In this lesson, students are introduced to using negative numbers in the context of money to represent debts or debits.
It is common to use money contexts to represent signed numbers. One point that often gets overlooked is that it is a convention that we do this, rather than a necessity. Any situation in which we use a negative number to represent a debt (for example), we could equally well just use a positive number and distinguish it by calling it a debt. The reason we use signed numbers in this context is that it allows us to represent a whole class of problems with the same expression. For example, if a person has \$50 in the bank and writes a \$20 check, we can represent the balance as \(50-20\). If they had written an \$80 check, we can still write the balance as \(50-80\), as long as we have adopted the convention that negative numbers represent what the person owes the bank (and assuming the bank allows overdrafts). Using a mathematical structure (the signed numbers) to represent a context (a checking account balance) is an example of modeling with mathematics (MP4).
- Apply addition of signed numbers to calculate an account balance after a deposit or withdrawal, and explain (orally and using other representations) the solution method.
- Explain (orally and in writing) how signed numbers can be used to represent situations involving money, including deposits or withdrawals, and assets or debts.
- Write an equation with an unknown addend to represent a situation where the amount of change is unknown.
Let's apply what we know about signed numbers to money.
This lesson presents opportunities to practice performing operations on signed values, but the emphasis is really on noticing that money can be represented with positive and negative values. If the computation requirements might get in the way of that understanding, consider providing access to calculators.
- I understand what positive and negative numbers mean in a situation involving money.
When you put money into an account, it is called a deposit.
For example, a person added \$60 to their bank account. Before the deposit, they had \$435. After the deposit, they had \$495, because \(435+60=495\).
When you take money out of an account, it is called a withdrawal.
For example, a person removed \$25 from their bank account. Before the withdrawal, they had \$350. After the withdrawal, they had \$325, because \(350-25=325\).