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

Grade 5 Fractions

5.NF.5

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.

 

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 

  • 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 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
 
  • 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)

 

 

Back to Top

 

 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.