Study Guide — HSN.VM.B.5
(+) Multiply a vector by a scalar
Represent and operate with vectors and matrices where applicable.
What this standard means
- 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).
- 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 (for c > 0) or against v (for c < 0).
- Apply (+) multiply a vector by a scalar with models and explanation
- Represents vectors graphically and algebraically
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Draw vectors with direction and magnitude 2. Add components separately 3. Interpret matrix operations in context
_See printable PDF for diagram._
Common mistakes
- Adding magnitudes without direction
- Matrix dimension mismatch
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSN.VM.B.5.
- [ ] Represents vectors graphically and algebraically
- [ ] Adds and scales vectors correctly
- [ ] Performs basic matrix operations when required
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors