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NCDPI -- AIG Instructional Resource: Background Information
Complete:
Date Submitted: 04/ 08/12
Resource Title: Vectors in Space
This is excellent. No other comments to be made.
Subject Area/Grade Level (s): Physics / 9-12
Time Frame 1.5 hrs class time
Common Core/Essential Standard Addressed:
Physics 1.1.1 Analyze motion graphically and numerically using vectors, graphs and calculations.
Additional Standards Addressed: vectors in mathematics; use of Edwin Abbott’s novel, a mathematical satire, Flatland
(integration across topics, within or across disciplines)
Brief Description of Lesson/Task/Activity: Students extend the concept of vectors beyond the dimensions of a two space to create a three
dimensional vector hunt. They first are exposed to vertical vector addition through online resources and then they work in pairs to create a
Vector Treasure Map as a challenge for each other. The hunt should be designed by a team to move other students through the school to a
destination using vectors in three dimensions. In the process, students accepting the challenge are taught the concept of three dimensional
vectors by the design team. This provides the advanced student with a more complete picture of vector mathematics and its application to
physics in many topics. It can also open the door for advanced topics (such as torque) in other units.
Type of Differentiation for AIGs (include all that apply)
 Enrichment
x Extension
x Acceleration
Adaptations for AIGs
X Content
 Process
X Product
Explanation of How Resource is Appropriate for AIGs
This resource extends the concept of vectors in a two dimensional plane to a three space which is more complex but much more a real world
application. It connects physics more completely to advanced mathematical concepts (such as three space with a matrix system of three
equations) and develops spatial acuity for the advanced thinker. It also allows for creativity in a topic that can become somewhat rote.
Needed Resources/Materials
Access to online resources introducing three dimensional vectors, protractors, meter sticks and/or metric tape rule, calculators
Sources (all sources must be cited)
1) http://www.cut-the-knot.org/Games/Vectors.shtml
2) http://www.intmath.com/vectors/7-vectors-in-3d-space.php
3) http://interactagram.com/math/vectors/threeDVector/
4) http://oscience.info/physics/components-of-vectors/
5) http://www.flatlandthemovie.com/
6) http://www.youtube.com/watch?v=C8oiwnNlyE4
7) http://www.flatlandthefilm.com/about_Abbott.php
The following links offer background information on 3D vectors for students:
8) http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-3/
9) http://www.intmath.com/vectors/7-vectors-in-3d-space.php
TEACHER NOTES
This material should be approached in a “flipped” fashion for the advanced thinker as they catch on quickly to vectors. Assign the lesson
from MIT (link #8 above) to be viewed as a 2 night assignment prior to in-class discussions of vectors. The students can then use class time to
create the Scavenger Hunt.
NCDPI AIG Curriculum Resource Outline
Describe processes, steps, and materials needed at each stage of the lesson/activity.
STAGE ONE: Engage
√Hook
 Prior knowledge
 Instructional input
 Modeling
Description: Show the video on Flatlands (see links 5, 6 and 7 under “sources”). Ask questions about the ideas presented in the book and
film about the challenges of explaining the idea of space to a two dimensional creature. Some examples would be “How difficult would it be
for us to envision other dimensions?” “Do you understand how challenging a third dimension would be to a being living only in a two space
world?” (See the Nova link http://www.pbs.org/wgbh/nova/physics/imagining-other-dimensions.html which discusses the ideas that String
Theory brings to physics of other dimensions.) There is an Interactive at http://www.pbs.org/wgbh/nova/physics/multidimensionalmath.html which allows a short excursion into 4-D math. Other questions: Ask the students to think of any movie where they saw time
travel; Could this be considered the fourth dimension?
Three dimensional vectors are important in extending the applications of physics to the world that we experience.
STAGE TWO: ELABORATE
√Guided and independent practice
 Guiding questions
Description:
First, assign the activity at 1) http://www.cut-the-knot.org/Games/Vectors.shtml and ask students to describe their difficulties with the
challenge. Then give them some problems with vector addition and subtraction in 3D. Some examples can be found in texts such as
Fundamentals of Physics (Halliday, Resnik, Walker) or like those at http://www4.ncsu.edu/~thwears/MA242_Vectors_2010_08_27_Solns.pdf.
A good way to follow progress is through a Physics Journal that advanced students can use to indicate progress and document independent
practice. Continue to check that the basic skills with 2 dimensional vectors are mastered.
STAGE THREE: EVALUATE
√Assessment
Description:
The assessment is the Scavenger Hunt that the student creates. The Hunt should use at least 4 vectors in addition and 4 vectors in subtraction.
The student may simply list the vectors in any order and ask the students undertaking the hunt to add or subtract as vectors in order to reach a
known destination. Alternatively, the students may choose to list the vectors with the order of addition and subtraction listed for an unknown
destination. A graphic representation of all vectors is also desirable.
As every school has a different layout, it is impossible to give an applicable example but the following questions can help students with their
design.
1) How accurate must your measurements be taken to have other students reach your destination?
2) Are your vectors all on one plane?
3) If your vectors involve three dimensions, then how will you teach other students how to do them?
4) Do you have at least 4 vectors that add and 4 vectors that subtract in your Vector Hunt?
5) Why does the order matter to those undertaking the hunt?
6) Are you stating the order or asking students to order the vectors.
Note: Vector addition and subtraction are commutative but only in the sense of producing the same final answer. Within a building, the
physical impossibility of passing through walls makes the order important!
A rubric should be created for grading the creation of the scavenger hunt as well as one for the participants. Points for originality, accuracy,
correct terminology, clarity, and destination choice are possible considerations.
TEACHER NOTES:
This activity is a critical one for creating interest in vectors. It can be extended in latter units to include torque and applications to magnetic
fields. Many students so not find vector addition in two dimensions very challenging and this is an opportunity to provide new information to
offer those challenges.