Lesson Plan: 5.NF.B.6 Problems with Fractions(This lesson should be adapted, including instructional time, to meet the needs of your students.)

Background InformationContent/Grade Level Number and Operations – Fractions/ Grade 5

Unit/Cluster Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Essential Questions/Enduring Understandings Addressed in the Lesson

How does multiplying a whole number by a fraction impact the product? How does multiplying a fraction by a fraction impact the product?How does multiplying a mixed number by a mixed number impact the product?

Multiplying a quantity by a number smaller than 1 produces a smaller quantity.Multiplying a quantity by a fraction does not always make the product smaller than its factors.

Standards Addressed in This Lesson 5.NF. B. 6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.

Lesson Topic Multiplying fractions by fractions and fractions by mixed numbers.

Relevance/Connections 5.NF.B.4 apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.B.5 Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product

greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a

product smaller than the given number; and relating the principle of fraction equivalenceab =

nxanxb to the effect of multiplying abby 1.

Student Outcomes Students will be able to solve multiplication of fractions by using various methods.Page 1 of 16

Prior Knowledge Needed to Support This Learning

4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number.

Method for determining student readiness for the lesson

Use the Warm-up as a formative assessment to determine the level of understanding for finding a fraction of a whole and a fractional part of a fraction.

Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

Warm Up Use models and drawings to develop your answers.

The fifth grade raised $126.00 for the school

fundraiser. If 13 of the money was raised by your class, how

much money was raised by your class?

If 34 of the students in the school participated in the

fundraiser and 12 of the participants were girls, what fraction

of the students in the school who participated in the fundraiser were girls?

Motivation Video of Baltimore Ravens player Ray Rice Play60 advertisement:http://www.youtube.com/watch?v=bF3QyoI_MJQ

Ray Rice encourages children to exercise every day. In order for Ray Rice and the Baltimore Ravens football team to stay

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

in shape, they exercise 5 days a week. On Monday, they spent

2 12 hours exercising; if

12 of the time were lifting weights,

how many hours were spent lifting weights? Use models and drawings to develop your answers.

Activity 1

UDL Components Multiple Means of

Representation Multiple Means for

Action and Expression

Multiple Means for Engagement

Key QuestionsFormative AssessmentSummary

UDL Components: Principle I: Representation is present in the activity. A

visual diagram multiplying a fraction times a whole number is one of the methods students are using.

Principle II: Expression is present in the activity. The five different methods of solving the fraction multiplication problems showed students multiple ways of expressing a solution.

Principle III: Engagement i s present in the activity. The task allowed for active participation, exploration and experimentation, as well as invited personal response, evaluation, and self-reflection regarding content and activities.

Note to the teacher: Visit the following website before you begin the lesson to review 5 ways to show multiplication of a fraction and a mixed number. Open the website and follow the steps given below to get to the explanations.

http://illustrativemathematics.org/1. choose K-8 Standards 2. choose 5th grade3. choose Number and Operation –Fractions4. choose show all

Students make sense of problems and persevere in solving them by seeing relationships among various methods of multiplying fractions.(SMP #1)

The students need to communicate precisely with others when showing their solutions to the fraction problems and try to use clear mathematical language when discussing their reasoning.(SMP#6)

Students will use repeated reasoning as they solve the same problem using five distinct methods.(SMP#8)

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

5. choose #66. choose See Illustrations7. choose Half of a Recipe.

Please note there are a few errors on this site. They are: Using a Number Line—the last sentence should read:

We can see that 1 58 is half way between 0 and 3

14 .

Using the Distributive Property—use the one below instead. There was apparently a glitch in the printing.

12 × (3 +

14 )

12× 3 +

12×

14

32 +

18

148 +

18 = 1

58

(Note the connection to 5.NF.B.4 in the solution above.) This strategy can be compared side-by-side with the "Drawing a Picture" solution. Taken together, these solutions represent essentially the same strategy represented pictorially and numerically.

After you have reviewed the 5 methods, review the problem with your students making sure to work all 5 methods with them using Attachment #1.

Put students in groups of 4. Pass out Attachment #2

which has 5 separate problems. Each student starts with one unique problem and fills out one section of

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

the sheet. Then they pass their sheet to the person on their left and fill in a blank section on the new sheet. Continue until all sections of each sheet are complete. Answers:

1. 212 million boats

2. 1638 in.

3.7

40 km

4. 138 ft.

5. 84 7

20 lbs.

Activity 2

UDL Components Multiple Means of

Representation Multiple Means for

Action and Expression

Multiple Means for Engagement

Key QuestionsFormative AssessmentSummary

UDL Components: Principle I: Representation is present in the activity. A

visual diagram multiplying a fraction times a whole number is one of the methods students are using.

