6.NS

The Number System

6.NS.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, requiring multiple exposures connecting various concrete and abstract models.6.NS.2Fluently (efficiently, accurately, and flexibly) divide multi-digit numbers using an efficient algorithm.6.NS.3Fluently (efficiently, accurately, and flexibly) add, subtract, multiply, and divide multi-digit decimals using an efficient algorithm for each operation.6.NS.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 18+48 as 6(3+8).6.NS.5Understand positive and negative numbers to describe quantities having opposite directions or values (e.g. temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge);6.NS.5aUse positive and negative numbers to represent quantities in real-world contexts,6.NS.5bExplaining the meaning of 0 in each situation.6.NS.6Understand a rational number as a point on the number line and a coordinate pair as a location on a coordinate plane.6.NS.6aRecognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, (e.g. −(−3) = 3,) and that 0 is its own opposite.6.NS.6bRecognize signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.6.NS.6cFind and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.6.NS.7Understand ordering and absolute value of rational numbers.6.NS.7aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret −3 > −7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.6.NS.7bWrite, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3°C > - 7°C to express the fact that -3°C is warmer than -7°C.6.NS.7cExplain the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |−30| = 30 to describe the size of the debt in dollars.6.NS.7dDistinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.6.NS.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
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