Lesson objective: Apply the understanding of the relationships between rational numbers.

This lesson provides an opportunity for students to apply their knowledge and understanding of adding and subtracting rational numbers to a real-life situation. Students are asked to find the error in a medical bill by applying the rules for adding and subtracting rational numbers.

Key Concept students will use:

- The relationship between addition and subtraction (If a+b=c, then c-b=a and c-a=b) holds for the set of rational numbers, and this relationship can be used to derive "rules" for operating with positive and negative numbers.

Skills students will use:

- Thinking about positive and negative directions helps to understand that the number p+q is a distance from p equal to the absolute value of q.
- Using the properties of operations to rewrite adding and subtracting problems.
- Applying the rules for adding and subtracting rational numbers.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they look for errors in applying the rules for adding and subtracting rational numbers and provide explanations for why the mistakes exist.

**Key vocabulary: **

- balance
- charge
- operations
- paid
- properties
- rational