Tire Sizing

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					                                         Math-in-CTE Lesson Plan Template
Lesson Title: Tire sizing                                               Lesson # 3
Author(s):                            Phone Number(s):                  E-mail Address(es):
  Andrew McAlpin                       (856) 767-7000 ext. 5234
  Nicholas Tarasevich                  (856) 767-7000 ext. 5326 
Occupational Area: Automotive Technology

CTE Concept(s): Acceptable Tire Size to a vehicle

Math Concepts: Ratio, Conversion, constructing a linear equation, chart reading

Lesson Objective:      Students will Demonstrate their ability to effectively change their size of rim without compromising the integrity
                       of the vehicle. They will do this with a real world approach and prove it mathematically.

Supplies Needed:       Tires and rims of various sizes, tire labels on the car door, paper, pencil, calculator

                         THE "7 ELEMENTS"                                                          TEACHER NOTES
                                                                                                  (and answer key)
1. Introduce the CTE lesson.                                            Additional information can be found at
Show picture of cars and trucks with correctly fitted tires and
rims, and also cars with incorrect tires and rims

Ask students:
                                                                         Students might say: “Because it looks cool!” “It’s part of my culture.”
Why trick a car out?                                                    “Girls will like me!”
Show Pictures then ask students:                                    Show pictures of various cars with large rims, small rims, and rims of
                                                                    normal size.

                                                                    Allow for discussion. Students will vary in opinion. Make sure to
What car looks better?
                                                                    value all of their comments if appropriate.

What car runs efficiently?
                                                                    Guide students to the conclusion that a tire size that follows the
                                                                    vehicle’s tire information placard found on the driver side door is the
                                                                    best to use.

What systems can be affected by the overall diameter of the tire?   Answers can include: Speedometer, odometer, ride, harshness of
                                                                    the vehicle, etc. One relation you might like to remind them of is the
How does this car handle on the road?                               relationship between the Diameter and Circumference of the car and
                                                                    how it directly affects the speedometer and odometer.
                                                                                             (Diameter) π = Circumferance
                                                                                                    Dπ = C

Can you have larger rims and an efficient ride?                     Explain to the students when you increase the diameter of the rim
                                                                    you must decrease the section height of the tire. The Overall
                                                                    Diameter must stay the same!
   2. Assess students’ math awareness as it relates to the CTE

                                                                   Remind the students how to read the P-metric tire size if needed
Quickly review how to read a P-metric tire size and the vocabulary
                                                                   Remind the students of the vocabulary used and the relationship
that goes with it.
                                                                   between them.
                                                                      Section width
                                                                      Section height
                                                                      Rim or wheel diameter (inches)
                                                                      Vehicle tire information placard (found on driver side door of vehicle)
                                                                      Height to width ratio aka aspect ratio
Mathematically show them what the Aspect Ratio means.

                                                                      Overall diameter of the tire
Physically show the students how to come up with the equation
for Overall Diameter. Ask them why must you add the section
height twice to the rim diameter instead of just once?
                                                                      Overall Diameter = 2 ∙ Section Height + Rim Diameter

Remind them that the rim diameter is going to be in inches but the
                                                                   This can be confusing so be sure to emphasize this fact!!
section height is in millimeters.

                                                          If your students have a problem with this mathematically, give them
Remind the students of the conversion method of inches to
                                                          the table provided and remind them that you will be converting your
millimeters and millimeters to inches
                                                          inches into millimeters to simplify your calculations. The table
1 inch = 25.4 millimeters                                 converts the rim diameters from inches into millimeters.
3. Work through the math example embedded in the CTE lesson.
Find the section height of the tire.                           Make sure you use a tire that is physically there in the shop. You will
                                                               use this later to check if they have done the math correctly.

                         Ex. P 225/70 R-15

                                                               Identify the information needed for the equation.
                                                               Section width = 225
                                                               Aspect ratio = 70

                                                               Since you will not be able to find the section height from the
                                                               information, have the students come up with a way to represent
                                                               section height. The students may suggest to use a question mark,
                                                               sh, or an x.
                                                               Section height = ? = sh = x

                                                               Plug in information then solve for x

Check your math by measuring the section height.
                                                               Divide both sides by 100

For your lower level students you may want to give them the Multiply both sides by 225
equation for section height.
Now that you know the section height. Find the Overall Diameter.   Now that we are looking for the overall diameter have the students
                                                                   come up with another variable to represent it.
                                                                   Overall diameter = x = od = y = ?
                                                                   Section height = 157.5 mm
                                                                   Rim Diameter = 15 inches = 381 mm
                                                                   You can find the rim diameter on the p-metric tire label on your tire,
                                                                   which was previously given.
                                                                   Explain that you had to convert the rim diameter to millimeters
                                                                   because you can’t add millimeters to inches. If they struggle with
                                                                   converting then they can use the table given.
                                                                   Plug in known values to solve for what you don’t know.

Physically measure the overall diameter with a specified tool
4. Work through related, contextual math-in-CTE examples.

A truck tire has a p-metric tire label of:                  Section width = 265 mm
LT 265/75 R-17                                              Aspect ratio = 75
Find the overall diameter                                   Section height = x

                                                            Section height = 198.75 mm
                                                            Rim diameter = 17 inches = 431.8 mm

                                                            Overall Diameter = 829.3
5. Work through traditional math examples.
Solve for x when y = 19                                                 Plug in 19 for y

                                                                        Subtract 10 from both sides

                                                                        Divide by 3

Solve for y when x = 10                                                 Plug in 10 for x


6. Students demonstrate their understanding.
Students will demonstrate their understanding by taking the vehicle’s
tire information and matching it with a tire and wheel combination.
Group work.

7. Formal assessment.
Project that will match various tire and rim combinations to a
vehicle’s specs.


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