# Lesson 5

Using Negative Numbers to Make Sense of Contexts

### Lesson Narrative

In this lesson, students are introduced to conventions for using signed numbers to represent money spent and received, as well as inventory gained and lost. While money contexts can be represented without signed numbers, there are many situations that are more efficiently modeled by signed numbers. 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). Since students do not operate on signed numbers in this grade, this lesson is simply an introduction to the convention of using signed numbers to represent a change in money or a change in inventory, an important convention in modeling financial situations with mathematics (MP4). In a later lesson, students will be introduced to the idea of an account balance. In grade 7, students will study addition and subtraction of signed numbers and apply those concepts in accounting situations.

### Learning Goals

Teacher Facing

• Interpret a table of signed numbers that represent how a quantity changed.
• Recognize that signed numbers can be useful to represent changes in a quantity in opposite directions, e.g., money received and money paid, inventory bought and inventory sold, etc.

### Student Facing

Let’s make sense of negative amounts of money.

### Student Facing

• I can explain and use negative numbers in situations involving money.
• I can interpret and use negative numbers in different contexts.

### Glossary Entries

• negative number

A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.

• opposite

Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.

For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.

• positive number

A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.

• rational number

A rational number is a fraction or the opposite of a fraction.

For example, 8 and -8 are rational numbers because they can be written as $$\frac81$$ and $$\text-\frac81$$.

Also, 0.75 and -0.75 are rational numbers because they can be written as $$\frac{75}{100}$$ and $$\text-\frac{75}{100}$$.

• sign

The sign of any number other than 0 is either positive or negative.

For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.

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