CCSS.Math.Content.HSN-VM.B.4
The Standard
(+) Add and subtract vectors.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students add vectors by combining their components and by placing arrows tip to tail. They subtract a vector by adding its opposite and interpret the resulting direction and magnitude.
What Mastery Looks Like
- Given two vectors, students find the correct sum or difference in component form and sketch it accurately. They can explain why reversing a vector changes subtraction into addition.
Common Misconceptions
- Students may add magnitudes instead of components, ignore direction, or connect arrows tail to tail when using the tip-to-tail method. They often subtract components in the wrong order or forget to reverse the second vector.
How to Assess It
- Exit ticket: Let u = <3, -2> and v = <-1, 4>. Find u + v and u - v, then sketch both results on a coordinate grid.
Lesson moves
Ways to Teach It
Use masking-tape arrows on a floor grid; students place two vectors tip to tail, then measure and record the resultant.
Ask students to explain in writing why u minus v equals u plus the opposite of v, using a labeled sketch.
Play Vector Match: students pair component-form operation cards with correct result cards and coordinate-grid diagrams.
Model an airplane velocity and a wind vector, then have students calculate the combined ground velocity and describe its direction.
Free download
Printable HSN-VM.B.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.B.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-VM.A.1
Adding and subtracting vectors requires knowing vectors as directed quantities and interpreting their segment and magnitude notation.
- CCSS.Math.Content.HSN-VM.A.2
Coordinate differences give vector components, which students use to add or subtract vectors component by component.
- CCSS.Math.Content.7.NS.A.1
Signed number-line addition and subtraction carry into combining vector components and understanding opposite directions.
What This Unlocks
Mastery here sets students up for these next.
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