NS.1.2.a

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a.  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Applying Rational Number Properties

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CPALMS: Students are shown a problem that illustrates why the product of two negatives is a positive and are asked to provide a rationale.

Negative Times

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CPALMS: Students are asked to explain why the product of a positive and a negative rational number is negative.

Understanding Products

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CPALMS: Students are asked to use long division to convert four different fractions to equivalent decimals and to identify those that are rational.

Find Decimal Using Long Division

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CPALMS: Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Negatives Explained

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CPALMS: Students are asked to describe a real-world context for a given expression involving the quotient of two rational integers.

Integer Division

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CPALMS: Students are given an integer division problem and asked to identify fractions which are equivalent to the division problem.

Quotients of Integers

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: Using this manipulative, students apply dimensional analysis (AKA factor-label method or unit-factor method) to solve unit conversion problems. There's also the opportunity to create your own unit conversion problems.

Converting Units Through Dimensional Analysis

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Assessment Questions
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Multiple Choice
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Any fraction can be converted into an equivalent decimal number with a sequence of digits after the decimal point, which either repeats or terminates. The reason can be understood by close examination of the number line.
Converting Fractions to Decimal Numbers
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Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics:The goal is to study the distributive property for products of whole numbers, focusing on using geometry to help understand why (-1) × (-1) = 1. This important property can be viewed as an application of the distributive property to whole numbers.

Distributive Property of Multiplication

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Illustrative Mathematics: The purpose is for students to understand the reason it makes sense for the product of two negative numbers to be positive.The idea is that if the properties of operations we use when doing arithmetic with positive numbers are universal, then we define multiplication on signed numbers the way we do.

Why is a Negative Times a Negative Always Positive?