Lesson 8 Skills Maintenance. Converting Fractions Activity 1. Transformations Activity slide or reflection. 2. slide or reflection

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1 Problem Solving: Lesson 8 Skills Maintenance Lesson Planner Skills Maintenance Converting Fractions, Transformations Building Number Concepts: Students learn how to multiply mixed numbers. LAPS helps us keep our work organized when we are working problems with a lot of steps to remember. Converting from mixed numbers to improper fractions is an important part of the process of multiplying mixed numbers that takes place in the alter step. Simplifying is another important step because the numbers we get when we multiply can be quite large. Students should remember to use their knowledge of number theory to help with this step. Objective Students will multiply mixed numbers. Problem Solving: In this lesson, students continue to look at real-world situations where they can apply the concepts they learn. This time, they look at floor plans as a real-world context where we multiply mixed numbers. Objective Students will multiply mixed numbers in the real-world context of floor plans. Homework Students convert mixed numbers to improper fractions, multiply mixed numbers, and find the area of two shapes in a simple tessellation. In Distributed Practice, students solve a mix of problems involving operations with fractions. Name Skills Maintenance Converting Fractions Activity 0 Unit Lesson 8 Date Convert the mixed numbers into improper fractions and vice versa Transformations Activity Identify the transformation that is taking place between each pair of shapes. Circle the correct answer.. slide or reflection. slide or reflection. slide or reflection. slide or reflection. slide or reflection 6. slide or reflection Skills Maintenance Converting Fractions, Transformations (Interactive Text, page 0) Activity Students convert mixed numbers to improper fractions, and vice versa. Activity Students tell if a transformation is a slide or a reflection. Unit Lesson 8

2 Problem Solving: Building Number Concepts: How do we multiply mixed numbers? (Student Text, pages 6) Connect to Prior Knowledge Begin by discussing the algorithm for converting mixed numbers to improper fractions. Remind students that when we multiply fractions, we multiply across. Explain that we use the same steps to multiply mixed numbers, but first we change them into improper fractions. Link to Today s Concept In today s lesson, we multiply mixed numbers and use LAPS to help us. Demonstrate Engagement Strategy: Teacher Modeling Demonstrate how to convert mixed numbers to improper fractions in one of the following ways: : Use the mbook Teacher Edition for pages of the Student Text. Overhead Projector: Display the mixed number on a transparency, and modify as discussed. Board: Show the mixed number on the board, and modify as discussed. Show the mixed number 9 7 on the board. Elicit from students the steps for converting 9 7 to an improper fraction. Write out the steps of the conversion according to student responses. Guide students as needed. Make sure to hit the following points: How do we multiply mixed numbers? We know that before we multiply mixed numbers, we convert them into improper fractions. Let s use 9 7 to review the steps for converting mixed numbers into improper fractions. Multiply the whole number by the denominator: 7 9 = 6 Unit Lesson = = 66 7 When we multiply fractions, we multiply across. When multiplication problems include mixed numbers, we follow the same steps, but first we change mixed numbers into improper fractions. LAPS helps us remember what to do. Let s solve a problem using LAPS. Example Multiply. L LOOK at the problem carefully. Then, add the answer to the numerator. Make sure the numbers are lined up correctly. Decide what operation is supposed to be performed. In this problem, we will use multiplication. There is a mixed number we will need to convert into an improper fraction. Listen for: First you multiply the denominator by the whole number. So 7 9 = 6. Next you have to add 6 to the numerator. So 6 +. This goes above the denominator, 7. When we add the numbers in the numerator, we get 66. The improper fraction is Show the problem from Example. L LOOK Remind students that the first step is to check that the numbers are lined up correctly and to decide what operation we are going to perform. In this case, we are multiplying. Unit Lesson 8

