Distance and Absolute Value Concepts

This lesson focuses on using subtraction to calculate the distance between rational numbers. It highlights common mistakes, such as counting the first number as one or describing distance as negative. The lesson introduces the concept of absolute value to find distance and provides exercises to practice these calculations. It also discusses the importance of context in problems involving elevation changes. The lesson concludes with a summary of key concepts, emphasizing that distance is always positive, while change can be positive or negative depending on context.

What mathematical operation is primarily used to find the distance between two rational numbers?

• Division

• Subtraction

• Multiplication

• Addition

Why is it important to ensure that distance is always described as positive?

• Because it is a mathematical rule

• Because it simplifies calculations

• Because distance represents a physical space which cannot be negative

• Because negative distances are more complex

What is the absolute value of a number used for in the context of distance?

• To find the midpoint between two numbers

• To determine the direction of a number

• To simplify subtraction

• To calculate the distance from zero

In Exercise 1, what is the distance between -4 and 5 using absolute value?

• 5

• 1

• 9

• 12

When modeling distances on a number line, what should you do first?

• Count the units between numbers

• Subtract the smaller number from the larger

• Use the distance formula

• Highlight the numbers

In Example 1, what is the distance between -3 and 2?

• 4

• 3

• 5

• 6

How does the context of a problem affect the interpretation of change in elevation?

• It does not affect the interpretation

• It affects the number line model

• It changes the distance formula

• It determines whether the change is positive or negative

In Exercise 3, what is the distance between -9 and 3?

• 9

• 10

• 12

• 11

What is the first step in Exercise 4 when finding the distance between two numbers?

• Use a calculator

• Model the problem on a number line

• Guess the distance

• Use the distance formula directly

What does finding the absolute value of a number mean in terms of distance?

• Finding the sum

• Finding the average

• Finding the midpoint

• Finding the distance from zero