Florida B.E.S.T. MA.912.NSO.3.6

MathGrades 9–12Represent and perform operations with vectors.

The Standard

Multiply a vector by a scalar algebraically or graphically.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students multiply each component of a vector by a given number. They also draw the scaled vector and determine how its length and direction change.
What Mastery Looks Like: Students correctly multiply every component by the same number. They draw the result with the correct length and direction, including for negative, fractional, and zero scalars.
Common Misconceptions: Students may add the scalar to each component instead of multiplying. They may scale only one component or forget that a negative scalar reverses direction.
How to Assess It: Give students v = ⟨3, -2⟩. Ask them to calculate and sketch -2v from the origin, then describe the change in length and direction.

Lesson moves

Build vectors with craft sticks on a coordinate mat, then use repeated copies to model 2v and reversed copies to model -2v.
Ask: How do 3v, 0.5v, and -v compare with v in length and direction? Students justify with components and sketches.
Create matching cards for a scalar, an original vector, a component result, and a graph; teams assemble complete sets.
Model a drone's velocity vector, then have students calculate and draw changes caused by doubling speed or reversing direction.

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