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Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  1. 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.
  2. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
  3. Apply properties of operations as strategies to multiply and divide rational numbers.
  4. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Standard #: MAFS.7.NS.1.2Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (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 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
  • Find Decimal Using Long Division Students are asked to use long division to convert four different fractions to equivalent decimals and to identify those that are rational.
  • Understanding Products Students are asked to explain why the product of a positive and a negative rational number is negative.
  • Negatives Explained Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.
  • Negative Times Students are shown a problem that illustrates why the product of two negatives is a positive and are asked to provide a rationale.
  • Applying Rational Number Properties Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.
  • Integer Division Students are asked to describe a real-world context for a given expression involving the quotient of two rational integers.
  • Quotients of Integers Students are given an integer division problem and asked to identify fractions which are equivalent to the division problem.
Lesson Plans
  • Radioactive Dating Lesson 4 - Recursive Division This lesson introduces students to the idea of recursive division and its application to radioactive dating with a worksheet and Scratch programming. This is the final lesson in the Radioactive Dating Unit.
  • Independent Compound Probability During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.
  • Increasing and Decreasing Quantities by a Percent This lesson helps students interpret and apply percent increase and percent decrease in real-world contexts. Students translate between percents, decimals, and fractions; represent percent change as multiplication by a scale factor; and explore the relationship between increases and decreases. Through guided activities and collaborative problem solving, students deepen their understanding of percent change as a multiplicative relationship.
  • Let's Understand Multiplication of Positive and Negative Numbers This lesson provides teachers with a way to show students why multiplying negative numbers results in a positive answer. The lesson starts with a review of decomposition, the distributive property, and finding missing addends. Then, with teacher guidance, groups of students apply these skills in a systematic way to apply properties of operations to discover the rules governing the signs of products for positive and negative factors and to multiply positive and negative numbers in mathematical and real-world problems. Finally, students independently demonstrate mastery of the lesson objectives by completing an independent practice assessment.
Original Student Tutorial
Problem-Solving Tasks
  • Equivalent fractions approach to non-repeating decimals The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.
  • Repeating Decimal as Approximation The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.
Tutorials
MFAS Formative Assessments
  • Applying Rational Number Properties Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.
  • Find Decimal Using Long Division Students are asked to use long division to convert four different fractions to equivalent decimals and to identify those that are rational.
  • Integer Division Students are asked to describe a real-world context for a given expression involving the quotient of two rational integers.
  • Negative Times Students are shown a problem that illustrates why the product of two negatives is a positive and are asked to provide a rationale.
  • Negatives Explained Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.
  • Quotients of Integers Students are given an integer division problem and asked to identify fractions which are equivalent to the division problem.
  • Understanding Products Students are asked to explain why the product of a positive and a negative rational number is negative.
Original Student Tutorials Mathematics - Grades 6-8
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