LESSON PLAN # ____1__                                     

Technology Lesson?      Yes       No    (circle one)

                               

Name(s): Anwar Parvez

 

Title of lesson: Vectors ( adding, subtracting, and scalar multiplication), Magnitude, and Direction

 

Length of lesson: Three class periods

 

Description of the class:

Name of course: Pre-cal

Grade level: 10th

Honors or regular: regular

 

Source of the lesson:

http://mathforum.org/~klotz/Vectors/vectors.html

 

TEKS addressed:                                                                                         

 

§111.35. Precalculus

 

   The student is expected to:

 

(A)  use the concept of vectors to model situations defined by magnitude and direction; and

 

(B)  analyze and solve vector problems generated by real‑life situations.

 

 

I.       Overview

Students are to understand how vectors work and why we use it in mathematics.  Not only teaching them but having students have hands-on with the lesson will enrich their minds.  If students understand how vectors work then they will better understand the magnitude and direction in mathematics, not only for now but the future. 

 

II.  Performance or learner outcomes

            Students will be able to know the meaning of vectors, and use them when adding and subtracting..  They will be able to learn how to use magnitude and direction with vectors.  Students will be able to graph vectors and understand how to compute scalar multiplication.

   

III. Resources, materials and supplies needed

Pencils

Worksheets

Geometry Sketchpad

 

 

 

IV. Supplementary materials, handouts. (Also address any safety issues

      Concerning equipment used)

Pre- test

2 work sheet

Post-test

Component handout

Vector Handout

 

V. Safety Issues

 

 

VI. Accommodations for learners with special needs (ELLs, Special Ed, 504, G&T)

       No accommodations needed

 

Five-E Organization

Teacher Does                    Probing Questions                     Student Does     




 

Engage:

Instructor will pass out pre-test which will help students start getting engaged with the lesson.

 

 

 

Pre-test will help students get involved and understand what will be the lesson for the next few days.   

 

 

 

Instructor will remind students they only have 5-10 minutes to complete their pre-test.

 

 

 

 

 

How should we approach this question?

 

1.) What are vectors?

 

 

 

2.) A vector is represented by an arrow, defining the direction, and the length of the arrow defines the vector's magnitude, true or false?

 

 

 

3.)  Vectors are straight lines

that never end, true or false?

 

 

 

4.) Vectors go in two directions, left and right, true or false?

     

 

Students will take time to understand the question

 

 

 

 

 

Students will ask questions if instructions are not clear.

 

 

 

Students will answer questions individually.

 

 

Students will work independently on this pre-test.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evaluation(Decision Point Assessment):

Instructor will call on individual students to give them his/her answers in order to evaluate their progress on understanding vectors.  The instructor will proceed by answering the problem and explaining step by step the process in find the correct answer. 

 

Next, the instructor will go over the answers and re-evaluate the students in order to proceed forward. 

 

 

 

 

What are vectors?

 

 

 

When do we use vectors?

 

 

 

What is magnitude?

 

 

 

What is direction and how does it relate to vectors?

 

 

 

 

 

Students should know by now that a vector is a directed line segment and two vectors are equal if and only if they have the same magnitude and the same direction.

   







 

Explore:

The instructor will now review vectors, magnitude, and direction.  This section will be done visually on geometric sketch pad.

 

 

 

The instructor will pass out handout relating to magnitude and direction for students reference, as well as problems that will deal with today’s lesson.

 

 

 

After focusing and receiving feedback from the students we will move to adding and subtraction vectors and scalar multiplication will be introduced respectively.  This section will be introduced together and will be mastered when students have shown they will be able to complete problems independently. Homework problems will be given for this section, labeled Set 1

 

 

 

 

Following the mastery what vectors are, the instructor will use geometric sketch pad to demonstrate what vectors are and how you would go about adding, subtracting, and scalar multiplication. 

 

 

 

 

This program is designed to help students learn through technology and brings the fun into learning.  Sketch pad shows how to construct vectors, how to graph vectors, and multiplying vectors as well.

 

The instructor will then assign a few problems to make sure students are on task and no one is left behind.  Problems will be displayed on the overhead as well as individual handout for students.  Students will work individually and the instructor will walk around and if any students do need help then the instructor will assist them with any problems. Homework problems will be given to students for this section as well, labeled set1.

 

 

 

How do you subtract vectors?

 

How do you add vectors?

 

 

How do you use scalar multiplication?

 

 

 

1.)  4 x ( 32, 12)

 

 

2.) When the tail of vector A is set at the origin of the xy‑axis, the tip of A reaches (3,6). When the tail of vector B is set at the origin of the xy‑axis, the tip of B reaches (–1,5). If the tail of vector A – B were set at the origin of the xy‑axis, what point would its tip touch?

 

 

 

 

 

 

     

 

 

Students may have trouble solving basic arithmetic. 

 

Students may get stuck on one step.

 

Students will raise there hands when they need help or to ask any questions.

 

 

Students will solve problems given by instructor. 

 

 

    

 

Explain:

Instructor will ask students for volunteers to come up and answer homework problems they were assigned.  Instructor will watch for errors and understand there methods they used to solve each problem.  Instructor will follow up with asking students if they have any questions with the problem we will be working on.

 

 

 

 

How did you get that particular answer?

 

Why did you get that variable?

 

Where there any problems that you didn’t understand?

 

What do you feel you need more work on?

 

 

Students will answer questions as a class

 

Random students from each will come up to the overhead and explain how they got that particular answer.

 

Students will ask questions when in doubt.

 

Evaluation(Decision Point Assessment)

 Instructor will look at their weaknesses and write them down in order to find out what to test them on for the evaluation. 

   

 

 

 

 

 

If their outcome is positive then it gives us pride to know they have mastered the objective. 

 

If the outcome is negative we will try to direct our attention toward that field and be sure to test them on it.

 

 

Extend / Elaborate:

Learning Experience(s)

 

Instructor will move on to graphing vectors.  This section should continue in to the next class period. 

 

This will allow the instructor to use Geometric sketchpad  in order to display how to graph vectors.  Set 2 will be given out dealing with graphing vectors.

 

 

The instructor will discuss the components of vectors and where to use vectors. 

 

 

 

 

Instructor will be reminding students to pay very close attention because homework will be given for material covered in class. 

 

 

 

After going through geometric sketchpad, the instructor will pass out an information sheet dealing with components of vectors.  This worksheet is a guide for future reference and homework problems that will be given to them.             

 

 

 

 

 

 

 

 

Students should have a better understand of vectors

 

Students will be able to understand what is needed in order to graph vectors.

 

Students may have trouble with directions if they were not paying attention.

 

Students should raise their hand and ask any questions they need to in order to complete the assignment.



 

 

   

 

 

 

 

 

   

 

  Evaluate:     

 

The instructor will ask students if they have any questions regarding homework set 2. 

 

 

 

Next the instructor will review the basic components of vectors, briefly.

 

 

 

Instructor will pass out a quiz to the students.  The quiz problems deal with graphing, adding, scalar multipliation, and subtracting vectors.  The idea is to quiz students over all material that has been covered over the past few days.

 

A question or two will be asked about components of vectors which was handed out to students the day before.

 

 

 

 

 

      

 

 

Have I mastered graphing vectors?

 

 

 

What do I need work on in order to understand the components of vectors?

 

 

 

 

Are there any questions?

 

 

 

 

 

What are some components of vectors?

 

 

If students are still have problems we will stop and direct the student’s attention to class and explain thoroughly how to approach any problem on the quiz.

 

 

 

Students will ask questions about anything they have learned.

 

 

Students will raise there hand if they do not understand directions or have complications with a problem.