Learning Activities (3) | Classroom Resources (2) |

View Standards
**Standard(s): **
[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]

This learning activity will be used during a lesson on Adding and Subtracting Vectors. Students will explore how to add vectors end-to-end, component-wise, and by the parallelogram rule, determine the direction of their sum, represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. The teacher will use the Adding and Subtracting Vectors Lesson to cover the “I DO” and “We Do” portions of the lesson.

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

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]

This learning activity will be used to introduce adding and subtracting vectors and is intended as an introduction or engagement activity. The students will watch the Adding and Subtracting Vectors video to learn how to add and subtract vectors. This activity will lead to learning how to add vectors end-to-end, component-wise, and by the parallelogram rule, determine the direction of their sum, represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

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

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]

This learning activity will be used to add and subtract vectors and is intended for an assessment activity. The students will complete the Adding and Subtracting Vectors Assessment to demonstrate mastery of how to add vectors end-to-end, component-wise, and by the parallelogram rule, determine the direction of their sum, represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

*This activity results from 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 :

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 :

[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]

[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.

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

In this PhET activity, students will explore vectors in 1D or 2D, and discover how vectors add together. Students will specify vectors in Cartesian or polar coordinates, and see the magnitude, angle, and components of each vector. Students will experiment with vector equations and compare vector sums and differences. This activity could be used to help teach a lesson on probability. This PheET activity can be downloaded and assigned to Google Classroom.