Math worksheet for practicing place value and number sense with the number 60,812.

Problem Analysis:

The task involves working with the "special number" 60,812 and performing various mathematical operations and comparisons. Let's break it down step by step.

---

Step 1: Identify the value of each digit

The special number is 60,812. We need to determine the value of each digit based on its place value.

- Value of the digit 2: The digit 2 is in the ones place, so its value is \( 2 \times 1 = 2 \).
- Value of the digit 1: The digit 1 is in the tens place, so its value is \( 1 \times 10 = 10 \).
- Value of the digit 8: The digit 8 is in the hundreds place, so its value is \( 8 \times 100 = 800 \).
- Value of the digit 0: The digit 0 is in the thousands place, so its value is \( 0 \times 1,000 = 0 \).
- Value of the digit 6: The digit 6 is in the ten-thousands place, so its value is \( 6 \times 10,000 = 60,000 \).

Answers:
- Value of the digit 2: 2
- Value of the digit 1: 10
- Value of the digit 8: 800
- Value of the digit 0: 0
- Value of the digit 6: 60,000

---

Step 2: Determine if the number is even or odd

A number is even if its last digit is divisible by 2. The last digit of 60,812 is 2, which is divisible by 2. Therefore, 60,812 is an even number.

Answer:
- Even or Odd: Even

---

Step 3: Fill in the empty boxes on the number line

The number line shows two points: 60,812 and 60,815. We need to fill in the missing numbers before and after these points.

- The number before 60,812 is 60,811.
- The number after 60,812 is 60,813.
- The number before 60,815 is 60,814.
- The number after 60,815 is 60,816.

Number line:
```
← [60,811] [60,812] [60,813] → [60,814] [60,815] [60,816] →
```

---

Step 4: Write the number in expanded form

The expanded form of a number breaks it down into the sum of the values of its digits.

- 60,812 can be written as:
\[
60,000 + 800 + 10 + 2
\]

Answer:
- Expanded form: 60,000 + 800 + 10 + 2

---

Step 5: Perform arithmetic operations

We need to calculate the following:

1. 1,000 less than 60,812:
\[
60,812 - 1,000 = 59,812
\]

2. 10,000 more than 60,812:
\[
60,812 + 10,000 = 70,812
\]

3. 100 less than 60,812:
\[
60,812 - 100 = 60,712
\]

4. 1 more than 60,812:
\[
60,812 + 1 = 60,813
\]

5. 10,000 less than 60,812:
\[
60,812 - 10,000 = 50,812
\]

Answers:
- 1,000 less than 60,812: 59,812
- 10,000 more than 60,812: 70,812
- 100 less than 60,812: 60,712
- 1 more than 60,812: 60,813
- 10,000 less than 60,812: 50,812

---

Step 6: Compare the numbers

We need to compare the given pairs of numbers using \( < \), \( > \), or \( = \).

1. 61,810 vs. 60,812:
- 61,810 is greater than 60,812.
- 61,810 > 60,812

2. 60,812 vs. 60,218:
- 60,812 is greater than 60,218.
- 60,812 > 60,218

3. 60,812 vs. 62,802:
- 60,812 is less than 62,802.
- 60,812 < 62,802

Answers:
- 61,810 > 60,812
- 60,812 > 60,218
- 60,812 < 62,802

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Value of the digit 2: } 2 \\
\text{Value of the digit 1: } 10 \\
\text{Value of the digit 8: } 800 \\
\text{Value of the digit 0: } 0 \\
\text{Value of the digit 6: } 60,000 \\
\text{Even or Odd: } \text{Even} \\
\text{Number line: } 60,811, 60,813, 60,814, 60,816 \\
\text{Expanded form: } 60,000 + 800 + 10 + 2 \\
\text{1,000 less than 60,812: } 59,812 \\
\text{10,000 more than 60,812: } 70,812 \\
\text{100 less than 60,812: } 60,712 \\
\text{1 more than 60,812: } 60,813 \\
\text{10,000 less than 60,812: } 50,812 \\
\text{Comparisons: } 61,810 > 60,812, \, 60,812 > 60,218, \, 60,812 < 62,802
\end{array}
}
\]