Math-in-CTE Lesson Plan Template
Lesson Title: Rotor Measurement / Lesson #1Author(s): / Phone Number(s): / E-mail Address(es):
John Capezza / 973-664-2351/908-414-6243 /
Tony Knuth / 908-603-9444 /
Occupational Area: Transportation Technology
CTE Concept(s): Brake Rotor Measurement
Math Concepts: Measurement/ Solving Inequalities/ Comparing Numbers
Lesson Objective: / Correctly measure various brake rotors for wear to determine service, usability and replacement
Supplies Needed: / Safety Glasses, Brake Rotors(different thicknesses if possible) Micrometer, Tape Rule, Rotor Specifications
The "7 Elements" / Teacher Notes
(and answer key)
1. Introduce the CTE lesson.
Today we have several examples of different brake rotors from similar vehicles. How can we determine the wear differences between them? How can we determine which are safe to use? / Compare and contrast the rotor differences, probe student responses, guiding them to find appropriate specifications, different wear patterns, rotor thickness and tools used in the measurement of the rotor. Have several samples of various thicknesses, new, used and discard.
Look for student responses of measured thickness as compared to specifications using inequalities.
2. Assess students’ math awareness as it relates to the CTE lesson.
In order to make a correct determination/measurement one must know rotor specification and correct tools to use.
How do we find the correct specifications?
Do we use a Tape Rule to measure or something else?
Show < > = Who can tell me what these are used for?
How have we used these symbols in the past? / Have a tape rule or steel rule available to compare to micrometer.
Have micrometers ready for sample measurements, mm & decimal
Have your rotor specifications ready, Standard measurement & discard thickness.
Have Students measure the rotor with a tape rule first, record measurement, then demonstrate correct measurement with the micrometer, note the difference on the precision of the micrometer.
Less than, Greater than, and equal signs (< > =) are used to show the differences in inequalities.
Look for an example of a mathematical inequality (ie. 5 + x < 3)
3. Work through the math example embedded in the CTE lesson.
Using our example rotors, let’s find out if our rotors need replacement.
We have a brake rotor from a 1989 Mercury Grand Marquis with a 5.0L engine
Specifications state that a new rotor should measure 1.03 in.
The wear limit states that our wear limit is 0.972 in.
Our rotor measures 0.991 in.
We will remove 0.018 in. on our resurfacing.
Show me how we can determine if this rotor is still useable.
m - 2c < dv
0.991 - 2(0.018) < 0.972
0.991 - 0.036 < 0.972
0.955 < 0 .972 / Let students solve the problem any way not using a mathematical formula. Give them a few moments to solve the problem. Ask students for collective answers.
Show graphic example of rotor measurement and hands on example.
You may want to spend some time to develop the inequality using pictures and example rotors.
Next introduce the formula for solving this problem.
m= measurement of rotor thickness
c= cut or resurfaced amount
dv= discard value or throw away value
m - 2c < dv
0.991 - 2(0.018) < 0.972
0.991 - 0.036 < 0.972
0.955 < 0 .972
Since our machined thickness is below our discard value the rotor is no longer useable
4. Work through related, contextual math-in-CTE examples.
We have a 2009 Hyundai Sonata with a 2.4L. The rotor thickness is 1.024 in. The discard thickness is 0.961 in. We resurfaced it and removed 0.022 in. Can the rotor still be used?
m – 2c < dv
1.024 – 2(0.022) < 0.961
1.024 – 0.044 < 0.961
0.980 < 0.961
Steve brought in his father’s 2008 Porsche Cayenne GTS. His brakes don’t feel right after he had his brakes serviced at the local repair shop. After inspecting the front brakes we want to measure the rotors. We note a score of 0.225mm.Our specifications state that new/standard rotor thickness is 34mm. The wear limit or discard thickness is 33.6mm. Can we resurface and use the rotor.
m – 2c < dv
34 – 2(.225) < 33.6
34 - .450 < 33.6
33.550 < 33.6
Replace Rotor / m – 2c < dv
1.024 – 2(0.022) < 0.961
1.024 – 0.044 < 0.961
0.980 < 0.961
Yes, the rotor can be reused because the refinished thickness is above minimum thickness.
m = rotor thickness
c= cut
dv=discard value
34 – 2(.225) < 33.6
34 - .450< 33.6
33.550 < 33.6
No, this rotor must be replaced it is below the discard value.
5. Work through traditional math examples.
Instead of m -2c<dv we change it to y + 4x > 26
Let’s solve this inequality if x=5 and y=3
y + 4x > 26
3 + 4(5) > 26
3 + 20 > 26
23 > 26 not true
Let’s try another one
8.2y < 30 + 4.8x
Solve this inequality if y=5.1 and x=3
8.2y < 30 + 4.8x
8.2(5.1) < 30 + 4.8(3)
41.82 < 30 + 14.4
41.82 < 44.40 True / y + 4x > 26
3 + 4(5) > 26
3 + 20 > 26
23 > 26 not true
8.2y < 30 + 4.8x
8.2(5.1) < 30 + 4.8(3)
41.82 < 30 + 14.4
41.82 < 44.40 True
6. Students demonstrate their understanding.
Now let’s complete some additional problems from the work sheet / Use attached Lesson#1 worksheet and answer key
7. Formal assessment.
Resurfacing a rotor on the lathe and calculating amount the rotor can be resurfaced
Have students calculate maximum amount a given rotor can be resurfaced, then resurface that rotor incrementally on the lathe staying within the discard threshold.
OR
Give students an addendum to the practical assessment using a similar worksheet as in item 6 / Assessment to be given after instruction on lathe
Have sample rotors ready for use
Have Specs. For rotor standard and discard
Students should have had ample practice using the lathe prior to test.
NOTES: