Math maze activity for Class 4 students focusing on place value and face value concepts.

Problem Description:

The task involves guiding a mouse through a maze by selecting the path that leads to the cheese with the highest place value of the encircled digits. The mouse starts at the bottom and must navigate to the "Mouse Trap" at the top by choosing the correct path based on comparing the place values of the encircled digits.

Solution Approach:

1. Understanding Place Value:
- The place value of a digit in a number depends on its position.
- For example, in the number `93510`, the encircled digit is `3`, which is in the thousands place. Its place value is \(3 \times 1000 = 3000\).

2. Comparing Place Values:
- At each junction, compare the place values of the encircled digits in the numbers leading to different paths.
- Choose the path with the higher place value.

3. Step-by-Step Navigation:
- Start from the bottom (the "Start" point).
- At each junction, evaluate the place values of the encircled digits and choose the path with the higher place value.
- Continue this process until reaching the "Mouse Trap."

Step-by-Step Solution:

#### Starting Point:
- The mouse starts at the bottom with the number `51283`. The encircled digit is `8`, which is in the tens place. Its place value is \(8 \times 10 = 80\).

#### First Junction:
- Paths lead to:
- `46395`: Encircled digit is `3` (thousands place), place value = \(3 \times 1000 = 3000\).
- `36909`: Encircled digit is `6` (ten-thousands place), place value = \(6 \times 10000 = 60000\).
- Choose the path with `36909` (higher place value: 60000).

#### Second Junction:
- Paths lead to:
- `64810`: Encircled digit is `8` (thousands place), place value = \(8 \times 1000 = 8000\).
- `53710`: Encircled digit is `3` (hundreds place), place value = \(3 \times 100 = 300\).
- Choose the path with `64810` (higher place value: 8000).

#### Third Junction:
- Paths lead to:
- `48165`: Encircled digit is `8` (thousands place), place value = \(8 \times 1000 = 8000\).
- `38150`: Encircled digit is `8` (hundreds place), place value = \(8 \times 100 = 800\).
- Choose the path with `48165` (higher place value: 8000).

#### Fourth Junction:
- Paths lead to:
- `98157`: Encircled digit is `8` (thousands place), place value = \(8 \times 1000 = 8000\).
- `88150`: Encircled digit is `8` (ten-thousands place), place value = \(8 \times 10000 = 80000\).
- Choose the path with `88150` (higher place value: 80000).

#### Fifth Junction:
- Paths lead to:
- `93510`: Encircled digit is `3` (thousands place), place value = \(3 \times 1000 = 3000\).
- `8215`: Encircled digit is `2` (hundreds place), place value = \(2 \times 100 = 200\).
- Choose the path with `93510` (higher place value: 3000).

#### Final Path:
- The mouse reaches the "Mouse Trap" by following the path with the highest place values at each step.

Final Answer:

The correct path for the mouse to reach the "Mouse Trap" is:
```
51283 → 36909 → 64810 → 48165 → 88150 → 93510
```

Thus, the colored cheese pieces should be those along this path. The final answer is:
\[
\boxed{51283 \rightarrow 36909 \rightarrow 64810 \rightarrow 48165 \rightarrow 88150 \rightarrow 93510}
\]