• The modeling activity can be used to assess students’ prior knowledge and understanding regarding addition of rational numbers with unlike denominators.
• Activity 1 can be used to assess each student’s ability to create a word problem involving the addition and/or subtraction of rational numbers while also understanding the solution process.
• Use the exit ticket to quickly evaluate student mastery.

As students come into class, have them evaluate the following expressions using a number line.

•                (−1/2)
• 0.75 + 2.95      (3.7)
•        (3 ¼)

Walk around the classroom as students are working through the example problems. Briefly discuss the answers and make sure students are comfortable modeling addition and subtraction of rational numbers on a number line before moving on.

“In Lesson 1 of this unit, we learned how to model addition and subtraction of rational numbers on a number line. Today, we are going to focus on performing these computations without the use of a number line. We will then use these skills to solve some real-life problems.”

Computations: Adding and Subtracting Rational Numbers

Before presenting some real-world problems, give students the opportunity to practice adding and subtracting rational numbers without the help of a number line. If necessary, go over the following examples together as a class.

Example 1:     

•        “Notice that one number in this problem is written as a fraction, but

the other is not. Often, when computing with fractions, it is best to write all numbers in fraction form.”

•       “When adding and subtracting with fractions, we need a

common denominator. The lowest common denominator in this case would be 5.”

•     “Once the denominators are the same, simply add or subtract the

numerators as indicated. The denominator will stay as is.”

•                    “Now we must make sure our fraction is in lowest terms. In this case

it is, but we may want to rewrite the fraction as a mixed number to get a better idea of the value.”

Example 2:      −4.64 + 9.85

• −4.64 + 9.85    “Think about the number line. Based on the signs of each addend, do

you suspect our final answer here will be positive or negative?” (Positive, the absolute value of 9.85 is larger than the absolute value of −4.64.)

• Think:            9.85 – 4.64    
•                           

          “Set up the problem vertically, making sure to line up the decimal point. Subtract by hand as normal.”

Distribute the Lesson 2 Computations Worksheet (M-7-5-2_Computations and KEY.docx). Instruct students to complete the worksheet individually. Walk around the room as students work to be sure they are on task and performing the computations accurately. Following the worksheet, provide time for students to discuss any problems they encountered, questions they have, or revelations they discovered. First, ask students to describe the computation process used to find each sum or difference. Then confirm their understanding by restating the correct process.

Problem Solving with Rational Numbers

Now it is time for students to apply their understanding of computation to solving real-world problems. Discuss the following examples together as a class.

• A log is  feet long. Kevin cuts  feet from the log. What is the length of the log now?
  • “Since Kevin cuts a certain length from the original length, the rational number  should be subtracted from the rational number . The problem can be solved by writing . In order to solve the problem, the mixed numbers can be written with common denominators. Using the least common denominator, the numeric expression can be rewritten as . Thus, the current length of the log is equal to  feet.”
• Last year, Steven’s total savings were $1,018.20. This year, he has $920.45 in his savings account. By how much have Steven’s savings decreased?
  • “The amount by which his savings have decreased is equal to the difference of 1018.20 and 920.45, written as 1018.20 – 920.45 or 97.75. Thus, Steven’s savings decreased by $97.75.”

Distribute Lesson 2 Word-Problem Examples (M-7-5-2_Word Problem Examples and KEY.docx). Have students discuss the solution process for each example problem in a manner similar to the process demonstrated above. Confirm the correct ideas students express. Then say: “Look through the problems you just received. Think of how the example word problems can be solved. Do you need to add or subtract the rational numbers? How will you go about doing this for fractions with unlike denominators, or for mixed numbers?”

Activity 1: Write-Pair-Share

Ask the whole class to think of some real-world contexts that involve the addition or subtraction of rational numbers. Students should make a list of at least five real-world contexts and provide one word problem. Ask students to share their ideas with a partner. Give students about 5 minutes to share contexts and word problems. During this time, each partner may ask questions of the other partner. Then, the whole class can reconvene. One member from each partner group will share the list of real-world contexts and word problems with the class. The teacher may wish to post the real-world contexts and word problems in a file on the class Web page or use them as a classroom display. These student examples would then serve as a reference tool.

Have students complete Lesson 2 Exit Ticket (M-7-5-2_Exit Ticket and KEY.docx) at the close of the lesson to evaluate students’ level of understanding.

Extension:

Use the suggestions in the Routine section to review lesson concepts throughout the school year. Use the small-group suggestions for any students who might benefit from additional instruction. Use the Expansion section to challenge students who are ready to move beyond the requirements of the standard.

• Routine: Throughout the school year, encourage students to be on the lookout for real-world situations that involve the addition or subtraction of rational numbers. Students can present the problems to the teacher, who will facilitate class participation in solving the rational number problem.
• Small Groups: Students who need additional practice can be pulled into small groups to work on the Lesson 2 Small-Group Practice worksheet (M-7-5-3_Small Group Practice and KEY.docx). Students can work on the matching together or work individually and compare answers when done.
• Expansion: Students who are prepared for a greater challenge can be given the Lesson 2 Expansion Worksheet (M-7-5-2_Expansion and KEY.docx). The worksheet includes more difficult numeric expressions involving rational numbers.