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 equivalence = to the effect of multiplying by 1.
Student Outcomes / Students will be able to solve multiplication of fractions by using various methods.
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 / Details / Which 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 of the money was raised by your class, how much money was raised by your class?
If of the students in the school participated in the fundraiser and 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:
Ray Rice encourages children to exercise every day. In order for Ray Rice and the Baltimore Ravens football team to stay in shape, they exercise 5 days a week. On Monday, they spent 2hours exercising; if of the timewere 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
Formative Assessment
Summary / 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 is 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.
Open the website and follow the steps given below to get to the explanations.
- choose K-8 Standards
- choose 5th grade
- choose Number and Operation –Fractions
- choose show all
- choose #6
- choose See Illustrations
- choose Half of a Recipe.
- Using a Number Line—the last sentence should read:
- Using the Distributive Property—use the one below instead. There was apparently a glitch in the printing.
× 3 + ×
+
1 + = 1
(Note the connection to 5.NF.B.4 inthe 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 has5 separate problems. Each student starts with one unique problem and fills out one section of 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.
- 2million boats
- 16 in.
- km
- 1ft.
- 84 lbs.
(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)
Activity 2
UDL Components
- Multiple Means of Representation
- Multiple Means for Action and Expression
- Multiple Means for Engagement
Formative Assessment
Summary / 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 is 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.
Divide class into 6 groups. Give each group one of the 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 jogged4 miles on Saturday.
- If of the miles were jogged on the beach, how many miles were jogged on the beach?
- Josephjogged of the miles on the boardwalk. How many miles were jogged on the boardwalk?
- How many miles did Joseph jog in the park?
- The next week Joseph travelled to Deep Creek Lake in Cumberland, MD. This weekend he hiked a trail that is 3 miles long.
- If he hiked of the trail on Sunday, how many miles did Joseph hike on Sunday?
- If one-half of the 3 miles trail is located in the state park, how many miles of the trail are located in the state park?
- 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.
- Redesign the wilderness playground by increasing the length 1 times, the width 1 times.
- Write the new dimensions in the table. Explain how you found the new dimensions.
Width / 3 ft. / 5 ft.
/ 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)
WE need to change the UDL components and update the SMPs.
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 yd and the width is 2yd. Find the area of the space that your class has been provided for the sign.
Answer: 1 square yards.
Supporting Information
Interventions/Enrichments
- Students with Disabilities/Struggling Learners
- ELL
- Gifted and Talented
Ensure that these students spend quality time using the picture drawings and the number lines.
Review all vocabulary necessary.
Gifted and Talented
Have 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 /
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Attachment 1
Drawing a Picture
Using a Number Line
Computing a Product
Use the Distributive Property
Use Decimal Numbers
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Solve these problems. Then compare with Sara’s answers which are above.
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