Question

Explain how to use a number line to calculate the distance between Mr. Wang's original number and Puja's final number. Show your work.

Answer 1

To calculate the distance between Mr. Wang's original number and Puja's final number using a number line, follow these steps:

### Step 1: Identify the Numbers
First, let's denote Mr. Wang's original number as \( A \) and Puja's final number as \( B \). For example, let’s say \( A = 3 \) and \( B = 8 \).

### Step 2: Draw a Number Line
Draw a horizontal line and mark a sequence of evenly spaced numbers. Write down the numbers around and including both \( A \) and \( B \). For our example:

```
... -2 -1 0 1 2 3 4 5 6 7 8 9 10 ...
```

### Step 3: Locate the Points on the Number Line
Identify and mark points \( A \) and \( B \) on the number line. For this example, \( A \) is at 3, and \( B \) is at 8. It should look like this:

```
... -2 -1 0 1 2 3* 4 5 6 7 8* 9 10 ...
```

### Step 4: Count the Units
Count the number of units from \( A \) to \( B \):

- Starting at 3, you move to:
- 4 (1 unit)
- 5 (2 units)
- 6 (3 units)
- 7 (4 units)
- 8 (5 units)

### Step 5: Calculate the Distance
The distance between \( A \) and \( B \) is the total number of units counted. The mathematical expression to represent this is:

\[
\text{Distance} = | B - A |
\]

Using our values:
\[
\text{Distance} = | 8 - 3 | = 5
\]

### Final Result
The distance between Mr. Wang's original number (3) and Puja's final number (8) is **5 units**.