Math-in-CTE Lesson Plan Template
Lesson Title: Toe in Toe Out°
Author(s):
Barry Tatelbaum
Lesson #
Phone Number(s):
(973) 412-4102
Auria Torres
(973) 412- 4413
E-mail Address(es):
btatelbaum@essextech.org
atorres@essextech.org
Occupational Area: Automotive Technology
CTE Concept(s): Range & Tolerances, Vehicle Readings vs Manufacturers Specifications, Vehicle Adjustments
Math Concepts: angles, degrees
Lesson Objective:
Students, using the correct alignment equipment, will be able to rectify necessary adjustments.
Supplies Needed:
Power Point, Handouts, Visual Aids, Alignment Machine & Simulator.
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
The owner of a vehicle has an unusual condition related
to the steering wheel position. When the vehicle is being
driven straight the steering wheel is off center. The
steering wheel has to be held crooked to go straight.
What could cause this type of situation?
Toe Angle: The toe angle identifies the exact direction the
tires are pointed compared to the centerline of the vehicle
when viewed from directly above.
Toe is expressed in either degrees or fractions of-an-inch,
and an axle is said to have positive toe-in when imaginary
lines running through the center lines of the tires
TEACHER NOTES
(and answer key)
Note: Teacher will provide visual aids demonstrating the “TOE” as it
relates to the vehicles alignment geometry.
intersect in the front of the vehicle and have negative toeout when the diverge.
Toe is stated as (IN) positive if the front of the tire is
pointed in towards the vehicle.
Toe is stated as (OUT) if the front of the tire is pointed
away from the vehicle.
Toe specifications and readings
decimals, millimeters, or, degrees.
are
displayed
in
Toe specifications are expressed as totals of the front
and rear axle. Ex. L/F @0.10° & R/F @ 0.20° = 0.30° total
Toe.
When toe is off on either rear wheels, it creates a thrust
angle. The Thrust line dictates the position of the front
wheels when driving straight. It is therefore imperative
that the rear wheel toe settings be adjusted to
manufactures specifications.
On this vehicle, the front wheels
are not aligned to the rear thrust
line. This can happen from normal
wear and stress, whether your
vehicle has adjustable or non
adjustable rear suspension.
To steer straight ahead, you would
have to steer the front wheels
slightly to the right.
A common result would be that the vehicle would "dog track" and possibly
"pull" to the side.
Of course, the angles are exaggerated so you can more easily see the
condition. But it takes only a small misalignment to create problems.
For vehicles with non-adjustable rear suspensions
There are certain math concepts needed to have an
understanding of “Toe Angles”. Angles and decimal
measurements are used to determine tolerance ranges
compared to manufactures specification. Math skills
needed decimal degrees, angles, tolerance, addition,
subtraction.
1. Angle readings are measured at all four wheels.
2. The steering is centered.
3. Front wheels are referenced to rear thrust line and set to specifications.
Result - All four wheels are parallel and the steering wheel is centred.
For vehicles with adjustable rear suspensions
1.
Angle
readings
are
measured
at
all
four
wheels.
2. Rear wheels are set to specification. (Rear thrust line corresponds to
vehicle
centerline.)
3.
Steering
wheel
is
centered.
4. Front wheels are referenced to the rear thrust line and set to specification.
Result: all four wheels are positioned straight ahead and parallel, and
the steering wheel is centered.
2. Assess students’ math awareness as it relates to the CTE
lesson.
Describe an example of a “tolerance” range?
List the basic angles you are familiar with?
Define the meaning of parallel and perpendicular.
Review the process of converting measurements through the
use of a table of measures.
Conversion Factors: 1” = 25.4mm
1° degree = 1”
3 Work through the math example embedded in the CTE lesson.
Solution A
A vehicle enters the shop with the complaint of a crooked Tolerance range front Total Toe. 0.05° to -0.45°
steering wheel. The vehicle is a 2000 Ford Taurus. The Toe
L/F @0.10° & R/F @ 0.20° = 0.30° Total Toe (out of tolerance
specifications are: Front Total Toe –0.20° preferred setting.
range.)
Tolerance range of 0.05° to – 0.45°. Rear Total Toe -0.36°
Tolerance range rear Total Toe –0.11° to -0.61°
preferred setting. Tolerance range of -0.11° to – 0.61°.
The vehicles alignment readings have been taken.
Results: L/F Wheel 0.10°
R/R @ 0.18° & L/R @ -0.32° = -0.14° Total Toe (within tolerance
range.)
R/F Wheel 0.20°
R/R Wheel 0.18°
To achieve the preferred specification:
L/R Wheel -0.32°
Front L/F wheel reading 0.10° Requires a adjustment of -0.20°
Front R/F wheel reading 0.20° Requires a adjustment of -0.30°
Define what numbers are the limits for an acceptable readings
within the tolerance range. Draw a line chart showing preferred Rear R/R wheel reading 0.18° Requires a adjustment of -0.36°
and tolerance range.
Rear L/R wheel reading -0.32° Requires a adjustment of +0.14°
Which wheels will need to be adjusted and by how much to
achieve the preferred Toe setting.
4. Work through related, contextual math-in-CTE examples.
Example A
A 2010 Cadillac has been scheduled for an alignment. Customer
states poor tire wear.
Manufactures TOE specifications:
Front Total Toe 0.20° Tolerance ± 0.20°
Rear Total Toe 0.20°Tolerance ± 0.20°
Solution
Vehicle Readings
L/F Wheel -0.20°
R/F Wheel 0.10°
L/R Wheel 0.50°
R/R Wheel 0.10°
Which Wheels are within the acceptable tolerance range?
Which wheels need be adjusted and by how much to achieve the
manufactures preferred setting ?
5. Work through traditional math examples.
To go from
To
Multiply by
cm
in
0.3937
in
cm
2.54
m
ft
3.2808
ft
m
0.3048
Km
mi
0.6214
mi
km
1.609
1. Use the chart and a calculator to convert each measurement. Make 1A. 16in = 40.6 cm (answers are rounded to the nearest tenth)
sure to show all work, round your answer to the nearest tenth.
B. 36 mm = 1.4 in
A.
16 in = ________cm
B. 36 mm = _______ in
C. 66 cm = 26 in
C. 66 cm = _______ in
2. Use a number line to indicate the range of values represented by
2A.
the following specifications.
A. 4.320 ± .225
B. 5
3
1
±
8
8
C. 2.760 ± .125
B.
4.095
4.320
4.545
5¼
5
3
8
5½
C.
2.635
3. Use the number lines created in exercise 2 to write the ranges as
compound inequalities.
2.760
3A.
4.095 ≤ v ≤ 4.545
A.
B.
5¼ ≤ v ≤ 5½
B.
C.
2.635 ≤ v ≤ 2.885
C.
6. Students demonstrate their understanding.
2.885
7. Formal assessment.
Utilizing alignment machine simulator, students will identify toe
readings and compare to manufacturers specifications.
Students will be able to determine the necessary degrees of
corrections for front and rear axles.
NOTES: