Multiply a Fraction by a Whole Number Using Models

Transcription

1 LESSON. Multiply a Fraction by a Whole Number Using Models FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards.NF.B.b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of /b, and use this understanding to multiply a fraction by a whole number. Also.NF.B.c MATHEMATICAL PRACTICES MP Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP Model with mathematics. F C R Coherence: Standards Across the Grades Before Grade After.OA.D..NF.B.b.NF.B.a.NF.A. F C R Rigor: Level : Understand Concepts...Share and Show ( Checked Items) Level 2: Procedural Skills and Fluency...On Your Own Level : Applications...Think Smarter and Go Deeper Learning Objective Use a model to multiply a fraction by a whole number. Language Objective Students write in their Journal how you can use a model to multiply a fraction by a whole number. Materials Board F C R For more about how GO! fosters Coherence within the Content Standards and ematical Progressions for this chapter, see page H. About the Professional Development Modeling Multiplication of a Fraction by a Whole Number Fraction models help students to visualize operations with fractions. Students model same-size groups of fractional parts to show multiplication of a fraction by a whole number. For example, is groups of of a whole. Students draw fraction circles divided into equal parts and shade equal parts of each whole to represent. Then, they count the number of fourths shaded and write the number over to get. So, =. of a whole groups of Using models helps students visualize the concepts first, and then they are able to transfer this understanding to numbers and symbols. Students gradually become able to describe how to multiply a fraction by a whole number without using a model or repeated addition: Multiply the whole number by the numerator of the fraction and use the same denominator. Professional Development Videos A Chapter Ch t

2 Daily Routines Common Core Problem of the Day. Mr. Vinn uses can of paint on Monday and of the same can of paint on Tuesday. What part of the can of paint does Mr. Vinn use in all? Vocabulary Interactive Student Edition Multimedia Glossary e Common Core Fluency Fluency Builder Standard.NBT.B. Materials Spinners (see eteacher Resources) Add Multi-Digit Whole Numbers Ask students to write the numbers in a -section spinner. Have students spin the spinner and use the digits to make multidigit addends. After students form the two addends, they can find the sum. Students can check their sums with a partner. Have students start with -digit plus -digit problems, and then try -digit plus -digit and -digit plus -digit problems. ENGAGE with the Interactive Student Edition Essential Question How can you use a model to multiply a fraction by a whole number? Making Connections Ask students to tell what they know about drawing fraction models. Draw a model that can be used to represent fifths. Check students models. Suppose you spend of an hour walking your dog every day. Shade the model to show this fraction of an hour. Check models. Learning Activity What is the problem the students are trying to solve? Connect the story to the problem. Ask the following questions. How many equal parts of a model do you shade to show a fraction? Possible answer: The same number as the numerator of the fraction. What does a fraction model with all of its parts shaded represent? Possible answer: whole or unit Do you think it would ever make sense to shade zero parts of a fraction model? Explain. Possible explanation: Yes, if you want to model 0. Literacy and ematics View the lesson opener with the students. Then have the class participate in the following activity. Have students give examples of situations in which they spend part of an hour doing something such as the part of an hour they spend in math class every day. Have them describe how they would show the part of an hour using a fraction model. Discuss whether there is more than one way to model the fraction. How can you use a model to multiply a fraction by a whole number? Lesson. B

