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Sequence of figures showing a growing pattern of squares with a consistent base of two shaded squares.

Three figures showing a pattern of squares with increasing height and width, each with a base of two shaded squares.

Three figures showing a pattern of squares with increasing height and width, each with a base of two shaded squares.

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Show Answer Key & Explanations Step-by-step solution for: A Collection of Visual Patterns Handouts | CollectEdNY
To solve the problem, let's analyze the given figures step by step and identify the patterns.

Step 1: Understand the Figures


We are given three figures (Figure 1, Figure 2, and Figure 3). Each figure consists of a grid of squares, some of which are colored orange. Our task is to observe how certain aspects change as the figure number increases.

#### Figure 1:
- Total squares: 9 (3x3 grid)
- Orange squares: 4

#### Figure 2:
- Total squares: 12 (4x3 grid)
- Orange squares: 6

#### Figure 3:
- Total squares: 15 (5x3 grid)
- Orange squares: 8

Step 2: Identify Patterns


We need to determine what changes as the figure number increases. Let's examine two key aspects:
1. Total number of squares in each figure.
2. Number of orange squares in each figure.

#### Pattern 1: Total Number of Squares
- Figure 1: 9 squares (3 rows × 3 columns)
- Figure 2: 12 squares (4 rows × 3 columns)
- Figure 3: 15 squares (5 rows × 3 columns)

From this, we can see that the total number of squares increases by 3 for each subsequent figure. This suggests a linear pattern:
\[ \text{Total squares} = 3 \times (\text{Figure number} + 2) \]

#### Pattern 2: Number of Orange Squares
- Figure 1: 4 orange squares
- Figure 2: 6 orange squares
- Figure 3: 8 orange squares

Here, the number of orange squares increases by 2 for each subsequent figure. This also suggests a linear pattern:
\[ \text{Orange squares} = 2 \times (\text{Figure number} + 1) \]

Step 3: Fill in the Blanks


The problem asks us to fill in the blanks with what changes as the figure number changes. Based on our observations:

1. As the figure number changes, the total number of squares also changes.
2. As the figure number changes, the number of orange squares also changes.

Final Answer


\[
\boxed{\text{the total number of squares, the number of orange squares}}
\]
Parent Tip: Review the logic above to help your child master the concept of visual patterns worksheet.
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