Math-in-CTE Lesson Plan Template
Lesson Title: Emission Control Systems
Author(s):
Ron Snow
Lisa Wood
Lesson # 17
Phone Number(s):
E-mail Address(es):
(856) 468-1445 ext. 2543 or
rsnow@gcit.org
2519
(856) 468-1445 ext. 2996
lwood@gcit.org
Occupational Area: Automotive Technology
CTE Concept(s): Exhaust Emissions
Math Concepts: Percentages, ratios, reading charts and graphs, temperature reading
Lesson Objective:
Students will understand what takes place in the engine, what pollutants emit from the exhaust system
and how it can be controlled.
Supplies Needed:
Smart board, elmo, handouts
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
Cars must pass
REGULATIONS
inspection
by
passing
EMISSION Smog visible cloud of airborne pollutants
Harmful to humans, animals and vegetation
Going GREEN… what does it mean in terms of emissions?
Formed when pollutants combine with oxygen and nitrogen in the
GLOBAL WARMING… What effects do car pollutants have presence of sunlight
on global warming?
Stoichiometric chart
HEALTH RISKS… excessive chemicals in the air
Pollutant levels
Chart on rich lean
2. Assess students’ math awareness as it relates to the CTE
lesson.
Can students read ratio charts?
Can students perform simple ratios from pictures?
Can students write ratios from word problems?
Can students change ratios to a percent?
Can students solve for equivalent fractions?
Introduce math vocabulary as it pertains to ratios
STOICHIOMETER
Supply hand outs with examples of ratios. (see answer key included
with lesson.)
Sample questions to ask by using either the smartboard exchange
website or the ratio powerpoint.
Verbal introduction by having students do a ratio to students and
empty desks.
What does a two to one ratio of the crankshaft gear and the
camshaft gear mean?
PPM
O2
Solve when the crankshaft gear turns three times, how many times
will camshaft turn? Write the fraction that represents each.
CO
NOX
2/1 = x/3
HC
RICH
CO2
LEAN
x=6
3. Work through the math example embedded in the CTE Give examples of air/fuel ratios. Have students identify where on the
lesson
chart the ratios are compared to as to rich or lean mixtures an parts
per million
Distribute a stoichiometric chart Looking at chart have
See list of questions (Ed Helper.com fractions worksheet)
students identify the pollutant levels at different A/F ratios.
Which levels are lean or rich?
What A/F ratio is changing to effect the mixture?
Solve for X to find the equivalent fractions. Teach the cross multiply
and divide method. Allow students to use calculator.
4. Work through related, contextual math-in-CTE examples.
The smaller gear (known as the pinion) has 13 teeth, while the second, Introduce students to other automotive systems where ratios are
larger gear (known as an idler gear, in this particular gear train) has 21 encountered.
teeth. The gear ratio is therefore 21/13, 1.62/1, or 1.62:1.
Gear Ratio (GR) = (Number of teeth on Gear or driven)/(Number of
teeth on Pinion or driver).
The ratio means that the pinion gear must make 1.62 revolutions to turn
the idler gear 1 revolution. It also means that for every one revolution of
the pinion, the idler gear has made 1/1.62, or 0.62, revolutions. In
practical terms, the idler gear turns more slowly.
Suppose the largest gear in the picture has 42 teeth, the gear ratio
between the second and third gear is thus 42/21, or 2:1, and hence the Since the intermediate (idler) gear contacts directly both the smaller
total gear ratio is 1.62x2=~3.23. For every 3.23 revolutions of the and the larger gear it can be removed from the calculation, also
smallest gear, the largest gear turns one revolution, or for every one giving a ratio of 42/13 = 3.23.
revolution of the smallest gear, the largest gear turns 0.31 (1/3.23)
revolution, a total reduction of about 1:3.23 (Gear Reduction Ratio
(GRR) = 1/Gear Ratio (GR)).
Since the number of teeth is also proportional to the circumference of
the gear wheel (the bigger the wheel the more teeth it has) the gear ratio
can also be expressed as the relationship between the pitch circles of
both wheels (where d is the pitch diameter of the smaller wheel and D is
the pitch diameter of the larger wheel):
Work with students in groups to work through the example
Pitch circles have diameters that would give the same gear ratio, but
with cylindrical surfaces that do not slip.
Since the diameter is equal to twice the radius;
as well
and so
In other words, the gear ratio is proportional to ratio of the pitch circles
and inversely proportional to the ratio of gear speeds.
5. Work through traditional math examples.Automobile drive trains Examples:
generally have two or more areas where gearing is used: one in the
transmission, w2004 Chevrolet Corvette C5 Z06 with a six-speed
manual transmission has the following gear ratios in the transmission:
Gear
2:20::4:40 or 2/20 = X/40
Ratio
1st gear 2.97:1
2nd
gear
2.07:1
1. In 1st gear, the engine makes 2.97 revolutions for every
revolution of the transmission’s output.
3rd gear 1.43:1
Question: Write this word problem in the form of a ratio.
4th gear 1.00:1
2. In 4th gear, the gear ratio of 1:1 means that the engine and the
5th gear 0.84:1
transmission’s output are moving at the same speed.
6th gear 0.56:1
Question: Write another ratio similar to 1:1
reverse 3.38:1
1. How many revolutions does the 1st gear make for every
revolution of the trans output?
3. 5th and 6th gears are known as overdrive gears, in which the
output of the transmission is revolving faster than the engine.
2. What speed is the 4th gear providing with a 1:1 ratio?
A. The ratio means that for every 3.42 revolutions of the
transmission’s output, the wheels make one revolution
3. The 5th and 6th gears ratios are causing the output of the
B. (3.42 to 1 = ________ to 2); (3.42 to 1 = ____to 3)
transmission to be as compared to the engine?
A. If the Corvette above has a differential ratio of 3.42:1.
How many revolutions will the wheels make?
B. If you multiply the differential ratio with the transmission ratio,
using 1`st gear how many revolutions will the engine make for
every revolution of the wheels?
C. The differential ratio multiplies with the transmission
ratio, so in 1st gear, the engine makes 10.16 revolutions
for every revolution of the wheels.
6. Students demonstrate their understanding.
Let’s work through some related examples.
Teacher to supply some worksheets with different types of examples
Call on students to give an explanation as how problems were solved
Watch video on How it works.com
ezschool.com
numeracyworld.com
helpingwithmath.com
All great websites to use for sample math questions.
7. Formal assessment.
Students will understand how ratios effect the engine, emission, See The gear problem from www.pleacher.com
and the transmission
Students will complete a quiz to demonstrate their knowledge
Air-Fuel Ratio and Emissions
acceptable exhaust emissions
without catalytic converter
(pre-1975)
HC
300 PPM or less
CO
3% or less
O2
0%-2%
CO2
12%-17% or higher
with catalytic converter
(post-1975)
30-50 PPM or less
0.3% - 0.5% or less
0%-2%
12%-17% or higher
See attached quiz