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 Lesson in Spanish
Activity
None
Priya wants to buy 3 tickets for a concert. Each ticket costs \$50. She has earned \$135.
What could Priya do in order to be able to buy the tickets?
One equation that represents this situation is . What do each of the numbers tell us about this situation?
Another equation that represents this situation is . What do each of the numbers tell us in this situation?
Student Response
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Building on Student Thinking
Activity Synthesis
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 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. . That makes sense because if she owes money, then pays back the money, then it should be at 0.)
4.2
Activity
Standards Alignment
Building On
Addressing
7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
In this activity, students solve problems about money that can be represented with addition and subtraction equations. Some problems ask students to calculate the total amount of money Kiran has, while others ask students to calculate the amount of the transaction. Students reason abstractly and quantitatively when they write equations and draw number lines to represent each situation (MP2).
Launch
If students do not read carefully, they may not realize that they are expected to write an equation and create a diagram for each question and only record a numerical answer. Ensure they understand what they are expected to do before they begin working.
Give students quiet work time, and follow with a whole-class discussion.
MLR2 Collect and Display. Collect the language that students use to describe Kiran owing more money than he has. Display words and phrases, such as “owe,” “borrow,” “lend,” and “debt.” During the Activity Synthesis, invite students to suggest ways to update the display: “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed. Advances: Conversing, Reading
Action and Expression: Provide Access for Physical Action. Activate or supply background knowledge. Provide students with access to blank number lines that go from -10 to 30 to support them representing each transaction. Supports accessibility for: Visual-Spatial Processing, Organization
Activity
None
For each transaction:
Use a variable to represent the unknown quantity, and write an equation.
Represent the transaction on a number line.
Find the unknown quantity.
At the beginning of the month Kiran had \$24. He spent \$16 at a craft fair. How much money did he have then?
After he earned some money babysitting, he had a total of \$28. How much did he earn?
Then he pledged to donate \$30 to the local animal shelter. Kiran said, “Uh oh. Now I have -\$2.” What do you think he meant by that?
Kiran spent \$5 on supplies to clean windows. How much money would he say he had after that?
Kiran washed some windows and earned enough money so that now he can pay off his pledge. How much money did he earn?
Student Response
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Building on Student Thinking
If some students struggle to write an equation for each problem, consider asking:
"What amount is unknown in this situation?"
"How is the unknown amount affected by Kiran's activities?"
Activity Synthesis
The goal of this discussion is for students to connect the different types of computations they have been doing to Kiran's situations involving money. A key idea is for students to understand that the rules they have learned for adding and subtracting signed numbers still work when applied to the context of negative amounts of money.
For each type of computation, ask students to connect it to one of Kiran's situations:
Adding numbers with the same sign (Kiran had -\$2 and then spent \$5 on cleaning supplies.)
Adding numbers with opposite signs (Kiran started with \$24 and spent \$16 at the craft fair. Kiran started out with a positive amount of money and then donated some to charity. Kiran owed money and then earned enough to pay off his pledge.)
Adding opposites makes 0 (Kiran earned enough money to pay off his pledge and ended up with \$0.)
Subtracting as addition with a missing addend (Kiran earned \$20 babysitting.)
Subtracting as adding the additive inverse (Kiran spent money at the craft fair; Kiran pledged money to the animal shelter.)
4.3
Activity
Standards Alignment
Building On
Addressing
7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
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.
Launch
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.
Engagement: Develop Effort and Persistence. Provide tools to facilitate information processing or computation, enabling students to focus on key mathematical ideas. For example, allow students to use calculators to support their reasoning. Supports accessibility for: Memory, Conceptual Processing
Activity
None
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.
Andre makes a withdrawal of \$40 to buy a music player. What is his new balance?
If Andre makes a deposit of \$100 into this account, will he still be in debt? Explain your reasoning.
If withdrawals and deposits were in the same column, how could each be represented using signed numbers?
Student Response
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Building on Student Thinking
Activity Synthesis
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.
Lesson Synthesis
Share with students, “Today we saw how signed numbers can be used to represent money.“
To review these concepts, consider asking:
“What does it mean if an account balance is positive?” (The account owner has money.)
“What does it mean if an account balance is negative?” (The account owner owes money. It’s a debt.)
“What does it mean if a transaction amount is positive?” (The person put money into their account. It’s a deposit.)
“What does it mean if a transaction amount is negative?” (The person took money out of their account. It’s a withdrawal.)
Student Lesson Summary
Banks use positive numbers to represent money that gets put into an account and negative numbers to represent money that gets taken out of an account. When money is put into an account, it is called a deposit. When money is taken out of an account, it is called a withdrawal.
People also use negative numbers to represent debt. If we take out more money from our account than we put in, then we owe the bank money, and our account balance will be a negative number to represent that debt. For example, if we had \$200 in our bank account, and then we wrote a check for \$300, we would owe the bank \$100, and our account balance would be -\$100.
starting balance
deposits and withdrawals
new balance
0
50
50
150
200
-300
-100
In general, we can find a new account balance by adding the value of the deposit or withdrawal to it. We can also tell how much money is needed to repay a debt using the fact that to get from a value to 0, we need to add its opposite.
Standards Alignment
Building On
6.NS.C
Apply and extend previous understandings of numbers to the system of rational numbers.
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
