CCSS.Math.Content.HSN-VM.A.2
The standard
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
What this standard means
Students need to turn two points into a vector by comparing x-values and y-values. They should know which point is the start and which point is the end, then subtract start coordinates from end coordinates in order.
Mastery looks like writing the vector components correctly, such as ⟨3, -2⟩, and explaining what each number means as horizontal and vertical change. Students often reverse the subtraction, mix up x and y, or treat the two points as separate answers instead of one directed movement.
Ways to teach it
- Give pairs of students grid paper, two colored dots, and arrows, then have them write the vector components for each arrow.
- Ask students to explain why moving from A to B gives a different vector than moving from B to A.
- Show three point pairs on the board and have students write the component form on mini whiteboards in two minutes.
- Use a map grid of a school or city block and ask students to describe the movement from one location to another as a vector.
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Related standards
- CCSS.Math.Content.HSN-VM.B.4
(+) Add and subtract vectors.
- CCSS.Math.Content.HSA-REI.C.8
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
- CCSS.Math.Content.HSN-VM.B.4c
Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Rep...
- CCSS.Math.Content.HSN-VM.A.3
(+) Solve problems involving velocity and other quantities that can be represented by vectors.