3 LESSON..NF.B.b Apply and extend previous of multiplication to multiply a fraction by a whole number. Understand DO NOT EDIT--Changes must be made understandings through File info a multiple of a/b as a multiple of /b, and use this understanding to multiply a fraction by a whole number. CorrectionKey=B 2 EXPLORE Lesson. Unlock the Problem Multiply a Fraction by a Whole Number Using Models MATHEMATICAL PRACTICES Number and Operations Fractions.NF.B.b Also.NF.B.c MATHEMATICAL PRACTICES MP2, MP, MP Essential Question How can you use a model to multiply a fraction by a whole number? Read and discuss the problem with the class. What do you need to find? the amount of time Unlock Unlock the the Problem Problem Rafael will practice in days Example Rafael practices the violin for hour each day. He has a recital in days. How much time will he practice in days? MP Make sense of problems and persevere in solving them. Think: is groups of of a whole. Shade the model to show groups of. How many equal parts are shaded in wholes? equal parts What fraction of the wholes is this? Explain. ; possible explanation: each part is. There = group of each of days, so you are finding groups of. In the model, how will you show of a whole? Shade of equal parts. Talk Use Talk to help students recognize that the product of a whole number and a fraction less than will always be less than the whole-number factor. DEEPER MP2 Reason abstractly and quantitatively. What if Rafael practiced for hour each day? How would the model change? How much time will he practice in days? Possible answer: each circle would be divided into equal parts. Four of the equal parts would be shaded in each circle to represent hour. In the groups, there would be 2 fifths shaded. So, Rafael 2 hours in days. would practice ELL Strategy: Differentiated Instruction Illustrate Understanding = 2 groups of groups of = = Image Credits: (r) TongRo Image Stock/Alamy Images are fourths, or Less than; possible explanation: 2 =. = 2 and that is less than. Since 2 is less than, you know that groups of 2 are less than groups of whole, or. Talk So, Rafael will practice for hours in all. MATHEMATICAL PRACTICES 2 Reason Abstractly If you multiply 2, is the product greater than or less than? Explain.. Explain how you can use repeated addition with the model to find the product. Possible explanation: there are circles with of each circle shaded. Use as an addend times: + + =. 2. Rafael s daily practice of hour is in sessions that last for hour each. Describe how the model shows the number of practice sessions Rafael has in days. Possible description: the total number of fourth-size pieces that are shaded is the number of practice sessions Rafael will have: practice sessions. Chapter Meeting Individual Needs MNLESE222C0L0.indd Reteach. 2 Lesson. Reteach Fraction of a Whole Number Find the product. Write the product as a whole number. You can use a model to multiply a fraction by a whole number. Next have students draw a model to represent 2 groups of 2 (e.g., 2 pizzas with 2 of each pizza uneaten). Repeat with other fractions. 2. So, group of 2 groups of groups of Chapter Resources MNLEANC0R0.indd Multiply groups of 2. Lesson. Enrich Multiply a Fraction by a Whole Number Using Models Students draw a model to illustrate multiplying fractions by whole numbers. Have students draw a model to represent group of 2 (e.g., 2 of a pizza). Have students explain what their model shows. Differentiated Instruction DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A 0/0/ :2 PM Enrich. DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A. Find the product of each. Use fraction strips. Show groups of Chapter of should you model? Example Use a model to multiply. Why do you multiply by to solve the problem? Possible answer: Rafael practices hour. How many equal groups Explain how you can tell if the product of a fraction and a whole number will be a whole number. Possible explanation: when the denominator.. of the fraction is a factor of the whole number, the product will be a whole number. 2 Reteach Chapter Resources /02/ : PM MNLEANC0E0.indd 0-0 Enrich /02/ :0 PM

