The Number System

7.NS.1Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line.7.NS.1aUnderstand that the additive inverse of a number is its opposite and their sum is equal to zero.7.NS.1bUnderstand that the sum of two rational numbers (p+q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q.7.NS.1cTranslate between the subtraction of rational numbers and addition using the additive inverse, p-q=p+(-q).7.NS.1dDemonstrate that the distance between two rational numbers on the number line is the absolute value of their difference.7.NS.1eApply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.7.NS.2Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers.7.NS.2aUnderstand that the multiplicative inverse of a number is its reciprocal and their product is equal to one.7.NS.2bUnderstand sign rules for multiplying rational numbers.7.NS.2cUnderstand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.7.NS.2dApply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers.7.NS.2eUnderstand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat.7.NS.3Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems.7.NS.4Understand and apply the concepts of comparing and ordering to rational numbers.7.NS.4aInterpret statements using less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line.7.NS.4bUse concepts of equality and inequality to write and explain real-world and mathematical situations.7.NS.5Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, and percentages). Exclude the conversion of repeating decimal numbers to fractions.
Goblins

1-on-1 AI tutoring aligned to 7.NS. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →