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| WV State Standards: |
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Math:
M.O.8.2.1, M.O.8.2.2, M.O..8.2.9, M.O..8.5.1,
M.O..8.5.4, M.O..8.5.5, M.O.A1.2.3, M.O.A1.2.5, M.O.CM.2.2,
M.O.CM.2.3, M.O.CM.2.4, M.O.CM.5.2, M.O.CM.5.5, M.O.CM.5.8,
M.O.PS.5.6, M.O.PS.5.10 |
Science:
CS.8.4.20, BTC.4.12, AES.4.33, AES.4.34,
AES.4.30, AES.4.36, AES.4.38, AES.4.35,
BTC.4.14, BTC.4.22 |
Technology:
TEC9-12.1.1, TEC9-12.1.2, TEC9-12.2.1,
TEC9-12.2.2, TEC9-12.3.1, TEC9-12.3.2,
TEC9-12.3.3, TEC9-12.3.4, TEC9-12.1.1 |
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| National Standards: |
Math: 1,
2, 3, 4, 6, 7, 8, 9 |
Science:
8, 9, 10, 12, 13 |
Technology:
1, 2, 3, 4 |
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| Blooms Taxonomy:
Knowledge,
Comprehension, Application, Evaluation |
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21st Century Skills:
Thinking and Problem Solving Skills
Critical Thinking and Systems Thinking
Problem Identification, Formulation, and
Solution
Creativity and intellectual curiosity
Communication skills
Self-Directional Skills
Social Responsibility |
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Objective(s)
In this lesson, students will have an
opportunity to explore real world data that pertains
directly to their process of designing an electrical power
transmission system. They will take what they
learned about resistance, couple it with data on aluminum
and copper wire, and make a qualitative decision on which
type of material to use for wire. The information given
for analysis is actual data gleaned from engineering
tables about the properties of aluminum and copper. It has
been filtered to screen out all but two very specific bits
of information. It would be important to let the students
know that there are other factors and constraints that go
into the decisions made on designing systems, but for the
purposes of the lesson they have been simplified. The
students will be given an opportunity, later, to explore the
details of transmission in greater depth.
Description:
A key component of national math standards
is the modeling of data in graphical, tabular, symbolic and
verbal forms. At the ninth grade level it is important for
the student to have a conceptual grasp of modeling data as a
prerequisite to the more advanced numeric analysis that will
occur in upper level algebra. Often, the only exposure a
student gets to complex graphical analysis is in a math
class. Unfortunately, the examples they encounter are
contrived and have no direct connection to their own
experience. That is, they have no “buy-in” in the concept.
Incorporating graph interpretation into an activity as a
tool can be a much more meaningful experience. In today's
lesson the student will be able to examine an actual graph
generated from a spreadsheet of data in a near raw form.
The graph will not be pretty but it will still contain
valuable information that is accessible to the student. The student will then be able to compare graphical
information to tabular and make verbal statements of a
relationship among the data. There will be no symbolic
representation in this lesson. For the purposes of the
decision needed, the student will have enough information
from the graph and table alone. The data is contained
within an Excel spreadsheet and in html format as well. It
can be printed out and copied if the student does not have
access to a computer for the lesson. Included with this
lesson is a student page of directions and questions as well
as an answer sheet to be turned in for grading. There is
also a homework or extra credit assignment that can be
utilized.
Introduction Motivation:
Students will be
introduced to EdVenture Island. This island
has recently been discovered and has a wealth of natural
resources to offer society. The students are being
contracted as engineers to develop a new power plant for the
island. The plant should do the least amount of harm to the
environment and be the most cost effective.
Learning Context:
Students will use internet
searches to learn how to build an electrical generator and
explore ways to increase its power output. They will use
Excel to collect, organize, and communicate their findings
using charts and graphs. In small groups they will be
asked to explore and design an electrical power generator to
serve the needs of EdVenture Island.
