PBI Final Project Lesson Plan II
Name:
Yu-Hsueh Lee
Title
of lesson: Graph Interpretation
Date
of lesson:
Length
of lesson: 90 minutes
Description
of the class:
Name of course: Algebra I
Grade level: 9th-12th Grade
Honors or regular: Regular
Source
of the lesson:
Information and resources found at the website: http://www.fueleconomy.gov
http://www.fueleconomy.gov/feg/fe_test_schedules.shtml
http://www.ec.gc.ca/energ/fuels/reports/sulpur2001/sulphur_rpt_2001_sec4_e.htm
http://www.atti-info.org/technology/alt_fuels.html#7
TEKS
addressed:
Algebra
I :
| Foundations for Functions |
2 |
Displaying and Interpreting Data |
517 |
Interprets situations in terms of
given graphs or creates situations that fit given graphs. (alg 1 b2C) B9,10,11 T9,10,11 (obj 2) |
I. Overview
Students will use their graph knowledge to indicate the dependent variable, independent variable, units on each axis to conclude the meaning of the graph.
II. Performance or learner outcomes
Students will be able to:
- identify the independent variable, the dependent variable(s), the units
for each variable, the type of graph.
- describe how the dependent variable changes with respect to the
independent variable.
- explain the physical phenomena from the graph.
III. Resources,
materials and supplies needed
- http://www.fueleconomy.gov/feg/fe_test_schedules.shtml
- http://www.ec.gc.ca/energ/fuels/reports/sulpur2001/sulphur_rpt_2001_sec4_e.htm
- http://www.atti-info.org/technology/alt_fuels.html#7
IV. Supplementary materials, handouts.
- Handout1 : Table v.s. Graph
- Handout2 : Driving in city v. s. highway
- Handout3 : Energy Cost per Mile : Comparing the cost of Electric vehicle and Gasoline vehicle.
Five-E Organization
Teacher Does
Probing Questions
Student
Does
| Engage: Pass out pre-test. 5 min. Pass out handout 1. The teacher explains the advantage of using graph v. s. table. Searching an alternative efficient fuel, we will encounter pool of data represented by tables or graphs. Table will give us detail data for each individual item, but it is not straightforward to tell the relationship between items we are comparing. Graph offers this advantage in comparing a pool of various resources. Ask students compare the table and the graph on the handout1. 10 min |
1. What information
does this table tell us? 2. How will
you tell the difference between each of source? 3. Group students
by two or three to draw a graph by using the information on
the table. Call student to show and explain their
graph. |
1. The volume of imported Fuel Production. The unit is cubit meter. 2. By comparing each resource from one another and listing out the order. Students may have different answers.
|
| Explore: Divide
the class into groups of three. Pass out Handout2. There are two graphs showing the speed while driving in the city with traffic and driving on highway, respectively. Ask each group discusses the graph, then each group explain their interpretation to the class. 20 min |
1. What is the dependent variable? Which is the independent variable? What is the unit for each axis? 2. What is MPH? 3. How does the dependent variable change with respect to the independent variable. 4. Comparing these two graphs, call students to explain their interpretation about the graph. |
1.
Vehicle Speed is the dependent variable. Test Time is independent variable. Units are MPH and seconds respectively. 2.
Mileage per Hour. 3.
The speed is changed as time is changing. 4.
While driving in city traffic, the car will idle very often
where the graph will hit the ÔTest TimeÕ axis.
But the graph on the highway schedule, it only hits the
bottom line when it starts and stops. |
Explain: Pass out handout3. The teacher explains that this graph
compare the cost of electric vehicle and gasoline vehicle. EV2, EV3 and EV4 are three different
electric vehicles, which runs 2 miles per KWH, 3 miles per KWH
and 4 miles per KWH, respectively.
Three solid lines represent their costs.
Two dotted lines represent two different gasoline vehicles,
22 miles per gallon and 18 miles per gallon respectively. Remember, the higher mileage the lower cost. 20 min |
1. What does
the left Y axis mean?
What is the unit? 2. What does
the right Y axis mean?
What is the unit? 3. What does
the X axis mean? What
is the unit? 4. How much per mile does the 18miles/gallon
gasoline vehicle cost per mile when the gasoline is $1.35 per
gallon? 5. How much
per mile does the EV2 vehicle cost when the electricity is $0.075
per KWH? |
1. Electricity
Cost per KWH. KWH
means KiloWatt per Hour. The unit is
KWH 2. Gasoline
cost per Gallon. The
unit is Gallon. 3. Energy Cost
per Mile. The unit is
Mile. 4. Around $0.075/mile 5. Around $0.04/mile. |
| Extend / Elaborate: Currently, the national average cost for electricity
is about 6.8 cents per kWh, while the average residential rate
is around 8.5 cents per kWh.
