CCSS.Math.Content.HSN-VM.B.5b
The standard
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).
Common Core State Standards for Mathematics
What this standard means
Students need to scale a vector by a number and describe what happens to its length and direction. They should know that multiplying by 3 makes the vector three times as long, multiplying by 1/2 makes it half as long, and multiplying by a negative number points it the opposite way.
Mastery looks like finding the new magnitude quickly, using the absolute value of the scale factor, and saying whether the direction stays the same or reverses. Students often get stuck by letting a negative scale factor make a negative length, or by forgetting that zero creates a vector with no direction.
Ways to teach it
- Use arrows on graph paper and have students draw 2v, 0.5v, -v, and -3v from the same starting point.
- Ask students to explain in two sentences why a vector can point opposite its original direction but cannot have negative length.
- Give four scalar multiples of one vector and ask students to list each magnitude and direction in a two-column table.
- Connect to wind velocity by asking how doubling wind speed or reversing wind direction changes a vector model on a weather map.
Plan a lesson for CCSS.Math.Content.HSN-VM.B.5b
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSN-VM.A.1
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for 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.B.5a
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(...
- CCSS.Math.Content.HSN-VM.B.4b
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.