4 0 Example 2 Use a pattern to multiply. You know how to use a model and repeated addition to multiply a fraction by a whole number. Look for a pattern in the table to discover another way to multiply a fraction by a whole number. Multiplication Problem Whole Number (Number of Groups) When you multiply a fraction by a whole number, the numerator in the product is the product of the whole number and the numerator of the fraction. The denominator in the product is the same as the denominator of the fraction.. How do you multiply a fraction by a whole number without using a model or repeated addition? Fraction (Size of Groups) Product 2 2 of a whole 2 2 of a whole 2 of a whole Possible answer: multiply the whole number by the numerator of the fraction, and use the same denominator.. Describe two different ways to find the product 2. ; possible descriptions: one way: show third-size fraction strips. Shade 2 parts in each strip. Count the total number of shaded parts and write the sum over. Another way: multiply 2 by and write the product over the denominator,. Example 2 Students use a pattern in a table to multiply a fraction by a whole number. How many sixths do you have if you multiply 2? 2 groups of : 2 sixths, or 2 If you multiply 2 2? 2 groups of 2 : sixths, or If you multiply 2? 2 groups of : sixths, or What happens to the number of sixths each time you multiply the number of sixths by 2? Possible answer: there are twice as many sixths. Which number in the fraction tells you how many sixths there are? the numerator What happens to the numerator each time you multiply it by 2? The numerator is 2 times greater. Why does the denominator stay the same each time? Possible answer: the equal parts in the whole remain the same. What is 2? Explain how you know. ; possible explanation: I multiplied the numerator by 2 because the number of sixths is twice as many: 2 =. I kept the same denominator because it tells me the number of equal parts in a whole. So, the product is. MP Construct viable arguments and critique the reasoning of others. A student shaded fraction strips to model 2. Because 2 whole strips were shaded, the student said that the product 2 = 2 does not fit the pattern. What error did the student make in reasoning? Possible answer: 2 = 2, which can be rewritten as 2. The student did not think about 2 written as a fraction. Advanced Learners Materials Spinner (-section) (see eteacher Resources) ematical / Logical Individuals Students make a -section spinner and number it,, 0, and 2. Have students spin the spinner three times to create a multiplication problem using this template: Students should place the numbers so the fraction is less than. Have students find the product of the completed multiplication problem. They can continue making problems as time allows. COMMON ERRORS Error Students may incorrectly multiply the whole number by the denominator and write it over the numerator. Example = Springboard to Learning Remind students that the numerator tells the number of equal parts being considered and the denominator tells the total number of equal parts in a whole. Students should multiply the whole number by the numerator to find the total number of parts being considered. The denominator stays the same because the number of equal parts in a whole remains the same. Lesson. 0

5 DO NOT EDIT--Changes must be made through File info CorrectionKey=A EXPLAIN Share and Show MATH Share Share and and Show Show BOARD. Find the product of. group of = MATH BOARD 0 2 groups of = Use the checked exercises for Quick Check. groups of = Quick Check If Then 2 Rt I groups of = Multiply. a student misses the checked exercises 2. Differentiate Instruction with Reteach. Personal Trainer.NF.B.b RtI Tier Activity (online). Possible answer: divide each whole into sixth-size parts and shade parts in each whole. How would you use your model to find the product? Possible answer: count the number of. = 0 0 If students complete the checked exercises correctly, they may continue with the remaining exercises. MP Look for and make use of structure. Exercises 2 require students to use higher order thinking skills to find an unknown number in a multiplication sentence involving multiplication of a fraction by a whole number. Explain how you found the answer to Exercise. Possible explanation: I knew that the whole number times the numerator must equal 0, so I thought? 0. I knew 2 0, so the unknown number is 2. Chapter 20. = Talk Multiply. MATHEMATICAL PRACTICES Model ematics Describe how to model Exercise. On On Your Your Own Own 0. 2 = 2 2. =. 2 = 2. = = = MATHEMATICAL PRACTICE 2. Look for a Pattern Algebra Write the unknown number. 2 = 2 shaded parts in the four circles or fraction strips and use that number as the numerator and as the denominator in the product. On Your Own Possible description: show on each of circles divided into sixth-size parts. How would you model the second factor? Use Talk to focus on students understanding of modeling the multiplication of a fraction by a whole number. How would you model the first factor? 2 = Talk 2 = Possible answer: draw whole circles or fraction strips. 2. = 0. 2 = Chapter Lesson MNLESE222C0L0.indd 0/0/ 2:2 PM

