Adding and Subtracting Mixed Numbers: The LAPS Process Problem Solving: Solving Word Problems With Mixed Numbers Lesson 2 Skills Maintenance Vocabulary Development LAPS Lesson Planner Skills Maintenance Improper Fractions, Transformations Building Number Concepts: Adding and Subtracting Mixed Numbers: The LAPS Process We begin looking at operations with mixed numbers. We start with addition and subtraction. LAPS is the organizer we use to help students organize their work when adding and subtracting mixed numbers. LAPS stands for look, alter, perform, and simplify. Objective Students will add and subtract mixed numbers using a system to help remember the steps. Name Skills Maintenance Improper Fractions Date Change the improper fractions into mixed numbers. Use the number line, fraction bars, and circles to help you.. 2.. 6 22 2 Transformations 0 2 0 2 Identify the transformation that is taking place between each pair of shapes. Circle the correct answer.. Slide or Flip 2. Slide or Flip. Slide or Flip. Slide or Flip 6 8 0 2 Unit Problem Solving: Solving Word Problems With Mixed Numbers Students are reintroduced to the Scatter Plots. The Scatter Plots buy an old house that needs to be renovated. We use this context for solving word problems involving mixed numbers. Objective Students will solve real-world problems involving mixed numbers. Homework Students use the number lines to convert the improper fractions to mixed numbers, use LAPS to add and subtract fractions, and solve two word problems involving mixed numbers. In Distributed Practice, students solve a mix of problems involving operations with fractions.. Slide or Flip Skills Maintenance Improper Fractions, Transformations (Interactive Text, page ) Students convert the improper fraction to its corresponding mixed number using a number line, fraction bars, and circles. Unit Lesson 2 Students identify the type of transformation from the picture shown. They choose from slide or flip. 28 Unit Lesson 2
Adding and Subtracting Mixed Numbers: The LAPS Process Problem Solving: Solving Word Problems With Mixed Numbers Building Number Concepts: Adding and Subtracting Mixed Numbers: The LAPS Process How can we remember the steps for adding and subtracting mixed numbers? (Student Text, pages 8) Adding and Subtracting Mixed Numbers: The LAPS Process How can we remember the steps for adding and subtracting mixed numbers? Let s look at this addition problem: + 2 Solving problems with mixed numbers requires many steps. It is easy to get confused or to forget a step. We have a word, LAPS, that will help us remember the steps for adding or subtracting mixed numbers. Vocabulary LAPS Connect to Prior Knowledge Discuss the problem + 2 with students. Ask: How can we use what we know about adding fractions to solve this problem? Listen for: The denominators are the same. We can add the numerators. Link to Today s Concept Tell students that today we use the LAPS process to help us add and subtract mixed numbers. Using LAPS helps us stay organized. Engagement Strategy: Teacher Modeling Explain the LAPS process in one of these ways: : Use the mbook Teacher Edition for page of the Student Text. Overhead Projector: Reproduce Student Text, page on a transparency. Show the letters LAPS vertically. L Look For the look step, tell students that we ask, Is it addition? Is it subtraction? Is it lined up properly? LOOK Carefully analyze the problem. Decide what operation should be performed. Is it addition or subtraction? Make sure the problem is lined up properly. ALTER Make any changes necessary to begin solving the problem. Find a common denominator and rewrite the problem if necessary. PERFORM Perform the operation. Add or subtract the fractions. Add or subtract the whole numbers. SIMPLIFY Find the GCF of the numerator and the denominator. Then factor out the answer to find the simplest form. Using LAPS to help us solve a problem is like swimming laps in a pool. Both require a lot of work. Here we use LAPS to remember how to work with mixed numbers. Unit Lesson 2 A ALTER For the alter step, explain that we ask, Is there a common denominator? If not, how can we find one? We rewrite the problem using numbers that have common denominators. P Perform Explain that the perform step means to perform the operation. Add or subtract the fractions. Add or subtract the whole numbers. S Simplify Mention that the simplify step should be familiar to students at this point because we already know how to simplify the answers to problems. The answers need to be in simplest form. Unit Lesson 2 2
