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.
PNG
699×902
37.6 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #350988
⭐
Show Answer Key & Explanations
Step-by-step solution for: A Collection of Visual Patterns Handouts | CollectEdNY
▼
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.
---
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
---
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 ✔
---
> 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.
---
#### 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.
---
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)
---
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.
---
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.