Money and Debts

10 min

Teacher Prep
Setup
Students in groups of 2. Explain borrowing money from a bank. Partner and whole-class discussion.

Narrative

In this Warm-up, students consider different ways to think about a situation involving money. They encounter a situation where the items being purchased cost more than the amount available and think about ways to represent the situation using equations. They consider how the expressions and equations connect to the situation, including amount available, amount owed, and the amount it would take to return to 0.  

This activity prepares students to represent bank account balances using expressions and equations and to represent debt using a negative number, which will be useful in upcoming activities.

Launch

Arrange students in groups of 2–3. 

Listen for language students use to describe the amounts in the situation, such as “cost,” “owe,” “borrow,” “lend,” and “debt.”

Student Task

Priya wants to buy 3 tickets for a concert. Each ticket costs $50. She has earned $135.

  1. What could Priya do in order to be able to buy the tickets?
  2. One equation that represents this situation is 135+15=3⋅50135+15=3 \boldcdot 50. What do each of the numbers tell us about this situation?
  3. Another equation that represents this situation is 135−3⋅50=-15135 - 3 \boldcdot 50 = \text-15. What do each of the numbers tell us in this situation?

Sample Response

Sample responses:

  1. She could work more first or borrow money.
  2. 135 is the amount Priya has, 15 is the additional amount she still needs, and 3⋅503 \boldcdot 50 is the total amount the tickets cost.
  3. 135 is the amount Priya has, 3⋅503 \boldcdot 50 is the total cost of the tickets, and -15 is the amount she owes or has to borrow. 
Activity Synthesis (Teacher Notes)

The goal of this discussion is for students to understand that debt can be represented by a negative number and that the additive inverse tells how much money is needed to pay off the debt.

Tell students that sometimes banks let people borrow money and pay it back at a future time. We sometimes call the amount owed “debt.” The equation  135−3⋅50=-15135 - 3 \boldcdot 50 = \text-15 could represent Priya’s account balance if she had $135 and bought the 3 tickets. 

Ask students:

  • How much more money will Priya need to earn to pay back the money she borrowed from the bank? ($15. The negative amount tells us that’s how much she owes.)
  • How much money will she have after she pays back the money she borrowed from the bank? How would you represent that as an equation? ($0. -15+15=0\text-15+15=0. That makes sense because if she owes money, then pays back the money, then it should be at 0.)
     
Standards
Building On
  • 6.NS.C·Apply and extend previous understandings of numbers to the system of rational numbers.
  • 6.NS.C·Apply and extend previous understandings of numbers to the system of rational numbers.
Addressing
  • 7.NS.1.a·Describe situations in which opposite quantities combine to make 0. <em>For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.</em>
  • 7.NS.A.1.a·Describe situations in which opposite quantities combine to make 0. <span>For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.</span>

15 min

10 min