5.NF.6 - About the Math, Learning Targets, and Rigor

Grade 5 Fractions

5.NF.6

About the Math

Full Standard

Solve real world problems involving multiplication of fractions and mixed numbers (e.g., by using visual fraction models or equations to represent the problem).

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

5th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

Report Card Measurement Topic: Demonstrates understanding of multiplication and division of different number types.

 
4th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

 

Learning Targets (I can)

  • Represent word problems that multiply fractions and mixed numbers with physical models, drawings, and number lines.
  • Write equations for word problems that multiply fractions and mixed numbers.
  • Solve problems that multiply fractions and mixed numbers.
  • Determine reasonableness of solutions to word problems that multiply fractions and mixed numbers using the context of the word problem (does this make sense in the problem?).

 

About the Math

Solving word problems with addition, subtraction, multiplication and division of fractions follow the same problem solving structures for whole number situations.

  • Represent word problems that multiply fractions and mixed numbers with physical models, drawings, and number lines.
  • Solve problems that multiply fractions and mixed numbers.

These word problems should represent the various problem-solving structures linked above. Students should diagram and represent problems to connect to their equations. Students should not rely on key words for finding solutions.

  • Write equations for word problems that multiply fractions and mixed numbers.

Pictures and diagrams are useful for understanding problems. Students should connect them to equations. Students should then connect their equations back to the problem. In time, when appropriate, students should generate and use equations to solve their problems. Students can resort back to pictures and diagrams as needed. 

  • Determine reasonableness of solutions to word problems that multiply fractions and mixed numbers using the context of the word problem (does this make sense in the problem?).

Students can determine reasonableness in a variety of ways. Doing so takes a good bit of time and experience. Predicting and estimating results for comparison helps students develop a sense of reasonableness. Other strategies, including reflective self-questions, help as well. Teacher modeling and teacher self-talk help students understand the questions and thoughts they should consider. 

 

Progression of Standard within Grade 5

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
 
  • Represent word problems that multiply fractions and mixed numbers with physical models, drawings, and number lines.
  • Write equations for word problems that multiply fractions and mixed numbers.
  • Solve problems that multiply fractions and mixed numbers.
  • Determine reasonableness of solutions to word problems that multiply fractions and mixed numbers using the context of the word problem (does this make sense in the problem?).

 

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 4 Grade 6
  • Use the four operations to solve word problems (4.MD.2)
  • Multiplicative comparison (4.OA.1)
  • Multiply or divide to solve word problems involving multiplicative comparison (4.OA.2)
  • Recognizing statistical questions (6.SP.1) 
  • Distribution of data (6.SP.2)
  • Display data in plots on number lines, dot plots, histograms, and box plots (6.SP.4)

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • A lemonade recipe serves six people and requires 2 ⅔ cup sugar. How much sugar will you need if you make the recipe to serve 9 people?
  • You have a piece of paper that measures 1ft.x1ft. If you want the paper to be ¾ of it’s size in both length and width, what will be the final measurements of the paper (in inches)?
  • The community pool measures 12 ⅜ feet x 16 ⅔ feet. John wants to build a pool that is 1 ¾ times the size of the community pool- in length and width. What will be the dimensions of your John’s pool?
  • India and Jess have been given a bag of individually wrapped chocolates. If India takes ¼ of the chocolates and Jess takes ⅕ of the chocolates, how many chocolates might have been in the bag and how many might still be in the bag?
  • Write a story problem with two fractions with a product greater than 1.

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 6 • Multiplying Fractions

Multiplying Fractions by Fractions (no mixed numbers):

Module 7 • Multiplying and Dividing Fractions

Multiplying Fractions including Mixed Numbers:

 

 

Additional TaskS

These links provide instructional ideas connected to this standard. 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages

 

Teaching Student-Centered Mathematics

 

6-8

 

Expanded Lesson: Division-of-Fractions Stories, Pages 141-142
Hands-On Standards, Common Core Fractions

5 48-52 Lessons 4 and 5
Problem Driven Math 5 59 Keeping On Track

Math In Practice

Teaching Fifth-Grade Math

 5 Module 9

 

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

 

 

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Assessment

Learning Targets

rubric

  • Represent word problems that multiply fractions and mixed numbers with physical models, drawings, and number lines.
  • Write equations for word problems that multiply fractions and mixed numbers.
  • Solve problems that multiply fractions and mixed numbers.
  • Determine reasonableness of solutions to word problems that multiply fractions and mixed numbers using the context of the word problem (does this make sense in the problem?).

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.