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

Grade 4 G/T Fractions

5.NF.5

About the Math

Full Standard

Interpret multiplication as scaling (resizing), by:

  1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  2. 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 a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

 

Learning Targets 

  • Explain the size of a product in comparison to the factors. (i.e. How does the product of 3/4 x 8 compare to 8? What is happening with the products of 1/2 x 4, 1/2 x 2, 1/2 x 1, and 1/2 x 1/2?)
  • Explain why a product changes when a given number is multiplied by a factor greater than 1 or a factor less than 1.

 

About the Math

  • Explain the size of a product in comparison to the factors. (i.e. How does the product of 3/4 x 8 compare to 8? What is happening with the products of 1/2 x 4, 1/2 x 2, 1/2 x 1, and 1/2 x 1/2?)
  • Explain why a product changes when a given number is multiplied by a factor greater than 1 or a factor less than 1.

The identity property of multiplication tells us that a number x 1 has a product equal to the number (itself). For example, 4 x 1 = 4. So when we multiply by a fraction that is less than 1, our product has to be less than the number we are multiplying the fraction by. For example, 4 x 1/3 = 1 1/3. The product (1 1/3) is less than the original factor 4 because the second factor (1/3) is less than 1. Conversely, when we multiply a number by a number greater than 1 (including fractions/mixed numbers) our product is greater than the original factor. For example, 4 x 5/4 = 5. The product (5) is greater than the first factor (4) because the second product is greater than 1. 

 

 

 

Progression of Standard within Grade 4 G/T

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
 
  • Explain the size of a product in comparison to the factors. (i.e. How does the product of 3/4 x 8 compare to 8? What is happening with the products of 1/2 x 4, 1/2 x 2, 1/2 x 1, and 1/2 x 1/2?)
  • Explain why a product changes when a given number is multiplied by a factor greater than 1 or a factor less than 1.

 

 

 

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)
  • Recognize and generate equivalent fractions (4.NF.1)
  • Multiplicative comparison (4.OA.1)
  • Multiply or divide to solve word problems involving multiplicative comparison (4.OA.2)
  • Understand the concept of a ratio (6.RP.1)

 

 

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Instructional Tasks

TASKS

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

  • Why is the product of 2x2 greater than 2 and the product of 2 x ½ less than 2?
  • What are two fractions with a product that is less than both fractions?
  • What are two fractions with a product greater than one of the fractions, but less than the other fractions?

 

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 4 • Multiplying  Fractions

Explain the Results of Multiplying a Whole Number by a Fraction:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

CC= Indicates recently added colleague created instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

 

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 Can You See it?, Activity 8.21, Page 133
Hands-On Standards, Common Core Fractions

5 46 "ExplorAction 1"

 

 

 

 

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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

  • Explain the size of a product in comparison to the factors. (i.e. How does the product of 3/4 x 8 compare to 8? What is happening with the products of 1/2 x 4, 1/2 x 2, 1/2 x 1, and 1/2 x 1/2?)
  • Explain why a product changes when a given number is multiplied by a factor greater than 1 or a factor less than 1.

 

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

 

 

 

 

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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.