + 3 smaller circles

- Observation:
- The number of smaller circles increases by 1 each time.
- First figure: 1 blue circle + 0 smaller circles
- Second figure: 1 blue circle + 2 smaller circles
- Third figure: 1 blue circle + 3 smaller circles

- Next Figure:
- The fourth figure will have 1 blue circle + 4 smaller circles.

- Drawing:
- Draw 1 large blue circle with 4 smaller blue circles around it.

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#### Pattern 4: Shapes with Increasing Size
- Sequence:
- First figure: 1 small diamond
- Second figure: 4 medium crosses
- Third figure: 9 large squares

- Observation:
- The shapes increase in size and number.
- The number of shapes follows a square pattern: \(1^2 = 1\), \(2^2 = 4\), \(3^2 = 9\).
- The shapes change from diamonds to crosses to squares.

- Next Figure:
- The fourth figure will have \(4^2 = 16\) shapes.
- The next shape in the sequence after squares could be another geometric shape, such as hexagons or pentagons. For simplicity, let's assume the pattern continues with a new shape (e.g., hexagons).

- Drawing:
- Draw 16 hexagons arranged in a 4x4 grid.

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Final Answers:

1. Next Figure for Triangles: Draw 10 triangles in a triangular pattern.
2. Next Figure for Squares: Draw 8 squares in a rectangular pattern.
3. Next Figure for Blue Circles: Draw 1 large blue circle with 4 smaller blue circles.
4. Next Figure for Shapes: Draw 16 hexagons in a 4x4 grid.

Boxed Final Answer:

\[
\boxed{
\text{1. 10 triangles, 2. 8 squares, 3. 1 large circle + 4 smaller circles, 4. 16 hexagons}
}
\]