Learning Goal
Part of: Apply and extend previous understandings of numbers to the system of rational numbers — 3 of 4 cluster items
Understand ordering and absolute value of rational numbers
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.
-- Standard 6.NS.C.7
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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.
-- Standard 6.NS.C.7
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.
Slides
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Slide Video
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Task-sets
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