CCSS.Math.Content.7.NS.A.1c
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.
Common Core State Standards for Mathematics
What this standard means
Students need to see subtraction as a change on a number line, not just a rule to memorize. They should rewrite a subtraction problem as adding the opposite, then use direction and distance to explain why the answer makes sense. They also need to connect the difference between two numbers with the distance between them.
Mastery looks like students solving with negatives, fractions, and decimals, then explaining their thinking with a number line or context. Common trouble spots are mixing up the sign of the answer with distance, forgetting to change subtraction to adding the opposite, and treating distance as negative.
Ways to teach it
- Hands-on: Have students use floor tape as a number line and walk problems like 2 minus 5 and negative 3 minus negative 7.
- Prompt: Ask students to explain why the distance from negative 4 to 3 is 7, not negative 7.
- Quick assessment: Give four subtraction problems and ask students to rewrite each as adding the opposite before solving.
- Real-world connection: Use temperatures from two cities and ask students to find the temperature change and the distance between the temperatures.
Plan a lesson for CCSS.Math.Content.7.NS.A.1c
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.6.NS.C.7c
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...
- CCSS.Math.Content.6.NS.C.7
Understand ordering and absolute value of rational numbers.
- CCSS.Math.Content.7.NS.A.2b
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If ...
- CCSS.Math.Content.7.NS.A.1b
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a ...