Lesson 2 How can we remember the steps for adding and subtracting mixed numbers? (continued) Have students turn to page 80 of the Student Text, where we demonstrate an addition problem using the LAPS strategy. Ask students to describe each of the steps in the LAPS strategy as you go through the example together. Listen for: L Look We look at the problem to see if the numbers are lined up. We look at the problem to see what the operation is. In this problem, it s addition. Steps for Using LAPS to Add Mixed Numbers L LOOK at the problem carefully. Make sure that the numbers are lined up correctly. Decide if addition or subtraction is supposed to be performed. In this problem, the fractions and whole numbers are lined up correctly, and we need to add. A ALTER the problem if necessary. Alter means change. Sometimes we need to change something about a problem before we solve it. When adding or subtracting fractions, the denominators need to be the same. In this problem, the denominators are the same, so we don t have to alter the fractions. P PERFORM the operation. Now we are ready to add. We begin by adding the fractional parts of the two numbers. Next, we add the whole numbers. S SIMPLIFY the answer. We have the answer we want because the answer is a mixed number in its simplest form. So, for this problem, we do not need to do anything in this step. + 2 + 2 + 2 + 2 Remember from the last unit that simplest form means there are no common factors that can be pulled out of the numerator and denominator. a alter We see if we need common denominators. In this problem, the fractions already have the same denominator. We do not need to alter anything. p perform Now we can perform the addition. We add the fractions + =. We add the whole numbers + 2 =. The answer is. 80 80 Unit Lesson 2 Be sure students look carefully at each step. Some of the steps do not apply, but it is important to go through the process each time to build the good habits that LAPS provides for students. S Simplify We have to simplify the fraction portion of the mixed number to its lowest terms. In this case, is already reduced, so is our answer. 00 Unit Lesson 2
Explain Have students turn to page 8 of the Student Text. Explain that we can also use LAPS to help us remember the steps for subtracting mixed numbers. how to solve the subtraction problem 2 using LAPS. Again, walk through the process with students, step by step. L LOOK Remind students to ask themselves, Is the problem lined up properly? Is it addition? Is it subtraction? Steps for Using LAPS to Subtract Mixed Numbers L LOOK at the problem carefully. Make sure the numbers are lined up correctly. Decide if addition or subtraction is supposed to be performed. In this problem, the fractions and whole numbers are lined up correctly, and we need to subtract. A ALTER the problem if necessary. Decide if the denominators need to change. The denominators are the same, so we do not need to change anything before we subtract these two numbers. P PERFORM the operation. Now we do the subtraction. First we subtract the fractional parts. Then we subtract the whole numbers. S SIMPLIFY the answer. We have the answer we want because the answer is a mixed number in its simplest form. So, for this problem, we do not need to do anything in this step. 2 2 2 2 A ALTER Point out that in this case, we do not need to alter the problem because the denominators are the same. However, students should remember to include this step as a check. P PERFORM Walk through the subtraction in the perform step, first subtracting the fractional parts and then the whole numbers. S SIMPLIFY Point out that the answer is already in its simplest form, but again, students should include the simplify step as a check. Check for Understanding Engagement Strategy: Think, Think Ask students the following questions. Tell them that you will call on one of them to answer a question after you ask it. Tell them to listen for their names. After each question, allow time for students to think of the answer. Then call on a student. Ask: What do the letters in LAPS stand for? (look, alter, perform, and simplify) Unit Lesson 2 8 What do we do in the look step? (We look at the operation and look to see if the numbers are lined up correctly.) What do we do in the alter step? (We look to see if we need to find a common denominator.) What do we do in the perform step? (We do the addition or subtraction.) What do we do in the simplify step? (We put the answer in simplest form.) 8 Unit Lesson 2 0
