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Standard #: MAFS.5.NF.2.5Archived 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.

Standard Information

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

Formative Assessments

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.
  • 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 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.

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.
  • 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.

Collections

MFAS Formative Assessments

Original Student Tutorials Mathematics - Grades K-5

  • 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.
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