Adding and Subtracting With Negative Numbers

Preinstructional Planning

Objectives

Students will:

• Identify real-world applications for addition and subtraction of negative numbers
• Complete addition and subtraction problems involving negative numbers using a number line

Materials

• How Low Can You Go: Adding and Subtracting With Negative Numbers printable
• Answer Key: Diving Into the Number System printable
• Standards Chart: Diving Into the Number System printable
• Whiteboard or chart paper and markers

Set Up 

1. Make a class set of the How Low Can You Go: Adding and Subtracting With Negative Numbers printable.
2. Print a copy of the Answer Key: Diving Into the Number System printable for your use.

Lesson Directions

Introduction to New Material

Step 1: Ask the class for examples of where negative numbers can be found in real-world applications. Answers include:

• Below-zero temperatures
• Depth below sea level, e.g., Death Valley, California; ocean depths; etc.
• Yardage in American football, e.g., when the quarterback is sacked behind the line of scrimmage
• Floors below ground-level in a building, e.g., underground parking garage levels
• Financially, people with more debts than assets are said to have a negative worth
• Losing so many points in a video game that the score becomes negative

Step 2: Draw a horizontal number line on the board with a range from -10 to 10, with a mark for 0 in the middle. Give the class the following scenario:

• Mandy has $7 and no debts. What is Mandy’s net worth? Mandy’s net worth is $7.
• Sam has no money and owes his parents $8. What is Sam’s net worth? Sam’s net worth is -$8.
• Mark these points at 7 and -8 on the number line.

Step 3: Indicate that you are going to go through scenarios about different students and how they handle money. Point out that “net worth” is a financial term that measures the value of a person or organization’s assets minus their liabilities. (Assets are items of value such as money, property, etc., and liabilities are debts owed.) People who own more than they owe are said to have a positive net worth, while people who owe more than their assets are worth are said to have a negative net worth. Work through the following examples on the number line with the class to show various combinations of adding/subtracting positive and negative numbers:

• Mandy receives $2 allowance from her parents. How much is her net worth now? Starting from 7 on the number line, draw an arrow to the right with a length of 2 that stops at 9. Mandy’s net worth is now $7 (7 + 2 = 9). Write the equation on the board. Note that we move to the right on a number line when adding a positive number.
• Mandy spends $4 on a broccoli/bacon latte. How much is her net worth now? Starting at 9 on the number line, draw an arrow to the left with a length of 4 that stops at 5. Mandy’s net worth is now $5 (9 - 4 = 5). Write the equation on the board. Note that we move to the left on the number line when subtracting a positive number.
• For his birthday, Sam’s parents agree to forgive $5 of his debt. How much is his net worth now? Starting at -8 on the number line, draw an arrow to the right with a length of 5 that stops at -3. Sam’s net worth is now $-3 (-8 - (-5) = -3). Write the equation on the board. Note that we move to the right when we subtract a negative number. Explain to the class that forgiving the debt is subtracting (taking away) his debt, a negative financial situation, so it is depicted as subtracting a negative number (which is equivalent to adding a positive number).
• Sam borrows another $5.50 from his parents and spends it on mathematician trading cards. What is his net worth now? Starting at -3 on the number line, draw an arrow to the left with a length of 5.5 that stops at -8.5. Sam’s net worth is now -$8.50 (-3 + -5.50 = -8.50) again. Note that we move to the left when we add a negative number (since we are decreasing value).

Step 4: Point out that a number line can also be drawn vertically. This can make it easier to work when depicting concepts that literally go up and down, such as elevation and depth, as well as concepts that can be figuratively thought of as going up or down, such as temperature changes or money being “raised” toward a fundraising goal. Draw a vertical number line with a range from -20 to 20 and run through the following two problems with the class:

a. It is -5°C outside at noon. The temperature drops 7 degrees over the next 12 hours. What is the new temperature? -12°C (-5 + -7 = -12)
b. The next day, it is 12°C at noon. The temperature drops 14 degrees over the next 12 hours. What is the new temperature? -2°C (12 - 14 = -2)

Guided Practice

Step 5: Group students in pairs and ask them to solve the following problems:

1. Wanda stepped onto an elevator on the 8th floor of her apartment and took it to the underground parking garage 3 floors below street level. How many floors did she travel? Answer: 11, because 8 - (-3) = 11.
   
   
2. Sylvester, a running back on the football team at Aaron Burr Middle School, ran for -3 yards with the ball. On the next play, he ran for -6 yards. Given that Sylvester’s goal was to run for the greatest number of yards, did Sylvester do better on the first or second play? Explain your answer. Answer: A run of -3 yards (a loss of 3 yards) is better than a run of -6 yards (a loss of 6 yards) because -3 is greater than -6.
   
   
3. A pelican was flying 75 feet over the surface of the Gulf of Mexico looking for dinner. It saw a tasty fish under the surface. It dove 82 feet in all to catch its prey. How many feet under the surface was the fish before it was caught, assuming the level of the surface of the Gulf is 0? Answer: -7 feet, because 75 - 82 = -7.

Step 6: Checking for Understanding: Review answers as a class and respond to any questions.

Independent Practice

Step 7: Assign the How Low Can You Go: Adding and Subtracting With Negative Numbers printable for classwork or homework.

Step 8: Checking for Understanding: Review the answers to the How Low Can You Go: Adding and Subtracting With Negative Numbers printable, which are provided on page 1 of the Answer Key: Diving Into the Number System printable. Make sure students explain their mathematical thinking. Address any misconceptions that may arise.

Post Instructional

Standards

• Grade 7: Adding and Subtracting Rational Numbers (CCSS 7.NS.1)
  
• Grade 6–8: Making Sense of Problems, Reasoning, Constructing an Argument, Modeling, and Attending to Precision (CCSS Practice MP1–4 and 6); NCTM Number and Operations

For more information, download the comprehensive Standards Chart: Diving Into the Number System printable.