South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Vectors: Follow That Arrow (Grades 9-12)

Master Teacher

Robert Scott

OVERVIEW

In this lesson we will continue the study of vectors. We will investigate the arithmetic of vectors and use them with applications about motion. Many of the physical concepts can be represented by vectors. The video in this segment will show students how to find the resultant and direction of a vector using ordered pairs with and without grids.

ITV SERIES

Vectors, Lesson 3: Ordered Pairs
Vectors, Lesson 4: Resolving Without Grids

LEARNING OBJECTIVES

Students will be able to use technology(calculators, computers, etc.) -to collect, catalog, and graphically represent data

Analyze data to construct explanations and conclusions

Matter and Energy Area III - Strand I Strand 1: Matter has characteristics propertied that are related to its structure.

find the magnitude and direction of a vector
describe a method for finding the sum of two vectors
find the difference between two vectors
show a vector as a model of a given physical quantity
solve physical problems of force and velocity using vector sum

MATERIALS

grid paper
ruler
protractor
calculator
transparencies grid

SC MATH/SCIENCE STANDARDS MET

Science Achievement Standards Process

Skills Design, conduct, and evaluate a scientific investigation

Use advanced technologies to extend investigation Use technology (calculators, computers, etc.) to collect, catalog, and graphically represent data

Analyze data to construct explanations and conclusions

Matter and Energy Area III - Strand I: Matter has characteristics propertied that are related to its structure.

Investigate and analyze characteristics of motions and the net result of applied forces by using mathematical equations, graphs, and vector diagram to describe them.

Describe motion of an object by its position, direction, and speed and acceleration. .

Translate a description of a physical problem into a mathematical equation to solve.

Analyze the relationship of displacement, time, rate of motion, and rate of change of motion.

Illustrate rate and change in motion mathematically and graphically.

Add vectors to determine the resultant.

Math Achievement Standards Numerical and Algebraic Concepts and Operations - High School Grades

Use tables and graphs as tools to interpret expressions, equations, and inequalities, using technology whenever appropriate, by:

Representing linear equations or inequalities as tables or graphs.
Develop an understanding of, and facility in manipulating algebraic expressions, performing elementary operations on matrices, and solving equations and inequalities by:
Solving equations and inequalities using a variety of methods to include graphing, spreadsheets, and symbol manipulation, explaining procedures used.

Patterns, Relationships, and Functions - High School Grades

Translate among tabular, symbolic, and graphical representations of functions, using technology whenever appropriate, by:

Using graphs to determine the value of one
variable from the value of the other.
Plotting graphs of linear and quadratic functions, investigating changes in function parameters, and describing the resulting changes in the graph of a function.
Gathering and plotting data, fitting a graph to plotted points, using the graph to illustrate the relationship between variables, predicting outcomes, and forming a generalized equation in a real-world context.

Geometry and Spatial Sense - High School Grades Use technology whenever appropriate to explore concepts and applications of geometry by:

Applying the Pythagorean theorem to solve real-world problems.

Apply trigonometry to problem situations involving triangles by:

Using the sine, cosine, and tangent ratios to solve problems, using technology whenever appropriate.

Explore periodic real-world phenomena using the sine and cosine functions by:

Using technology to apply the sine and cosine functions to repetitive physical phenomena such as ocean fides, sound waves, and electric current.

Analyze properties of Euclidean transformation and relate them to vectors by:

Using coordinates to perform transformations and describing the vector used to perform a translation

Measurement - High School Grades

Use rates, similarity relationships, and trigonometric ratios to solve problems involving indirect measurement in two or three dimensions, using technology whenever appropriate

PRE-VIEWING ACTIVITIES

Before beginning the tape, have students define the following terms:

vectors
magnitude
velocity
resultant force

Tell the class that today they will add vectors using ordered pairs. Tell them that they will use trigonometric ratios to find the resultant and direction of a vector.

FOCUS FOR VIEWING

Tell the students that they will be watching segments from the video programs Ordered Pairs and Resolving Without Grids. Tell the students to listen to the segments for the method of solving vectors with and without grids.

VIEWING ACTIVITIES

Begin the tape when the author says, "There are other ways of working with vectors." Stop the video when you see the words "Flat-Earth Wreckers" on the green ship. Have students complete the following sentence. The first number in an ordered pair is called the __________________ and the second number __________________. Two vectors added together to find the resultant is called the __________________ of the vector. Finding the horizontal and vertical components of a vector is called __________________. Fast forward to Lesson 4 where you see

Stop the tape after both magnitude and angle measure are given. Have students complete the problem, then play the tape for the solution. Turn off the tape and discuss the answer with the students. This concludes the video part of the lesson.

POST-VIEWING ACTIVITIES

Students are going to find the resultant with and without a grid. They will use the sine and cosine functions to find the angle measurement.

ACTION PLAN

Ask students to investigate the job market and list some of the careers where vectors are used.

ACTIVITY SHEETS (PDF)

Activity Sheet 1