Unit: Model and Graph Rational Numbers
Standards:
MAFS.6.NS.3.5
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Students will understand that positive and negative numbers are used together to
describe quantities having opposite directions or values.
Students will use positive and negative numbers to represent quantities in real world contexts.
Students will explain the meaning of 0 in each situation.
MAFS.6.NS.3.6a,b,c
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Students will recognize opposite signs of numbers as indicating locations on opposite
sides of 0 on the number line.
Students will recognize that the opposite of the opposite of a number is the number itself.
Students will recognize that 0 is its own opposite.
Students will understand signs of numbers in ordered pairs as indicating locations in
quadrants of the coordinate plane.
Students will recognize that when two ordered pairs differ only by signs, the locations of
the points are related by reflections across one or both axes.
Students will find integers and other rational numbers on a horizontal or vertical number
line diagram.
Students will position integers and other rational numbers on a horizontal or vertical
number line diagram.
Students will find pairs of integers and other rational numbers on a coordinate plane.
Students will position pairs of integers and other rational numbers on a coordinate plane.
MAFS.6.NS.3.7a,b,c,d
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Students will interpret statements of inequality as statements about the relative position
of two numbers on a number line diagram.
Students will write statements of order for rational numbers in realworld contexts.
Students will interpret statements of order for rational numbers in realworld contexts.
Students will explain statements of order for rational numbers in realworld contexts.
Students will understand the absolute value of a rational number as its distance from 0
on the number line.
Students will interpret absolute value as magnitude for a positive or negative quantity in a realworld situation.
Students will distinguish comparisons of absolute value from statements about order.
MAFS.7.NS.1.1a,b,c
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Students will apply and extend previous understandings of addition and subtraction to
add and subtract rational numbers.
Students will represent addition and subtraction on a horizontal or vertical number line diagram.
Students will describe situations in which opposite quantities combine to make 0.
Students will understand p + qas the number located a distance |q| from , in the positive
or negative direction depending on whether is positive or negative.
Students will show that a number and its opposite have a sum of 0 and are additive inverses.
Students will interpret sums of rational numbers by describing realworld contexts.
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Students will understand subtraction of rational numbers as adding the additive inverse, p − q = p
+ (− q).
Students will show that the distance between two rational numbers on the number line is
the absolute value of their differences.
Students will apply the distance between two rational numbers on the number line as the
absolute value of their differences in realworld contexts.
Unit Scale:
4.0 - Student evidence should show that they can:
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independently go beyond the classroom to design a realworld connection to model and graph
rational numbers that represents a situation in its context.
3.0 - Student evidence should show that they can:
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understand that positive and negative numbers are used together to describe quantities having
opposite directions or values; use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.
understand a rational number as a point on the number line; extend number line diagrams and
coordinate axes familiar from previous grades to represent points on the line and in the plane with
negative number coordinates. Recognize 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, and that 0 is its own opposite. Understand signs of numbers in
ordered pairs as indicating Revised 05/17/2016 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. Find 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.
understand ordering and absolute value of rational numbers. Interpret statements of
inequality as statements about the relative position of two numbers on a number line diagram.
Write, interpret, and explain statements of order for rational numbers in realworld contexts.
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 realworld situation.
Distinguish comparisons of absolute value from statements about order.
apply and extend previous understandings of addition and subtraction to add and subtract
rational numbers; represent addition and subtraction on a horizontal or vertical number line
diagram. Describe situations in which opposite quantities combine to make 0. Understandp + q
as the number located a distance|q| from , in the positive or negative direction depending on
whether is positive or negative; show that a number and its opposite have a sum of 0 (are additive
inverses); interpret sums of rational numbers by describing realworld contexts. Understand
subtraction of rational numbers as adding the additive inverse, p − q = p + (− q); show that the
distance between two rational numbers on the number line is the absolute value of their
difference, and apply this principle in realworld contexts.
2.0 - Student evidence should show that they can:
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know that positive and negative numbers are used together to describe quantities having opposite
directions or values.
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recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the
number line.
identify a point and its opposite quadrants.
find or position integers on a horizontal number line.
understand inequality statements and ordering of rational numbers.
recall the absolute value of a rational number is its distance from 0 on the number line.
understanding addition and subtraction of rational numbers and its representation on a
number line diagram.
recall situations in which opposite quantities combine to make 0.
recall p + q as a number located a distance |q| from and a number and its opposite are additive
inverses.
recall subtraction as adding the additive inverse and the distance between two numbers on the
number line is the absolute value of their difference.
1.0 Student evidence should show that they can:
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identify opposite numbers.
identify a point and its opposite quadrants.
identify integers on a horizontal number line.
recall ordering of rational numbers.
recall addition and subtraction of rational numbers.
recognize opposite quantities combine to make 0.
recognize opposite numbers are additive inverses.
define additive inverse and absolute value of rational numbers.
Academic Vocabulary:
Absolute value, axes, coordinate plane, integer, negative, number line, opposite, positive, quadrant,
rational number