NF.2.5.b

Interpret multiplication as scaling (resizing), by:

b. 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.

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Formative Assessments
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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.
Estimating Products
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Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying.
Multiplying by a Fraction Less Than One
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Students are asked to reason about the size of the product of fractions and whole numbers presented in context.
More Than or Less Than Two Miles
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Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying.
Multiplying a Fraction Greater Than One
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: This interactive applet provides a visual model of fraction multiplication using rectangular arrays.
Fractions-Rectangle Multiplication
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Hook/Performance Tasks
Hook/Performance Tasks
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Students are given information about a race and the time of the boys running but asked about the speeds.
IM:  Running a Mile
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Students need to explain who raised more money for a class trip.
IM:  Fundraising
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The goal of this task is to compare three quantities using the notion of multiplication as scaling.
IM:  Comparing Heights of Buildings
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Students explain their thinking with look at the relationship between the magnitude of the factors and the magnitude of the product.
IM:  Reasoning about Multiplication
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Students need to explain their thinking when a calculator displays a certain number of a calculator.
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This task is designed to assess students' ability to compare 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.
IM:  Mrs. Gray’s Homework Assignment
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Students must compare the size of each of two products to one factor on the basis of the other factor without performing any computations.
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The purpose of this task is for students to compare a number and its product with other numbers that are greater than or less than one.
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This task is structured so that a teacher can diagnose the depth of a students' understanding of what it means to multiply a number by a fraction specifically in terms of scaling.
IM:  Scaling Up and Down