Florida B.E.S.T. MA.912.NSO.3.7
The Standard
Compute the magnitude and direction of a vector scalar multiple.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students multiply a vector by a scalar and find the new magnitude. They decide whether the direction stays the same, reverses, or is undefined.
What Mastery Looks Like
- Students correctly use |kv| = |k||v|. They state that positive scalars preserve direction, negative scalars reverse it, and zero produces no defined direction.
Common Misconceptions
- Students may multiply the magnitude by the signed scalar instead of its absolute value. They may miss that a negative scalar reverses direction, or give the zero vector a direction.
How to Assess It
- Give students v = ⟨3, 4⟩ and ask for the magnitude and direction of −2v. Require a sketch and a one-sentence explanation.
Lesson moves
Ways to Teach It
Use grid paper and arrows to draw a vector, then build its multiples for scalars 2, one-half, −1, and 0.
Ask students to explain why multiplying a vector by −3 changes its length and direction but not its line of action.
Play a matching game with vector cards, scalar cards, and result cards showing correct magnitudes and directions.
Model a boat’s velocity, then calculate how doubling speed or reversing motion changes the magnitude and direction of its velocity vector.
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Related Standards
- MA.912.NSO.3.9
Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.
- MA.912.NSO.3.5
Solve mathematical and real-world problems involving vectors in three dimensions using the dot product and cross product.
- MA.912.NSO.3.6
Multiply a vector by a scalar algebraically or graphically.
- MA.912.NSO.3.1
Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in compone...
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