SUBJECT: PreCal/Trig

GRADE: 11/12

UNIT TITLE:  Unit 7 Trig. Functions (cont., Applications)-end 3 weeks, 2/26-3/17  

TIME FRAME: 4 weeks

ESSENTIAL QUESTION:  How are vectors utilized to solve real-world problems that consist of multiple scalar quantities and directions?

CCSS Standards

Student-Friendly Objectives

Student Learning Experiences/Tasks

Assessment

Vocabulary

Resources: Literary Works/ Websites/ Chapters

N.VM.1  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, lvl, llvll, v} 

Students will be proficient in the calculation of various quantities for their magnitude as well as their respective direction by utilizing concepts of the Pythagorean Theorem.

Students will use ruler and protractor tools to construct vectors, measure their length and direction, and support their measures algebraically.

Daily bellringers, weekly quizzes, chapter and unit tests, constructions, textbook problems (Ch6.1

Vector, scalar, magnitude, Pythagorean Theorem, intial point, terminal point

Textbook (Ch6.1)

N.VM.3  Solve problems involving velocity and other quantities that can be represented by

vectors

Students will be proficient in solving real-world problems involving force, velocity, and acceleration by utilizing the mechanics of vectors and trigonometry skills.

Students will confront an activity involving the velocity of an object and determine the magnitude and direction of the resultant velocity as well as resolve measured velocity into horizontal and vertical components.

Textbook problems (Ch.6.2), exploration activity

Resultant velocity, vector components

Textbook (Ch6.1, 6.2, 6.3)

N.VM.4, N.VM.5  Perform operations on vectors in component form                         • identify vector

    components from an initial          and terminal point

• scalar multiplication

• vector addition and subtraction

Students will demonstrate their proficiency with the basic operations of vectors (multiplication by a scalar, addition, subtraction) by implementing the rules of vectors both graphically and algebraically.

Students will provide their own vectors and perform various operations on them as a group.

Textbook problems (Ch6.1, 6.2)

Scalar quantity

Textbook (Ch6.1-6.3)

N.VM.4, N.VM.5  Represent and perform vector

operations geometrically

• scalar multiplication

• vector addition (triangle and parallelogram models)

• vector subtraction (adding a negative vector, missing addend model)

Students will be proficient with the parallelogram method of adding vectors and graphically demonstrating the initial to terminal point method.

Student will work in groups of two and explain to one another the steps involved in graphically and algebraically the addition and subtraction of vectors and how it realtes to the dot product.

Textbook problems (Ch6.2)

Dot product, parallelogram method

Textbook (Ch6.2), Physics Text

N.VM.5b  Compute the magnitude of a scalar multiple cv using llcvll = lclv; ;

compute the direction of cv knowing that when lclv not equal to 0, the direction of cv is either along v (f or c > 0) or against v (f or c < 0)

Students will master the dot product and calculate unit vectors.

Students will engage in a group activity that requires the use unit vectors and the dot product mechanics.

Textbook problems (Ch6.3)

Textbook (Ch6.3), Cornell Notes