ࡱ> c T<jbjb(p(p (pBB\)=,,,***8*D+dצx+(++++jjj֥إإإإإإ,uRǪ,jii0jjjl++=lllj+,+֥l@d@j֥ll>h,"l+ *kl:4"0צB]l]h"l,dHDHSPIRIT 2.0 Lesson: Travelscalar or Travector ==========================Lesson Header ========================== Lesson Title: Travelscalar or Travector Draft Date: 7-2-2012 1st Author (Writer): Elissa Gilger Instructional Component Used: Distance and Displacement Grade Level: High School Content (what is taught): Distinguish between scalar and vector quantities Calculate distance and displacement Application of Pythagoreans Theorem Context (how it is taught): Watching video clips leading to a discussion about the differences between distance and displacement Walk patterns to learn the affect direction has on calculating displacement Calculate the displacement of a CEENBoT in bumpbot mode Activity Description: Students will begin by watching video clips of people running a 100 m and 800 m race on a circular track. A teacher guided discussion will follow distinguish between distance and displacement as direction is an important factor. Next, students will visible walk specific patterns and determine how to calculate the displacement of each pattern. Finally, students will use CEENBoTs in bumpbot mode redirected by barriers from a start to finish line. They will calculate the displacement for the CEENBoT as it travels and verify their results by timing the actual run. Standards: Math: MA3, MD2 Science: SB1, SE2 Technology: TD2, TD3 Engineering: EA6 Materials List: Internet Projector CEENBoT Meter stick Masking tape Asking Questions: (Travelscalar or Travector) Summary: Students will watch video clips that will lead to a discussion distinguishing between distance as a scalar quantity and displacement as a vector quantity. Outline: Watch two video clips of people running 100 m and then 800 m Asked leading questions to learn the differences between distance and displacement Activity: Students will watch two video clips of people running during a track and field event. Then, students will be asked the leading questions to distinguish between distance and displacement. QuestionsAnswersWhat is the formula for speed?Speed = distance/timeWhat distance did the runners travel in each video?100 m and 800 mWhat is velocity and how does it differ from speed?Velocity also measures the motion of an object, but velocity is a vector quantity, while speed is a scalar quantity. Simply put the direction an object travels affects its velocity. Also, the formula for velocity is displacement/time.If the runners in the first video had a displacement of 100 m, but the runners in the second video had a displacement of 0 m, how does displacement differ from distance?Distance measures the total length traveled and is not concerned about direction. Displacement measures length from beginning to ending points and is concerned about direction. Attachments: Notre Dame Track & Field-2012 Big East Outdoor 100m  HYPERLINK "http://www.youtube.com/watch?v=aWcSNt6wlPA" http://www.youtube.com/watch?v=aWcSNt6wlPA Amber Whitley Indoor Track & Field 2012 800m  HYPERLINK "http://www.youtube.com/watch?v=xZ4Fezj1F5Y" http://www.youtube.com/watch?v=xZ4Fezj1F5Y  Exploring Concepts: (Travelscalar or Travector) Summary: Students will walk out three displacement patterns and learn how direction affects the calculation of displacement or vectors in general. Outline: Walk the first pattern learning to add vectors in the same direction Walk the second pattern learning to subtract vectors in the opposite direction Walk the third pattern learning to use Pythagoreans Theorem when vectors are perpendicular to each other Activity: Students will demonstrate displacement vectors by walking in a pattern directed by the teacher and then solved for by the students. The first pattern will be walking forward 4 steps and then walking forward 5 steps. Students will recognize to solve the displacement they will need to add the vectors together, so vectors in the same direction are added. Next, a student will walk forward 4 steps and backward 3 steps. To solve, the two vectors must be subtracted, so vectors in opposite directions are subtracted. The final pattern will have a student take 3 steps forward turn making a 90 angle and then walk 4 more steps. With the teacher guiding, students will recognize a triangular shape appears with the displacement being the hypotenuse of the right triangle. To solve, students must use Pythagorean s Theorem (a2 + b2 = c2). Instructing Concepts: (Travelscalar or Travector) Euclidean Vector Putting  Euclidean Vector in Recognizable Terms: A Euclidean vector is a quantity with magnitude (amount) and direction. Euclidean vectors are used in physics, engineering, and mathematics to calculate many different qualities when position or trajectory of an object is important. Examples of vector quantities would be displacement, velocity, acceleration, and force. The opposite of a vector quantity is a scalar quantity or one that does not include direction. Examples of scalar quantities would be distance, speed, mass, time, area, and circumference. Putting Euclidean Vector in Conceptual Terms: A graphical depiction of a Euclidean vector typically is an arrow. The length of the arrow denotes the magnitude and the arrow point denotes the direction. The directional form recorded (degrees, radian etc.) depends on the coordinate system used.  vector. However, if the vectors are at angles other than 90. The resultant vector can be solved for by combining the x and y components from joined vectors. Viewing the diagram to the left: Rx=Ax+Bx and Ry=Ay+By, to find