Learning Activities (2) | Classroom Resources (1) |

View Standards
**Standard(s): **
[MA2015] PRE (9-12) 9 :

9 ) (+) Multiply a vector by a scalar. [N-VM5]

a. (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as *c*(*v*_{x}, *v*_{y}) = (*cv*_{x}, *cv*_{y}). [N-VM5a]

b. (+) Compute the magnitude of a scalar multiple *c***v** using ||*c***v**|| = |*c*|v. Compute the direction of *c***v** knowing that when |*c*|v ≠ 0, the direction of *c***v** is either along **v** (for *c* > 0) or against **v** (for *c* < 0). [N-VM5b]

This learning activity will be used to introduce multiplying a vector by a scalar and is intended for an introduction activity. The students will watch the Scalar and Vector video to learn how to multiply a vector by a scalar. This activity will lead to learning how to represent scalar multiplication graphically by scaling vectors and possibly reversing their direction and compute the magnitude of a scalar multiple.

*This activity was created as a result of the ALEX Resource Development Summit.*

9 ) (+) Multiply a vector by a scalar. [N-VM5]

a. (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as *c*(*v*_{x}, *v*_{y}) = (*cv*_{x}, *cv*_{y}). [N-VM5a]

b. (+) Compute the magnitude of a scalar multiple *c***v** using ||*c***v**|| = |*c*|v. Compute the direction of *c***v** knowing that when |*c*|v ≠ 0, the direction of *c***v** is either along **v** (for *c* > 0) or against **v** (for *c* < 0). [N-VM5b]

This learning activity will be used during a lesson on using scalar multiplication with vectors. Students will explore how to perform scalar multiplication component-wise and represent scalar multiplication graphically. This activity will lead to learning how to compute the magnitude of a scalar multiple *c***v** using ||*c***v**|| = |*c*|v. The teacher will use the Scalar Multiplication of Vectors Lesson to cover the “I Do,” “We Do,” and “You Do” portions of the lesson.

*This activity was created as a result of the ALEX Resource Development Summit.*

View Standards
**Standard(s): **
[MA2015] PRE (9-12) 5 :

[MA2015] PRE (9-12) 6 :

[MA2015] PRE (9-12) 7 :

[MA2015] PRE (9-12) 8 :

[MA2015] PRE (9-12) 9 :

[MA2015] PRE (9-12) 10 :

5 ) (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., **v**, |**v**|, ||**v**||, v). [N-VM1]

[MA2015] PRE (9-12) 6 :

6 ) (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. [N-VM2]

[MA2015] PRE (9-12) 7 :

7 ) (+) Solve problems involving velocity and other quantities that can be represented by vectors. [N-VM3]

[MA2015] PRE (9-12) 8 :

8 ) (+) Add and subtract vectors. [N-VM4]

a. (+) 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 magnitudes. [N-VM4a]

b. (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. [N-VM4b]

c. (+) Understand vector subtraction **v** - **w** as **v** + (-**w**), where -**w** is the additive inverse of **w**, with the same magnitude as **w** and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. [N-VM4c]

[MA2015] PRE (9-12) 9 :

9 ) (+) Multiply a vector by a scalar. [N-VM5]

a. (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as *c*(*v*_{x}, *v*_{y}) = (*cv*_{x}, *cv*_{y}). [N-VM5a]

b. (+) Compute the magnitude of a scalar multiple *c***v** using ||*c***v**|| = |*c*|v. Compute the direction of *c***v** knowing that when |*c*|v ≠ 0, the direction of *c***v** is either along **v** (for *c* > 0) or against **v** (for *c* < 0). [N-VM5b]

[MA2015] PRE (9-12) 10 :

10 ) (+) 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 of vectors. [N-VM11]

Module 2, Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical frameworks for these operations. Students solve problems involving velocity and other quantities that can be represented by vectors. Parametric equations are introduced allowing students to connect their prior work with functions to vectors.