6 MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS Unlock the Problem. SMARTER Lisa makes clothes for pets. She needs yard of fabric to make dog coat. How much fabric does she need to make dog coats? a. What do you need to find? how much fabric Lisa needs to make dog coats b. What information do you need? Lisa needs yard of fabric to make dog coat. She will make dog coats. c. Show the steps you use to solve the problem. = d. Complete the sentence. Lisa needs yards of fabric to make dog coats. Possible answer: I can use a model to solve the problem. dog coat = yard 2 dog coats = 0 yards dog coats = yards WRITE Show Your Work ELABORATE Unlock the Problem MATHEMATICAL PRACTICES SMARTER MP Make sense of problems and persevere in solving them. For Exercise, work through the scaffolded problem with students to help them focus on using the problem-solving steps of reading the problem to determine what they are to find and what information they need, choosing a strategy to use the information, and answering the question the problem asks.. DEEPER Manuel s small dog eats 2 bag of dog food in month. His large dog eats bag of dog food in month. How many bags do both dogs eat in months? 2 0 bags or 2 bags. SMARTER Select the correct product for the equation = 2 = = 2 2 = 2 2 Image Credits: (t) Petra Wegner/Alamy Images on the Spot Video Tutor Use this video to help students model and solve this type of Think Smarter problem. on the Spot videos are in the Interactive Student Edition and at SMARTER Exercise assesses students ability to multiply a fraction by a whole number. If students select as the answer to the first equation, they have selected a fraction with the correct numerator, but have not paid attention to the denominator. EVALUATE DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES Formative Assessment Activities Fraction Bingo! Differentiated Centers Kit Students complete purple Activity Card by creating pictorial models of fractions and finding equivalent fractions. Literature A Melody in Fractions Students read the book and learn how fractions and equivalent fractions are used to read music. Essential Question Using the Language Objective Reflect Have students write in their Journal to answer the Essential Question. How can you use a model to multiply a fraction by a whole number? Possible answer: divide a whole into equal parts as shown by the denominator. Shade the number of equal parts as shown by the numerator. Show as many of these wholes as the whole-number factor. The product is the total number of shaded parts written over the denominator. Journal WRITE Explain how you can use a model to find. Include a drawing and a solution. Lesson. 2

7 Practice and Homework Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write section to determine student s understanding of content for this lesson. Encourage students to use their Journals to record their answers. Multiply a Fraction by a Whole Number Using Models Multiply.. 2 = 0. 2 = =. = Practice and Homework Lesson. COMMON CORE STANDARD.NF.B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers... 0 = = Problem Solving. Matthew walks mile to the bus stop each morning. How far will he walk in days?. Emily uses 2 cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes batches of muffins? 2 miles cups. WRITE Explain how you can use a model to find. Include a drawing and a solution. Check students drawings. Chapter COMMON ON CORE PROFESSIONAL DEVELOPMENT Talk in Action This Talk in Action is an example of dialogue for Exercise. Teacher: Describe how you found the product of 2. Eddie: Teacher: I drew a model. I made circles each divided into equal parts. I shaded 2 parts on each circle. Then I counted the number of parts shaded. There were parts shaded, so 2. How did you know what to draw to model the problem? Eddie: 2 means groups of 2. I knew that the whole had to be divided in equal parts and 2 would be shaded in each whole to represent 2. Then there would be of these 2. Teacher: That s right. Did anyone find the product another way? Giselle: I mentally added and got. Teacher: How did you know what to add? Giselle: Teacher: Anthony: Teacher: I know multiplication is repeated addition, so 2 means adding 2 four times. Good! Can someone describe another way to find the product? I multiplied the whole number, by the numerator 2, and wrote the product over the denominator. I got, too. Nice job everyone! You described different ways you can find the product. Chapter

8 Lesson Check (.NF.B.b). Aleta s puppy gained pound each week for weeks. Altogether, how much weight did the puppy gain during the weeks? 2. Pedro mixes teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into gallons of water? Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section. 2 pounds teaspoons Spiral Review (.NF.A.2,.NF.B.b,.NF.B.c,.NF.B.a). Ivana has pound of hamburger meat. She makes hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?. Write as a sum of fractions two different 0 ways. pound Possible answer: ; Lance wants to find the total length of boards. He uses the expression + (2 + ). How 2 2 can Lance rewrite the expression using both the Associative and Commutative Properties of Addition? 2 + ( ). Fill in the blank with a symbol that makes this statement true: 2 > FOR MORE PRACTICE GO TO THE Personal Trainer Lesson.