Mars-Bound

by Evelyn Baldwin, Brigitte Wetz, and Liz Brown

Introduction

Anchor Video
Concept Map

Project Calendar

Lesson Plans

Letter to Parents

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Resources

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Grant

Investigation Lesson – Vectors – Pre-Calculus

LESSON PLAN – Vectors

 

Name(s):

Elizabeth Brown

 

Title of Lesson:

Introduction to Vectors

 

Source of Lesson:

The Math Forum @ Drexel

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

 

Length of Lesson:

50 minutes

 

Description of the Class:

Pre-Calculus – Mars Rover Curriculum

 

TEKS Address - Pre-calculus:

 

(6)  The student uses vectors to model physical situations. 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 work with a vector simulation on-line to visually see the abstract concept of vectors.  They make observations about the vectors when the plane is moved around to determine the relationships of vectors in 2 dimensions.

 

I.              Performance Objectives

The student will be able to:

·         

 

II.   Resources, Materials, and Supplies needed for a class of 24

 

Computer

Geometer sketch pad

 

 

 

 

 

 

Five E Organization

 

                   Teacher Does                                            Student Does

 

Engage:

Time: 5 minutes

Show the shuttle launch clip to students.

 

http://www.geocities.com/CapeCanaveral/Launchpad/1499/

 

Ask the students the following:

  • What just happened?
  • How do you suppose the vehicle was launched?
  • What is force? What does a force do?

 

Tell the students that we are going to investigate the idea of forces, and that they need to get into their lab groups.

 

 

Students watch the video clip

 

 

  • The space shuttle was launched
  • The rockets pushed it up.

 

  • I don’t know. Forces make things move.

 

Students get into their designated groups.

 

 

Explore:

Time: 30 minutes

Explain the lab procedures to the students briefly. (The directions will be provided on the lab sheet.)

 

Each student will be pulled by a partner down the hall, on the coaster carts. Distances of 5, 10 and 15 meters will have already been marked on the floor. While doing this, another member of the group will record the time that it takes to travel each designated distance. The student pulling the cart must maintain the same force reading on the balance throughout the entire distance (though the reading can be different for different people). The process is repeated until each member of the group has had a chance to ride on the cart.

 

Each student is to plot her own data.

 

 

Once the data is plotted, the members of the group should compare their graphs to one another.

 

During the exploration, I will ask the groups the following questions (also, questions similar to these will be on the lab sheet):

  • Is the distance graph a straight line, what about the velocity line or the acceleration line?

 

 

  • What is the slope of the velocity line and the acceleration line?

 

  • What is the value of the acceleration line? What does this mean?

 

 

  • Is your graph like your partner’s? How are they the same? Different? Why?

 

  • Based upon your graphs, predict what will happen to the graphs if there were two of you on the cart at the same time? Only half of you?

 

 

 

Students listen to instructions.

 

 

 

Students work diligently in their groups, asking any questions if they have them.

 

 

 

 

 

 

 

 

 

 

 

 

Students plot their own data and compare the different graphs.

 

Students compare their graphs to their neighbor’s graphs and note the similarities and differences.

 

 

 

 

 

  • The distance is a curved line. The velocity and acceleration are straight lines, though the acceleration is flat and the velocity is tilted.
  • The velocity has a slope. The acceleration has a slope of zero (it is flat).
  • The acceleration is y = the slope of the velocity. Interesting. The acceleration is constant.

 

 

  • The graphs look almost the same, but the values are different. Maybe they are different because the forces we used were different.
  • Hmm…I don’t know. Let me look at what my neighbor got.

 

 

Explain:

Time: 10 minutes

After the groups have gathered and analyzed their own data, we will discuss what we found.

 

The first thing the students should notice is that their velocity continued to increase. This will be obvious to them from their experience of riding on the cart. The students will also have a graphical representation of what they had experienced while riding on the cart. Ask one group to show their findings, and to discuss them with the class.

 

Since each student will have ridden the coaster carts more than once with a different amount of force being applied each time, they will also come to the understanding that the more force applied the greater the acceleration.

 

When students compare their graphs with that of their partner’s they will see that everyone experienced a constantly changing velocity (acceleration). Therefore, a constant force produces a constant acceleration.

 

Finally, the students will see that the acceleration experienced by each one of them was not the same. The difference in the acceleration that each one of them experienced is related to the amount of force being applied and the amount of mass to which the force was being applied (a = F/m or F=ma).

 

 

Students discuss results with the class.

 

 

Extend/Elaborate:

Time: 5 minutes

It is at this time that we will discuss force diagrams. I will have a volunteer come to the board and draw the cart. Then I will have another student draw an arrow indicating the force on the cart. Finally, I will ask the class if there are any other forces acting on the cart.

 

After some discussion, they will realize that gravity is also pulling on the cart. Why then, is the cart not falling down? Then I will briefly discuss the concept of the normal force. I will then have student draw arrows indicating the gravitational force and the normal force. Are these forces equal? Why or why not?

 

 

 

Finally, if time permits, I will ask another student to draw the frictional force on the cart. Is the frictional force equal to the pulling force? Why or why not?

 

 

Students will participate in the discussion.

 

One student will come to the board and draw an arrow showing the force being applied to the cart.

Students don’t think there are any other forces.

 

I remind them that gravity is acceleration. Then I tell them to look at the force equation. This leads them to believe that there is a gravity force. They say they don’t know why the cart isn’t falling down. Maybe because the floor is in the way.

 

One student draws the two forces. They are equal since the cart isn’t moving up or down.

 

The student tries to draw the arrow in the right direction. She may or may not do this correctly.

Hmm…They aren’t equal since the cart is moving. The pulling force is greater.

 

Evaluate:

No time L

I remind students to turn in their lab sheets. These will be used as an assessment of today’s activities.

Furthermore, they will be assigned homework out of the book dealing with forces.

 

 

 

Students turn in their lab sheets.