the resultant vector use Pythagorean s Theorem (Rx2+Ry2=R2). The reverse process is known as resolving vectors using triangle trigonometry relationships to solve for the x and y components when only the resultant vector is known. An example would be if Rs magnitude and angle were known in the diagram above, solving for Rx=Rcos and Ry=Rsin. Other components such as angles may also be solved for using the triangle trigonometry relationships. These are several common methods of calculating resultant vectors or components of resultant vectors, although other methods are employed depending on the application and number of dimensions involved. Putting Euclidean Vector in Process Terms: A graphical process may also be useful in solving for resultant vectors. Using the diagram above, drawing vectors A and B to scale placed in a tail-to-tip position as well as in the correct direction will provide a solution for the resultant vector, Rs, magnitude and direction, just by measuring R on the drawing. Putting Euclidean Vector in Applicable Terms: Euclidean vectors have many functions in physics, engineering, and mathematics. Vectors are utilized in solving geometric, displacement, velocity, acceleration, force, electric field, trajectory, and directional derivatives types of problems to name a few. Such a list provides a glimpse at the wide spread applicability of Euclidean vectors. Organizing Learning: (Travelscalar or Travector) Summary: Student pairs will calculate the displacement of a CEENBoT in bumpbot mode being directed only by barriers from a start to finish line. Outline: Tape a Bumpbot Square according to directions on a carpeted floor Place barriers (4, 1, 3, 5) in the correct locations based on correct angle placement Calculate the total displacement between barriers Use the known variables of velocity and time for CEENBoT to reposition after encountering a barrier to determine the overall time it should take a CEENBoT to travel the course Time the CEENBoT traveling the course to determine if student calculations were correct Activity: Student pairs will tape a Bumpbot Square to a carpeted floor. Next, they will calculate the displacement of the CEENBoT as it travels in bumpbot mode being redirected by barriers from a start to finish line. Using the displacement value, velocity of the CEENBoT, as well as the time it takes for the CEENBoT to reposition itself at a 90 angle after each barrier, students will calculate the time it should take for the CEENBoT to travel the barrier course they built. Students will then time the CEENBoT as it travels the course to determine if their calculations (specifically displacement) are correct. Others skill developed during this lab are measurements, application of angles, problem solving, and team work. For a detailed laboratory description see attached file: S152_SPIRIT_Travelscalar_or_Travector_O_Lab.doc NOTE: To have the CEENBoT function at a constant speed and backups a constant distance when in bumpbot mode it must have a program installed using the AVR Programmer. The program can be downloaded in the attached zip file (S152_SPIRIT_Travelscalar_or_Travector_O_Vectors_CEENBoT_Vectors_Program.zip) and installed using CEENBoT Commander. Resource: Vectors CEENBoT Commander Program: S152_SPIRIT_Travelscalar_or_Travector_O_Vectors_CEENBoT_Vectors_Program.zip Attachments: Bumpbot Square: S152_SPIRIT_Travelscalar_or_Travector_O_BumbBot_Square.doc Bumpbot 1 & 2 Barrier Demonstration: S152_SPIRIT_Travelscalar_or_Travector_O_BumbBot_Square_Examples.doc Bumpbot Displacement Lab: S152_SPIRIT_Travelscalar_or_Travector_O_Lab.doc Understanding Learning: (Travelscalar or Travector) Summary: Students will answer writing and calculation prompts to demonstrate their knowledge of scalar and vector quantities specifically the difference between distance and displacement. Outline: Formative Assessment of Vectors (Displacement) Summative Assessment of Vectors (Displacement) Activity: Students will complete written and quiz assessments related to vectors. Formative Assessment: As students are engaged in the lesson ask these or similar questions: Are students able to distinguish between a scalar and vector quantity? Were students able to solve for displacement using the correct method? Are students labeling the displacement or vector values with a direction? Summative Assessment: Students can complete the following writing prompt: Explain how does a vector differ from a scalar quantity and provide two examples for each. Students can complete the following quiz questions: Read each description and calculate the distance as well as the displacement for each one below. A jogger runs 3 miles a day Distance Displacement Keith heads North 2 blocks and then heads East 4 more blocks Distance Displacement A squirrel runs up a tree 2 feet and then back down the tree 3 feet Distance Displacement     2012 Board of Regents University of Nebraska Protractor Laser pointer Stopwatch CEENBoT Commander and AVRISP In-system programmer 5 wooden barriers (12 in x 4 in 2 pieces of wood screwed together making an L shape) Putting Euclidean Vector in Mathematical Terms: Euclidean vectors are also referred to as geometric vectors because geometric principles are applied to calculate the resultant vector or overall magnitude and direction operating after all the vectors are taken into account. If the vectors are in the same direction (! and !) simply add the vectors together. If the vectors are in opposite directions (! and !) simply subtract the vectors from each other. 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