Unit 7, Lesson 8
Money and Debts
Accelerated 6
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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.
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.”
Priya wants to buy 3 tickets for a concert. Each ticket costs $50. She has earned $135.
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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
Ask students:
Notice and Wonder
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In this activity, students use addition and subtraction to solve problems about debts and withdrawals. They make sense of a bank statement and the possible ways to represent deposits, withdrawals, balances, and debt (MP1). As they persevere in solving problems with the bank statement, they compare representations of withdrawals with representations of debt, using two methods: addition with negative numbers and subtraction.Monitor for students who express their reasoning as addition and subtraction equations or expressions.
Tell students to close their books or devices (or to keep them closed). Display the image of the bank statement for all to see. Give students 1 minute of quiet think time, and ask them to be prepared to share at least one thing they notice and one thing they wonder. Record and display responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image.
If the terms “deposit” and ”withdrawal” do not come up during the conversation, make sure students understand the meaning of these terms. A deposit is money put into an account, and a withdrawal is money taken out of an account.
Give students 3–4 minutes of quiet work time, and follow with a whole-class discussion.
Here is a bank statement.
A checking account statement for Andre person. A 5-column table shows the activity in his account for the month of October. Column 1 is labeled “Date,” column 2 is labeled “Description,” column 3 is labeled “Withdrawals,” column 4 is labeled “Deposits,” and column 5 is labeled “Balance.” There are 8 rows describing each transaction Andre made with the bank. Row 1: Date: 10, 3, 2017; Description, Previous balance; Withdrawals, blank; Deposits, blank; Balance, 39 point 8 7 dollars. Row 2: Date: 10, 5, 2017; Description, Check Number 256; Withdrawal, 28 point 5 0 dollars; Deposits, blank; Balance, 11 point 37 dollars. Row 3: Date: 10, 6, 2017; Description, A T M deposit – Cash; Withdrawals, blank; Deposit, 45 point 0 0 dollars; Balance, 56 point 3 7 dollars. Row 4: Date: 10, 10, 2017; Description, Wire transfer; Withdrawals, 37 point 9 1 dollars; Deposits, blank; Balance: 18 point 4 6 dollars. Row 5: Date: 10, 17, 2017; Description, Point of Sale Grocert Store; Withdrawals, 16 point 4 3 dollars. Deposits, blank; Balance, 2 point 0 3 dollars. Row 6: Date: 10, 25, 2017; Description, Funds Transfer from Savings; Withdrawals, blank; Deposits, 50 point 0 0 dollars; Balance, 52 point 0 3 dollars. Row 7: Date: 10, 28, 2017; Description, Check Number 257; Withdrawals, 42 point 0 0 dollars; Deposits, blank; Balance, 10 point 0 3 dollars. Row 8: Date 10, 29, 2017; Description, Online Payment Phone Services; Withdrawals, 72 point 5 0 dollars; Deposits, blank; Balance, negative 62 point 4 7 dollars.
The goal of this discussion is for students to see the different ways that withdrawals, deposits, and debts can be represented using signed numbers. Begin by inviting previously selected students to share their responses and reasoning to the first two questions.
Then ask students to share their responses to the last question. The decision about which numbers to represent with positive versus negative values hinges on whether you are thinking from the perspective of the person or the perspective of the account. Point out that the final balance is represented with a negative number to show that the person owes the bank money. Therefore, from the perspective of the account, deposits are positive values and withdrawals are negative values.
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If some students struggle to write an equation for each problem, consider asking:
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