3 Lesson 8 How do we multiply mixed numbers? (continued) Demonstrate Continue through the LAPS process. A ALTER Pay particular attention to this step, where we convert to an improper fraction,. Remind students about multiplying the denominator,, and the whole number,, and adding the sum to the numerator,. A ALTER the problem if necessary. Now we change the mixed number into an improper fraction. The problem is now set up for the next step. P PERFORM the operation. This part is easy. We multiply across. S SIMPLIFY the answer. The answer is not in its simplest form. We need to convert to a mixed number. We divide the denominator into the numerator. Answer: 6 = = 6 6 = 6q = 6 R Now that we know the steps, we can also solve a multiplication problem with two mixed numbers. Remember, we multiply = 9. Then we add 9 + =. This is the new numerator. We put it over to create the improper fraction. P PERFORM Point out that once we create the improper fraction, we can multiply across to get the answer, 6. S SIMPLIFY Note to students that the answer is not in its simplest form. We can see that the product is an improper fraction, with a value greater than. So we divide the denominator into the numerator to get the mixed number 6. Explain that we can use these steps to multiply two mixed numbers. Unit Lesson 8 Unit Lesson 8

4 Demonstrate Have students look at Example on page 6 of the Student Text, where we multiply by. Again, go through all the LAPS steps, paying particular attention to the alter step. L Look Point out that the numbers are lined up correctly. Explain that we look at the problem and decide which operation should be performed. In this case, we are multiplying. A Alter Make sure students understand the algorithm for converting mixed numbers into improper fractions. For, we multiply = 0 and add 0 + = to get the improper fraction. For, we multiply = 6 and add 6 + = 9 to get the improper fraction 9. P PERFORM Note that the process for multiplying mixed numbers is the same as multiplying fractions as long as we remember to convert the mixed numbers to improper fractions: 9 = 09 0 S Simplify Check to see if the answer is in its simplest form. It is not, so we divide the denominator into the numerator to get 0 R9. The answer is Example Multiply. 6 Unit Lesson 8 L LOOK at the problem carefully. Make sure the numbers are lined up correctly. Decide what operation is supposed to be performed. In this problem, we will use multiplication. There are two mixed numbers we will need to convert into improper fractions. A ALTER the problem if necessary. We change both mixed numbers into improper fractions. We change the first mixed number: Now we change the second mixed number: The problem is now set up for the next step. P PERFORM the operation. This part is easy. We multiply across. We ll use a calculator if we need to. S SIMPLIFY the answer. The answer is not in its simplest form. We need to convert it into a mixed number. To do this, we divide the denominator into the numerator. Answer: Apply Skills Turn to Interactive Text, page. = = = R = 0q09 = Use the mbook Study Guide to review lesson concepts. Remember, we multiply = 0. Then we add 0 + =. This is the new numerator. We put it over to create. Remember, we multiply = 6. Then we add 6 + = 9. This is the new numerator. We put it over to create 9. Multiplying mixed numbers is easy if we change the mixed numbers into improper fractions first. Then we can multiply across. Check for Understanding Engagement Strategy: Pair/Share Have students work in pairs to multiply two mixed numbers together. Have them use the problem Q 7 = 8 = 8 R. Ask them to write the letters LAPS vertically on the page and write each step out for the problem. Have students use Example as a model, if necessary. When pairs finish, have volunteers share their steps and solutions with the class. Discuss Call students attention to the Power Concept, and point out that it will be helpful as they complete the activity. Multiplying mixed numbers is easy if we change the mixed numbers into improper fractions first. Then we can multiply across. Unit Lesson 8

5 Lesson 8 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 multiplying mixed numbers. Activity Students multiply mixed numbers using LAPS. Monitor students work as they complete the activity. Watch for: Do students know to convert the mixed numbers to improper fractions in the alter step? Can students perform the operation? Can students simplify the answer? Remind students that they can review lesson concepts by accessing the online mbook Study Guide. Apply Skills Activity Multiply the mixed numbers using LAPS. Change all the mixed numbers into improper fractions in the A alter step. Then multiply. In the S simplify step, change the fraction back into a mixed number.. 7 L The problem is aligned and it is multiplication. A = 0 and = 9 P 0 9 = 90 S 90 = 7 6 = L The problem is aligned and it is multiplication. A 8 = 9 8 and = P 9 8 = 99 6 S 99 6 = L The problem is aligned and it is multiplication. A = and = P = 9 S 9 = 8 9. L The problem is aligned and it is multiplication. A = and = 6 P 6 = 0 0 S 0 0 = Unit Lesson 8 Unit 6 Unit Lesson 8

