MAFS.5.NF.2.5Archived Standard

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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.
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    For given fractions in items, denominators are limited to 1-20. Non-fraction factors in items must be greater than 1,000. Scaling geometric figures may not be assessed. Scaling quantities of any kind in two dimensions is beyond the scope of this standard.
  • Calculator :

    No

  • Context :

    Allowable

Sample Test Items (3)
  • Test Item #: Sample Item 1
  • Question:

    Two newspapers are comparing sales from last year.

    • The Post sold 34, 859 copies.
    • The Tribune sold one-and-a-half times as many copies as the Post.

    Which expression describes the number of newspapers the Tribune sold?

     

  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 3
  • Question:

    For MAFS.5.NF.2.5a:

    Fill in circles to match the value of each expression to the correct description.

     

  • Difficulty: N/A
  • Type: MI: Matching Item

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Multiplying by a Fraction Greater Than One:

Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying.

Type: Formative Assessment

Multiplying by a Fraction Less than One:

Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying.

Type: Formative Assessment

More Than or Less Than Two Miles:

Students are asked to reason about the size of the product of fractions and whole numbers presented in context.

Type: Formative Assessment

Estimating Products:

Students are given three products, each involving a whole number and a fraction, and are asked to estimate the size of the product and explain their reasoning.

Type: Formative Assessment

Lesson Plans

Coding Geometry Challenge #10 & 11:

This set of geometry challenges focuses on scaled drawings and area as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Real-World Fractions:

This lesson focuses on providing students with real-world experiences where they will be required to multiply fractions. Students will be required to use visual fraction models or equations to represent the problem.  This is a practice and application lesson, not an introductory lesson.

Type: Lesson Plan

Multiplying a Fraction by a Fraction:

In this lesson, students will solve problems related to training for a marathon to apply and make sense of multiplying fractions. The student will complete a function table to help illustrate patterns in the numerator/denominator relationships. This lesson utilizes the linear model as a concrete representation and moves towards the standard algorithm (a/b) x (c/d) = ac/bd.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Original Student Tutorials

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Type: Original Student Tutorial

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task

MFAS Formative Assessments

Estimating Products:

Students are given three products, each involving a whole number and a fraction, and are asked to estimate the size of the product and explain their reasoning.

More Than or Less Than Two Miles:

Students are asked to reason about the size of the product of fractions and whole numbers presented in context.

Multiplying by a Fraction Greater Than One:

Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying.

Multiplying by a Fraction Less than One:

Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying.

Original Student Tutorials Mathematics - Grades K-5

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Type: Original Student Tutorial

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task