Lesson Description
This lesson introduces the concept of absolute value, shows how to plot absolute values on a number line, and demonstrates how absolute value is used in arithmetic and problem solving.
Learning Objectives
- Understand the definition of absolute value.
- Represent absolute values on a number line.
- Apply absolute value in arithmetic calculations.
Topics Covered
- Definition of absolute value
- Number line representation
- Solving arithmetic problems with absolute value
Key Terms
- Absolute Value: The distance of a number from zero on a number line, always positive.
- Number Line: A line on which numbers are placed at intervals to visualize their order and distance.
- Magnitude: The size or amount of a number without considering its sign.
Lesson Examples
Example 1: Finding Absolute Value
- Determine the absolute value of -7.
- Ignore the negative sign: 7 is the distance from 0.
- Result: |-7| = 7.
Example 2: Using Absolute Value in Arithmetic
- Calculate |-5| + |3|.
- Find absolute values: |-5| = 5, |3| = 3.
- Add: 5 + 3 = 8.
Practice Problems
- Find the absolute value of -12.
- Find the absolute value of 0.
- Calculate |-4| + |-6|.
- Plot -3, 2, and 0 using absolute values on a number line.
Tips & Common Mistakes
- Always remember absolute value is non-negative.
- Do not confuse absolute value with the original number’s sign.
- Use number lines to visualize absolute value distances from zero.
Summary
Absolute value measures how far a number is from zero, ignoring its sign. Representing numbers on a number line helps understand their absolute distances and supports problem solving in arithmetic and Pre-Algebra.
Challenge Problems
- Calculate |-8| + |-3| and explain the steps.
- Compare |-5| and |4|; which is greater?
- Create a real-world example using absolute values to represent distances.