Lesson 2 How do we check our answer using fraction bars? (Student Text, page 82) Have students turn to Example on page 82 of the Student Text. It is a demonstration of subtraction using fraction bars. Explain to students that fraction bars provide us with a way to check our answers to see if they are correct. In this example, we look again at the problem 2. Start by showing 2 using fraction bars. Make sure students see how the six fraction bars represent 2 and why we need six fraction bars to demonstrate this number. Show students how we use Xs to cross out. We cross out one whole fraction bar. We cross out one part, or, of another of the fraction bars. Be sure students see that there are four whole fraction bars left and of another fraction bar. The answer is. This is the same answer we got using LAPS. Explain to students that we look at fractions with unlike denominators in the next lesson, but we first practice using the LAPS strategy with easier problems. Our goal is to think about an organized strategy, LAPS, for solving complex, multistep problems. Check for Understanding Engagement Strategy: Think Tank Distribute strips of paper to the students, and write the problem + 6 Q0 2 R on the board. Have students solve the problem, reminding them to use LAPS to help them. Tell students 82 How do we check our answer using fraction bars? Let s check our answer from the subtraction problem using fraction bars to see if we get the same answer as we did using LAPS. Example 82 Unit Lesson 2 Use fraction bars to check that 2 =. We start by showing 2 using fraction bars. We shade whole fraction bars and 2 of another. Next, we take away, or subtract,. Then we remove the parts that we put an X on. We have whole fraction bars and of another fraction bar left. This represents. The answer we found using the fraction bars is. The answer we found using LAPS was. It s the same answer. Apply Skills Turn to Interactive Text, page. Use the mbook Study Guide to review lesson concepts. to write their names and answers on the strips of paper. When students finish, collect the papers in a container. Draw out an answer to read aloud. If it is correct, congratulate the student. If it is incorrect, have a student volunteer give the correct answer. Review the solutions with the class. If there is time, check the answer with fraction bars. 2 If you feel students need more practice before moving to the independent practice, try these additional problems: 0 8 2 8 Q 8 R 8 + 2 Q R 2 Q8 R 02 Unit Lesson 2
Apply Skills Name Date Apply Skills (Interactive Text, page ) Have students turn to page in the Interactive Text, which provides students an opportunity to practice LAPS. Apply Skills Adding and Subtracting Mixed Numbers: The LAPS Process Shade the first number, then use Xs to subtract the second number.. 2 2 Students use fraction bars to solve a subtraction problem involving fractions. Students use LAPS to solve one addition and one subtraction problem. Be sure to explain to students that even though we are not using some of the steps from LAPS in today s practice, we need to remember all of the steps eventually when we look at more complex problems. Monitor students work as they complete the activities. Watch for: Can students shade the first fraction correctly? Can students determine the resulting answer from the fraction bars? Can students remember what the LAPS steps are and what they mean? Can students solve the problems using LAPS? Use LAPS to solve the mixed number problems. Complete each step in the boxes.. 6 + 6 L A Unit Lesson 2 8 6 The problem is lined up and we are adding. The problem is set up appropriately because the denominators are the same. P 6 + 6 = 8 6 S 2. L A No simplification needed. 2 Problem is lined up and we are subtracting. Problem is set up appropriately because the denominators are the same. P = 2 S No simplification needed. Remind students that they can review lesson concepts by accessing the online mbook Study Guide. Unit Lesson 2 0
Problem Solving: Solving Word Problems With Mixed Numbers Lesson 2 Problem Solving: Solving Word Problems With Mixed Numbers How do we solve real-world problems with mixed numbers? THE SCATTER PLOTS WOULD BE AN UP-AND-COMING GARAGE THE SCATTER BAND EXCEPT PLOTS ARE FOR AN ONE UP THING: AND COMING THEY HAVE ROCK TO BAND. PRACTICE THEY PRACTICE IN THEIR IN DRUMMER S THEIR DRUMMER S APARTMENT. APARTMENT. THEY ARE VERY LOUD AND GET LOTS OF COMPLAINTS FROM ALL OF THE NEIGHBORS. KEEP IT DOWN IN THERE!! How do we solve real-world problems with mixed numbers? (Student Text, page 8) Explain Have students look at page 8 of the Student Text. Introduce the problem-solving theme for this unit. In today s lesson, we reintroduce the Scatter Plots, a fictitious musical band. We first introduced the Scatter Plots in Level of TransMath as a context for looking at ways to display data; reading information from tables and charts; determining distances on maps as the band went on tour; and computing, analyzing, and projecting CD sales and other numeric data for the band. In this unit, the Scatter Plots buy an old house and fix it up to use as their practice studio. This setting provides a real-world context for word problems involving mixed-number operations. An