Standard #: MAFS.5.NF.2.5 (Archived 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: 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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

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?

 

N/A MC: Multiple Choice
Sample Item 2

Select all the expressions that have a value greater than 1,653.

 

N/A MS: Multiselect
Sample Item 3

For MAFS.5.NF.2.5a:

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

 

N/A MI: Matching Item


Related Courses

Course Number1111 Course Title222
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 Resources

Formative Assessments

Name Description
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.

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.

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.

Lesson Plans

Name Description
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.

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.

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.

Looking for Patterns in a Sequence of Fractions

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

Original Student Tutorials

Name Description
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.

Problem-Solving Tasks

Name Description
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.

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.

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.

Fundraising

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

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.

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.

Student Resources

Original Student Tutorials

Name Description
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.

Problem-Solving Tasks

Name Description
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.

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.

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.

Fundraising:

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

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.

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.



Parent Resources

Problem-Solving Tasks

Name Description
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.

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.

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.

Fundraising:

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

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.

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.



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