NY Next Generation Math NY-7.NS.1.c
The Standard
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 real-world contexts.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students understand subtraction of rational numbers as adding the additive inverse. They represent p minus q as p plus negative q and use the absolute value of a difference to find distance between rational numbers.
What Mastery Looks Like
- A student rewrites -2 - 5 as -2 + (-5) and finds -7 on a number line. The student calculates the distance from -4 to 3 as the absolute value of -4 - 3, or 7.
Common Misconceptions
- Students may change both signs when rewriting subtraction or move in the direction of the original subtrahend. They may report a negative distance or confuse distance from zero with distance between two points.
How to Assess It
- Ask students to rewrite and solve 3.5 - (-2) and find the distance between -1.5 and 4. Require number-line or equation evidence for both.
Lesson moves
Ways to Teach It
Use signed number cards and a number line to replace each subtraction with addition of the opposite.
Ask students why the distance between two rational numbers cannot be negative.
Play rewrite-and-distance match with subtraction expressions, additive-inverse forms, number-line models, and absolute-value statements.
Find changes and distances between temperatures, elevations, or account balances represented by rational numbers.
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Related Standards
- NY-6.NS.7
Understand ordering and absolute value of rational numbers.
- NY-7.NS.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or...
- NY-7.NS.1.b
Understand addition of rational numbers; p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is posi...
- NY-6.NS.7.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 q...
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