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Sequence of figures showing increasing block patterns.

Three figures made of orange blocks showing a pattern: Figure 1 has 5 blocks, Figure 2 has 7 blocks, and Figure 3 has 9 blocks.

Three figures made of orange blocks showing a pattern: Figure 1 has 5 blocks, Figure 2 has 7 blocks, and Figure 3 has 9 blocks.

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Show Answer Key & Explanations Step-by-step solution for: A Collection of Visual Patterns Handouts | CollectEdNY
Let's analyze the pattern in the figures step by step.

---

Step 1: Observe the Figures



We are given three figures made of orange squares. Each figure has:
- A horizontal base (bottom row)
- A vertical stack (top part) centered on the base

Let’s count the number of squares in each:

#### Figure 1
- Base: 3 squares
- Vertical stack: 2 squares
- Total: 5 squares

#### Figure 2
- Base: 5 squares
- Vertical stack: 3 squares
- Total: 8 squares

#### Figure 3
- Base: 7 squares
- Vertical stack: 4 squares
- Total: 11 squares

---

Step 2: Identify the Pattern



Let’s look at how the base and stack change with the figure number:

| Figure Number | Base Length | Stack Height |
|---------------|-------------|--------------|
| 1 | 3 | 2 |
| 2 | 5 | 3 |
| 3 | 7 | 4 |

We can see:
- Base length increases by 2 each time: 3 → 5 → 7 → ...
- Stack height increases by 1 each time: 2 → 3 → 4 → ...

So:
- Base = 2 × (figure number) + 1
- For Figure 1: 2×1 + 1 = 3
- For Figure 2: 2×2 + 1 = 5
- For Figure 3: 2×3 + 1 = 7
- Stack height = figure number + 1
- Figure 1: 1 + 1 = 2
- Figure 2: 2 + 1 = 3
- Figure 3: 3 + 1 = 4

---

Answer to Question 1:



> As the figure number changes, the number of squares in the base and the height of the vertical stack also changes.

Alternatively, more precisely:
> As the figure number changes, the size of the base and the height of the tower also changes.

Or even better:
> As the figure number changes, the number of squares in the figure also changes.

But since the question asks what *also* changes, and we're observing both base and stack changing, a good answer is:

As the figure number changes, the number of squares in the base and the height of the vertical stack also changes.

---

Answer to Question 2: Draw Figure 4 and Figure 5



#### Figure 4:
- Figure number = 4
- Base = 2×4 + 1 = 9 squares
- Stack = 4 + 1 = 5 squares
- So: a horizontal base of 9 squares, with a vertical stack of 5 squares centered on it.

#### Figure 5:
- Figure number = 5
- Base = 2×5 + 1 = 11 squares
- Stack = 5 + 1 = 6 squares
- So: base of 11 squares, stack of 6 squares centered.

---

Drawing Instructions (Text Representation)



Since I can't draw images here, I'll represent them using text.

#### Figure 4:
```





□ □ □ □ □ □ □ □ □
```

(Vertical stack of 5 squares, centered on a base of 9 squares)

#### Figure 5:
```






□ □ □ □ □ □ □ □ □ □ □
```

(Vertical stack of 6 squares, centered on a base of 11 squares)

---

Final Answers:



1. As the figure number changes, the number of squares in the base and the height of the vertical stack also changes.

2.
Figure 4:
- Base: 9 squares
- Stack: 5 squares (centered)

Figure 5:
- Base: 11 squares
- Stack: 6 squares (centered)

You can now draw these accordingly — just make sure the vertical stack is centered on the base.
Parent Tip: Review the logic above to help your child master the concept of algebra patterns worksheet pdf.
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