6 Problem Solving: What are floor plans? (Student Text, page 7) Connect to Prior Knowledge Remind students about the house project we discussed previously. Lesson 8 What are floor plans? Floor plans are drawings that builders use to construct homes. The builder knows how much material to buy based on these drawings. 8 " 8 " Problem Solving: Let s look at the parts of this floor plan. " " " " " " Link to Today s Concept In today s lesson, we compute area by using information from a floor plan. Demonstrate Have students look at page 7 of the Student Text. Introduce the idea of a floor plan. The measurements on floor plans, or blueprints, are often mixed numbers. We need to know the area of pictured rectangles. The area formula involves multiplication. Remind students that the area of a rectangle = length width. Read the text at the bottom of the page, and point out that plans are drawn in smaller units than the actual measurements of the room. For example, an inch in a drawing might be equal to a yard in the true measurement of the room. We see that: " The dimensions of the rooms are labeled on the floor plans and are used to compute the area. The rooms are rectangular. The area is computed by multiplying the length of the room by the width of the room. The design is drawn in smaller units, such as inches, and a key is given for computing the actual area of the room. For instance, one inch on the ruler could be equal to one yard. In this case, one inch equals six feet. Problem-Solving Activity Turn to Interactive Text, page. " Use the mbook Study Guide to review lesson concepts. key in. = 6 ft. 7 Unit Lesson 8 7 Unit Lesson 8 7

7 Lesson 8 Problem-Solving Activity Name Date Problem-Solving Activity (Interactive Text, page ) Have students turn to page in the Interactive Text, which provides students an opportunity to practice calculating area. Explain that Todd s summer cabin needs new carpeting. Students figure out how much carpet is needed by computing the area. Have students compute the area by multiplying length times width. Monitor students work as they complete this activity. Watch for: Can students determine the amount of carpet needed for each of the rooms using the area formula? Can students multiply the mixed numbers correctly? Do students remember to convert the mixed numbers to improper fractions? Can students add up all the areas at the end and come up with a total? Problem-Solving Activity Look at the floor plan for Todd s summer cabin. Todd wants to carpet the entire lower floor except for the porch. Use the dimensions given for each room to compute how much carpet will be needed. Remember, to find the area of a rectangle you multiply length width. Unit Lesson 8 bathroom kitchen Carpet needed: Bathroom Kitchen Living Room Total Todd s Summer Cabin porch 0 square yards 9 square yards 9 square yards 99 square yards living room Use the mbook Study Guide to review lesson concepts. Bathroom Dimensions yards yards Kitchen Dimensions 8 yards yards Living Room Dimensions yards yards Porch Dimensions yard yards Once students complete the activity, discuss their answers together in class. Remind students that they can review lesson concepts by accessing the online mbook Study Guide. 8 Unit Lesson 8

8 Homework Homework Go over the instructions on page 8 of the Student Text for each part of the homework. Activity Students convert mixed numbers into improper fractions. Activity Students multiply mixed numbers using LAPS. Activity Students find the area of two shapes in a simple tessellation. Activity Distributed Practice Students solve a mix of problems involving operations with fractions. Activity Convert the mixed numbers into improper fractions Activity Multiply the mixed numbers using LAPS. Remember to change the mixed numbers into improper fractions in the A Alter step, and then change the answer back into a mixed number in the S Simplify step See Additional Answers below. Activity Shape A and Shape B are used in a simple tessellation. The length and the width of each rectangle is shown at right.. What is the area of Shape A? 9 8. What is the area of Shape B? 7 9 Activity Distributed Practice Solve inches.. Shape B inches Shape A inches inches 8 8 Unit Lesson 8 (Additional Answers continue on Appendix, pages A A6.) Unit Lesson 8 9