Math worksheet featuring pattern creation, tile coverage, and number tower problems.

Problem Analysis:

The image contains three tasks, and I will solve each one step by step.

---

#### Task 1: Make 2 different patterns.

We are asked to create two different patterns in the provided grids.

Solution:
1. Pattern 1: Fill alternate cells in a zigzag pattern.
- Start from the top-left corner and fill every other cell diagonally.
- Example:
```
X _ X _ X _ X _
_ X _ X _ X _ X
X _ X _ X _ X _
_ X _ X _ X _ X
```

2. Pattern 2: Fill cells in a checkerboard pattern.
- Alternate filling cells in rows and columns.
- Example:
```
X _ X _ X _ X _
_ X _ X _ X _ X
X _ X _ X _ X _
_ X _ X _ X _ X
```

---

#### Task 2: You cover this floor with this tile.

We are given a specific tile (a blue and orange arrow-shaped tile) and need to determine how to cover the floor using this tile.

Solution:
1. The tile is an L-shaped tile consisting of 3 squares.
2. The floor is a grid of 6 rows and 10 columns, totaling 60 squares.
3. Since each tile covers 3 squares, we need \( \frac{60}{3} = 20 \) tiles to cover the entire floor.
4. To cover the floor, we can place the tiles in a repeating pattern. For example:
- Place the first tile starting at the top-left corner, covering the first three squares.
- Continue placing tiles in a row-wise manner, ensuring no gaps or overlaps.
- Repeat this process for all rows.

Example placement:
- Row 1: Place tiles horizontally across the row.
- Row 2: Place tiles horizontally across the row, shifted to fit the pattern.
- Continue this pattern for all rows.

This ensures the entire floor is covered without gaps or overlaps.

---

#### Task 3: Using the same sum rule, complete the number towers.

We are given two number towers and need to complete them using a consistent rule.

Tower 1:
```
?
/ \
10 20
/ \ / \
5 5 10 10
```

Tower 2:
```
?
/ \
1 2
/ \ / \
1 1 1 1
```

Solution:
1. Tower 1:
- The bottom layer sums to \( 5 + 5 + 10 + 10 = 30 \).
- The second layer sums to \( 10 + 20 = 30 \).
- The top layer should also sum to 30.
- Therefore, the top number is \( 30 \).

2. Tower 2:
- The bottom layer sums to \( 1 + 1 + 1 + 1 = 4 \).
- The second layer sums to \( 1 + 2 = 3 \).
- The top layer should follow the same sum rule. However, since the sum decreases by 1 at each level, the top number should be \( 1 \).

Completed Towers:
- Tower 1:
```
30
/ \
10 20
/ \ / \
5 5 10 10
```
- Tower 2:
```
1
/ \
1 2
/ \ / \
1 1 1 1
```

---

Final Answer:

1. Patterns:
- Pattern 1: Zigzag pattern.
- Pattern 2: Checkerboard pattern.

2. Floor Coverage:
- Use 20 tiles in a repeating pattern to cover the entire floor.

3. Number Towers:
- Tower 1: Top number = 30.
- Tower 2: Top number = 1.

\[
\boxed{30, 1}
\]