Question

Constructed Response Question
A. Mr. Wang writes a number on the whiteboard. Sally adds 5.5 to Mr. Wang's number to find a new number. Then, Tom subtracts 4.5 from Sally's number to find a new number. Then, Tarik subtracts 1.5 from Tom's number to find a new number. Finally, Puja adds 9.25 to Tarik's number to find the final number, which is 1.75.

Use a number line to find the number that Mr. Wang originally wrote on the whiteboard. Show your work and explain how the number is determined.

Thus, Mr. Wang's original number is -7.











Constructed Response Question
B. 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 find the distance between Mr. Wang's original number and Puja's final number using a number line, we can follow these steps:

1. **Identify the Two Key Numbers**:
- Mr. Wang's original number, which we found to be **-7**.
- Puja's final number, which is given as **1.75**.

2. **Set Up the Number Line**:
- Draw a horizontal line and mark points on it, including -7 and 1.75.
- Make sure to label the significant points: -7, 0, and 1.75.

3. **Determine the Distance**:
- Distance on a number line is calculated by finding the absolute difference between two numbers. We can express this as:
\[
\text{Distance} = | \text{Final Number} - \text{Original Number} |
\]
- Plugging in the numbers gives us:
\[
\text{Distance} = | 1.75 - (-7) |
\]
- This simplifies to:
\[
\text{Distance} = | 1.75 + 7 | = | 8.75 |
\]

4. **Calculate the Final Answer**:
- The absolute value of 8.75 is simply 8.75, since it is already a positive value.

5. **Conclusion**:
- The distance between Mr. Wang's original number (-7) and Puja's final number (1.75) is **8.75**.

**Final Answer**: The distance between Mr. Wang's original number and Puja's final number is **8.75**.

This step-by-step explanation demonstrates how to visually represent the calculations on a number line while confirming the distance using the concept of absolute value.