CCSS.Math.Content.HSN-VM.B.5a
The standard
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
Common Core State Standards for Mathematics
What this standard means
Students need to show what happens when a vector is multiplied by a number. They should draw the new vector longer, shorter, or in the opposite direction when the number is negative. They also need to multiply each component by the same number.
Mastery means students can move between an arrow drawing and component form without mixing up length, direction, and sign. Common trouble spots are treating scalar multiplication like adding to each component, forgetting that negative scalars reverse direction, and drawing scaled vectors from different starting points without keeping the same direction.
Ways to teach it
- Use graph paper and arrow cards, then have students create 2v, 0.5v, and -3v from the same starting point.
- Ask students to explain why multiplying a vector by -2 changes both its length and its direction.
- Give three vectors and scalars, then ask students to compute components and sketch each result in five minutes.
- Connect to wind velocity by scaling a wind vector for a stronger gust or reversing it for wind from the opposite direction.
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Related standards
- CCSS.Math.Content.HSN-VM.B.5b
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ? 0, the direction of cv is either along v...
- CCSS.Math.Content.HSN-VM.B.4a
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the mag...
- CCSS.Math.Content.HSN-VM.C.11
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations...
- CCSS.Math.Content.HSN-VM.B.5
(+) Multiply a vector by a scalar.