The gasoline price has gone up high to $3.00 per gallon. Discuss as a group, what the best choice you will elect with
and without considering the environment impact.
20 min |
1. When does the EV2 vehicle and the 22miles/gal
vehicle cost per mile? 2. When does the EV3 vehicle and the 18miles/gal
vehicle cost per mile? 3. Give your
interpretation before and after the intersection of two lines. 4. Use the
current electricity and gasoline price, what will be your choice? |
1. When the
gasoline price is $1.45/gallon and the electricity price is
$0.13/KWH. 2. When the
gasoline price is $1.80/gallon and the electricity price is
$0.29/KWH. 3. Before the
intersection, the electric vehicle costs less than gasoline
vehicle. After the intersection, the gasoline
vehicle cost less than the electric vehicle. 4. Students
will have various answers.
|
|
Evaluate: Pass out the post-test. 5 min |
|
The students will complete and turn in the
post –test sheet. |
Pre-Test
.
- What is the dependent variable?
- What is the independent variable?
- What is the unit of the X axis? What is the unit of the Y axis?
- In June 2004, how much is the gasoline price?
- When is the highest gasoline price in 2003 to 2005?
- What does the line climbing from left to right mean?
- Comparing September, 2005, does the gasoline price increase or drop?
Resource: http://tonto.eia.doe.gov/oog/info/gdu/gasdiesel.asp
Post-Test
- What is the dependent variable?
- What is the independent variable?
- What is the unit of the X axis? What is the unit of the Y axis?
- In June 2004, how much is the gasoline price?
- When is the highest gasoline price in 2003 to 2005?
- What does the line climbing from left to right mean?
- Comparing September, 2005, does the gasoline price increase or drop?
Resource: http://tonto.eia.doe.gov/oog/info/gdu/gasdiesel.asp
Handout1
TABLE 4.1:
Fuel Production / Imports
National Summary for 2001
|
Type of Fuel |
Fuel Production / Imports
|
|
|
(m3) |
(% of total) |
|
| Aviation
Turbo Fuel |
6,071,733 |
7.2 |
| Motor
Gasoline |
38,911,587 |
46.1 |
| Aviation
Gasoline |
125,198 |
0.1 |
| Kerosene/Stove
Oil |
1,320,978 |
1.6 |
| Low-Sulphur
Diesel Fuel |
20,625,948 |
24.4 |
| Diesel
Fuel |
3,500,151 |
4.1 |
| Light
Fuel Oil |
4,306,518 |
5.1 |
| Heavy
Fuel Oil |
8,376,166 |
9.9 |
| Plant
Consumption |
1,237,273 |
1.5 |
|
|
|
|
| TOTAL
|
84,475,551 |
100.0 |
This
page is for teacherÕs reference only.
Resource:
http://www.ec.gc.ca/energ/fuels/reports/sulpur2001/sulphur_rpt_2001_sec4_e.htm
Handout2
The city schedule represents low-speed
driving in stop-and-go
traffic and considerable idling.
The highway schedule simulates non-metropolitan driving at
higher speeds,
with
no stops and negligible idling.
Resource:
http://www.fueleconomy.gov/feg/fe_test_schedules.shtml
Handout3
Resource: http://www.atti-info.org/technology/alt_fuels.html#7
This page is for teacherÕs reference only:
Currently, the national average cost for electricity is about 6.8 cents per kWh, while the average residential rate is around 8.5 cents per kWh. Some electric utility companies have special rates in place that are cheaper at night when the demand for electricity is low. These rates can be as low as 3 cents per kWh. Older electric vehicles in commercial fleets have energy efficiencies of about 2 mi/kWh while new electric vehicles such as GM's EV1 have energy efficiencies of over 6 miles per kWh. Heavy duty vehicles such as trucks and buses average about 1 mile per kWh.
To determine the energy cost per mile of a gasoline vehicle, pick the location on the right axis(Gasoline Cost per gallon) and $1.35. Draw a horizontal line to the left until you intersect the Gas 18 mi/gal line. Now draw a vertical line down until you intersect the bottom axis (Energy Cost per mile). This indicates the fuel for a gasoline vehicle with an energy efficiency of 18 mi/gal costs around 7.5 cents per mile when gasoline costs $1.35 per gallon.
This indicates that even an older less energy efficient electric vehicle(2 mi/kWh) at the national average of 7 cents per kWh, is cheaper to operate at 4 cents per mile than the more efficient(Gas 22 mi/gal) vehicle operating with the national average of $1.25 per gallon at over 7 cents per mile.
Resource: http://www.atti-info.org/technology/alt_fuels.html#7