In the course of this investigation, they will be assigned
a renewable or non-renewable resource available for the
production of that power. Each group will prepare a report
on that resource that will be presented to the remainder of
the class in the form of a PowerPoint presentation. After
all presentations are made, the class will then decide which
type of resource will be used to supply power to the island.
Time Required
Two 45 minute class periods
Pre-Requisite Skills
Students should have a basic
knowledge of what electricity (static and non static) is. They
should also understand how a generator works. Knowledge of
PowerPoint is also necessary but can be taught during the activity.
21st Century Tools (Technology Tools)
- Internet searching and
PowerPoint
Procedure
- The students will work
through a series of steps intended to guide their exploration of
the graphs and tables. They will begin with Chart 1. This is a
graph that may be a little different than ones they are used
to. While the only independent variable is diameter, the y-axis
is comprised of two separate variables that can coexist on similar
scales. It is purposefully used
here to force students to pay close attention to what
information they are actually seeing. Chart 1 is a complete
graph of all of the data in Sheet 1 and covers a rather large
range of functional values. The actual data points have been
replaced with smooth curves to better aid the student in seeing
the specific trends. If students have access to computers and
software that can open and edit the spreadsheet, they can change
to a scatter plot by right clicking in the chart and choosing
“Chart Type” then selecting the discrete data point option under
“XY Scatter”. This will permit them to see each data point and
still pick out a trend in the data.
- Students will not be asked to identify the specific
functional relationship but only to choose one of two
possibilities--Direct or Inverse. Notions of different types
of regression, complex variations, or even piece wise behavior
are left for later lessons or courses. If a group is struggling
with identifying a relationship it is suggested that the teacher
probe first to see exactly what problem the students may
be having with the graph and then guide by careful questioning
to help focus the students process. It is important that the
students arrive at a choice of relationships on their own.
- Throughout this activity,
after each subsection, the students will be asked to choose a
type of wire for a transmission system. Their choice is neither
right nor wrong. What is important is their thought process and
they should be encouraged to carefully detail why they made the
choice they did. If they change to another type later, they
shouldn't go back and change an earlier choice or rationale.
This, too, models actual scientific process in which earlier
theories are replaced with newer as more information is
discovered.
- For #5, students may have
difficulty because of the resolution of the graph. For that
reason, the questions about the meaning of an x-intercept and
its possibility were included to help the student think about
reading too much from a rough graph. The answer to #6 is no but
the meanings could give insight into student thought processes
and/or misconceptions about resistance.
- Questions 7 and 8 are
intended to give students further practice in recognizing trends
and verbalizing the relationship.
- Questions 9 and 10 are a
bridge to the tabular data.
- The activity associated
with Chart 2 is an optional extension if time permits. It
allows for a closer look at four functions on one graph. While
it is a graphical representation of a system of equations, there
are no meaningful points of intersection. Its primary intent is
to introduce the term – system of equations – within an
understandable format. Questions 2 and 3 relate to a much more
human characteristic of decision making. It is difficult to
determine what choice a group will make regarding wire, based on
a review of the graphs or table. The graph clearly shows
copper's superiority to aluminum across the diameters. If that
is the students criteria, they may have no trouble choosing
copper. Interesting arguments could occur though, if money
enters the picture. It is important to point out a basic
engineering concept, at some point in this process. While one
material may be theoretically better than another at every
possible point (such as copper's resistance in relation to
thickness), often another material may not be perfect but it
certainly can be “good enough”. And when money enters the
picture, especially if costs are wildly divergent, good enough
may be just right.
21st Century Assessment/Evaluation
Another possibility would be to have a power company representative come in to
answer questions from the students. Or, if you are a technology
rich school, you may be able to arrange a teleconference with a
company that has the means or
drag a speakerphone into the class and make the call from your
room. The amount of information that can be attained in 10 minutes
coupled with being Just-In-Time for the students receptiveness can
have quite an impact on student learning.
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