important part of gaining conceptual understanding of a topic is to be able to connect it with a familiar context. These word problems give students some real-world connections for thinking about mixed-number operations. Be sure to encourage students to use the LAPS method to keep their work organized in word problems as well. Let s help the Scatter Plots solve a problem. Problem: A cracked pipe in the bathroom needs to be fixed. The Scatter Plots bought a pipe that is feet long. The pipe that needs to be fixed is 2 feet long. How much pipe do they need to cut off the new pipe in order to replace the broken one? The Scatter Plots need to cut 2, or 2, feet off of the new pipe in order to replace the old one. Problem-Solving Activity Turn to Interactive Text, page. SO THE BAND PUT ALL THEIR MONEY TOGETHER AND BOUGHT AN OLD HOUSE AT THE EDGE OF TOWN. NOW THEY CAN PRACTICE WITHOUT DISTURBING OTHERS. BUT THEY CAN T JUST PRACTICE AND DREAM OF MAKING IT BIG. THE OLD HOUSE NEEDS A LOT OF REPAIRS. IT HAS GRIMY CARPETING, BROKEN PIPES, AND A RICKETY STAIRCASE. THE SCATTER PLOTS HAVE A LOT OF REPAIRS TO MAKE BEFORE THEY CAN REALLY ROCK N ROLL. 2 2 = 2 Use the mbook Study Guide to review lesson concepts. Unit Lesson 2 8 Walk through the problem with students, making sure they understand why we need to use subtraction for this problem. Have them recall the LAPS steps as you work through the problem. 8 Have students read the comic strip to put the word problem in context. Then read the word problem at the bottom of the page. 0 Unit Lesson 2
Problem-Solving Activity Name Date Problem-Solving Activity (Interactive Text, page ) Have students turn to page in the Interactive Text, which provides them an opportunity to solve word problems using mixed numbers. Students solve word problems about the Scatter Plots new house. Monitor students work as they complete this activity. Watch for: Can students remember the LAPS steps for keeping their work organized? Can students identify the operation in each word problem and set up the problem? Can students solve the problem and come up with the correct answer? Once students complete the activity, discuss the answers together in class. Remind students that they can review lesson concepts by accessing the online mbook Study Guide. Problem-Solving Activity Solving Word Problems With Mixed Numbers Before the Scatter Plots can move things to the second floor of the house, they need to fix the staircase. This will require accurate measurement. Help the Scatter Plots by solving the four problems.. The step at the bottom of the staircase is broken. The Scatter Plots have a board 8 feet long. The board only nee to be 8 feet long. How much of the board needs to be cut off? 8 8 = 2 8 feet 2. There is a hole in the floor at the top of the staircase. Two boards are needed to cover the hole. Each board is feet wide. How wide is the hole in the floor? + = 22 feet. Another part of the floor needs to be replaced. It can be done with two boards. The first board is 6 feet long and the second board is 6 feet long. How long is the part of the floor that needs to be replaced? 6 + 6 = 6 feet. One railing on the staircase is cracked. The only board the band members have to fix the problem is 8 feet long. The new railing should be 8 feet long. How much will have to be cut off to make the board fit? 8 8 = 6 8 feet Use the mbook Study Guide to review lesson concepts. Unit Lesson 2 Unit Unit Lesson 2 0
Lesson 2 Homework Homework Go over the instructions on page 8 of the Student Text for each part of the homework. Students use the number lines to convert the improper fractions to mixed numbers. Convert the improper fractions to mixed numbers. 0 2. 2 2 6 8 0 0 2.. Use LAPS to add and subtract the fractions. Label each step.. 2 2 + 0 2 0 2 6 0 2 0 2 6 8 8 2. 2 8 + 2 8 8 0 0 2 2 Students use LAPS to add and subtract fractions. Activity Students use LAPS to solve two word problems involving mixed numbers. Activity Distributed Practice Students solve problems involving operations with fractions for ongoing practice of these skills.. 0 8 2 2 Activity. 6 0 6 Solve the word problems involving addition and subtraction of mixed numbers. Use LAPS to organize your work.. There are no curtains in the living room of the house that the Scatter Plots bought. The band members measure the windows and find out that they are feet tall. They want the curtains to be another feet below the windows. How long do the curtains have to be? 2. The fence around the front of the house is falling apart on two sides. The fence is 6 8 yards along the driveway and 86 8 yards in front of the house. How long is this part of the fence? Activity Distributed Practice Solve.. + 2 2.. 8 2 6. 8 8 6 2. 2 8 2 feet 8 yards 8 8 Unit Lesson 2 06 Unit Lesson 2