Principle II: Expression is present in the activity. The five different methods of solving the fraction multiplication problems showed students multiple ways of expressing a solution.

Principle III: Engagement i s present in the activity. The task allowed for active participation, exploration and experimentation, as well as invited personal response, evaluation, and self-reflection regarding content and activities.

Directions:Divide class into 6 groups. Give each group one of the

Students make sense of problems and persevere in solving them by seeing relationships among various methods of multiplying fractions.(SMP #1)

The students need to communicate precisely with others when showing their solutions to the fraction problems and try to use clear mathematical language when discussing their reasoning.(SMP#6)

Students will use repeated reasoning as they solve the same problem using five distinct methods.(SMP#8)

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

following problems. (Two groups will have the same problem.) Teacher will post each problem on a sheet of chart paper. (6 sheets of chart paper will be placed around the room.) Groups will solve the problem assigned and show their work on a piece of chart paper.

Then groups will go around the room and look at solutions to the problems. If they agree with the solution they will place one color dot on the page and a different color dot if they do not agree.

Entire class discussion should follow. Joseph has been training for the Baltimore Marathon

every weekend. Last weekend he was on vacation in Ocean City, MD and he jogged on the beach, on the

boardwalk and in the park. He jogged 4 34 miles on

Saturday.

o If 12 of the miles were jogged on the beach, how

many miles were jogged on the beach?

(Answer: 238 miles)

o Joseph jogged 14 of the miles on the boardwalk.

How many miles were jogged on the boardwalk?

(Answer: 13

16 miles)

o How many miles did Joseph jog in the park?

WE need to change the UDL components and update the SMPs.

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

(Answer: 13

16 miles)

The next week Joseph travelled to Deep Creek Lake in Cumberland, MD. This weekend he hiked a trail

that is 3 34 miles long.

o If he hiked 23 of the trail on Sunday, how

many miles did Joseph hike on Sunday?

(Answer: 212 miles)

o If one-half of the 3 34 miles trail is located in

the state park, how many miles of the trail are located in the state park?

(Answer: 178 miles)

Your science class project is to recreate a larger wilderness playground for the animals at Marshy Point Nature Center. The current dimensions for the wilderness playground are shown in the table.

o Redesign the wilderness playground by

increasing the length 1 14 times, the width 1

12

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Learning Experience

Component DetailsWhich Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

times.

(Answer: 212 miles)

o Write the new dimensions in the table. Explain how you found the new dimensions.

Length 4 12 ft. 5

58 ft.

Width 3 23 ft. 5

12 ft.

Closure Students should work this problem individually.

Your fifth grade class has been given an end of the year project. Your class is to create a sign to represent school

pride. The length of the space is 34 yd and the width is 2

35

yd. Find the area of the space that your class has been provided for the sign.

Answer: 11920 square yards.

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Supporting InformationInterventions/Enrichments

Students with Disabilities/Struggling Learners

ELL Gifted and Talented

Students with Disabilities/Struggling Learners and ELLEnsure that these students spend quality time using the picture drawings and the number lines.Review all vocabulary necessary.

Gifted and TalentedHave these students create problems using fractions times mixed numbers and illustrate all 5 methods to solve these.

Materials Grid paper, colored pencils, fraction bars, colored tiles

Technology Smart boards and document cameras

Resources http://www.youtube.com/watch?v=bF3QyoI_MJQhttp://illustrativemathematics.org/

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0

Attachment 1

Drawing a Picture

Using a Number Line

Computing a Product

Use the Distributive Property

Use Decimal Numbers

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There are 7 and one half million pleasure boats in the U.S. of these boats are motorboats. How many pleasure boats are not motor boats?

Drawing a PictureU

sing a Num

ber Line

Computing a Product

Use the Distributive Property

Solve these problems. Then compare with Sara’s answers which are above.

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Attachment 2 (a)

Joaquin is 65 inches tall. Juan is of his height. How much taller is Joaquin than Juan.

Drawing a Picture

Using a Number Line

Computing a Product

Use Decimal Numbers

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Attachment 2 (b)

It took Barack’s turtle an hour to travel of a kilometer. At this rate, how far can the turtle travel in 1 hours?

Drawing a Picture

Using a N

umber Line

Computing a ProductU

se the Distributive Property

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Attachment 2 (c)

Eunhee is making a model car that the length of her dad’s car. How long is the model if the actual car is 16 feet long?

Drawing a Picture

Using a Number Line Computing a Product

Use Decimal Numbers

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Attachment 2 (d)

About of the human body is water. How many pounds of water are in a person weighing 120 pounds?

Use Decim

al Num

bers

Use the Distributive Property

Drawing a Picture

Using a N

umber Line

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Attachment 2 (e) More Challenging Problem

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