Understand ordering and absolute value of rational numbers

Start lessonBegins with Ordering rationals on the number line · Slides

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6.NS.C.7

Understand ordering and absolute value of rational numbers. a. Interpret 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. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 degreesC > -7 degreesC to express the fact that -3 degreesC is warmer than -7 degreesC. c. Understand 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. d. Distinguish 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.

Understand ordering and absolute value of rational numbers.

a. Interpret 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.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 degreesC > -7 degreesC to express the fact that -3 degreesC is warmer than -7 degreesC.

c. Understand 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.

d. Distinguish 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.

What you'll learn

Compare two rational numbers using a number line: a < b when a is to the left of b on a horizontal number line (or below b on a vertical one), and a > b when a is to the right (or above).
Write, interpret, and explain order statements for signed quantities in real-world contexts -- for example, -3 degreesC > -7 degreesC, -50 ft > -200 ft, -20 dollars > -75 dollars -- and translate between symbolic and verbal forms.
Define and compute the absolute value |a| as the distance from 0 to a on the number line, including for fractions and decimals; recognize that |a| is always nonnegative and that |0| = 0.
Interpret |a| as the magnitude of a signed quantity (the size of a debt, the depth of a dive, the severity of a cold reading).
Distinguish a comparison of order from a comparison of absolute values, and recognize that for two negative values, the one with the larger absolute value is the smaller on the number line -- that "less than" and "larger absolute value" are different questions answered separately.

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