Math-in-CTE Lesson Plan Template
Lesson Title: Gear Ratios and Torque Multiplication
Author(s):
Liz White
Phone Number(s):
Lesson #5
E-mail Address(es):
elizabeth.white3@gmail.com
Keith Brown
keibrown@nvcc.edu
Occupational Area: Automotive Technology-Power Trains
CTE Concept(s): Torque multiplication and gear ratios
Math Concepts: Comparing ratios, problem solving with ratios, linear relationships, reading a graph
Lesson Objective:
Supplies Needed:
 To understand and calculate gear ratios
 To understand and demonstrate the relationship of torque and rotational speed
 To understand and properly express the relationship between the driving and
driven gears
Text books, blackboard, set of gears, Gear Ratio PowerPoint
THE "7 ELEMENTS"
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.

How do you get 4000 lbs of wheels and steel moving from a Answer 1: Gears! Explain that gears are used to multiply
torque at low speeds and increase rotational speed at
stop and keep it going without over revving the engine?
higher speeds (overdrive). The objective is to keep the
engine within its ideal operating RPM range over varying
driving conditions. This is achieved by using multiple gear
sets in a transmission

What can be done to get a race car to the end of the ¼ mile
faster?

Answer 3: Install higher final drive gears (numerically
What would you do to a vehicle to achieve a higher top lower)-2:1
speed?
Explain that final drive gears are often expressed relative
to how they affect the top speed of the vehicle although
they are correctly expressed mathematically, indicating the
revolutions of the drive gear to the driven gear
Answer 2: Install lower final drive gears (numerically
higher)-4:1
2. Assess students’ math awareness as it relates to the CTE
lesson.

If you have 20 oranges and 10 apples, what is the ratio
of oranges to apples?

Refer to the charts “Money in the Stock Market (2004)
and (2009)” and calculate the ratios based on the chart
values

2:1 (2 orange for each apples)

Students should interpret the first graph and
calculate a ratio that indicates a positive
return (10:1 output to input)

Students should interpret the second graph
to have a ratio that indicates a negative
return (1:5 output to input)
3. Work through the math example embedded in the CTE lesson.

How many times will the drive gear turn to rotate the
driven gear once with a ratio of 4:1?

The drive gear will turn 4 times to rotate the
driven gear once.

Refer to the graphs “Torque relationship and Speed
relationship slides 1 and 2” to determine how to calculate

Slide 1-Torque is always multiplied by the ratio:
Blue line =2:1, Red line 1:1
torque and speed

Speed is always divided by the ratio

100 ft-lbs of torque is input to a gear ratio of 4:1, how
much is output?

Talk about how to calculate the input, output,
gear ratio

1000 rpm is input to a gear ratio of 4:1, what is the output?

400 ft-lbs (multiply the input torque by the ratio)

250 rpm (divide the input rpm by the ratio)
4. Work through related, contextual math-in-CTE examples.

Refer to the second set of graphs “Torque and speed
relationships, slides 3 & 4” and answer the questions

If the input torque is 150 ft-lbs and the output torque is 450 ftlbs, is this is under, direct, or over drive? What is the ratio

If the input rpm is 1000 and the output rpm is 400, is this
under, direct, or overdrive? What is the gear ratio?

Calculate two gear sets (4 gears) in mesh by first finding each
gear set ratio then multiplying them together

Students are asked the same questions as in the first
two slides. Now, an overdrive ratio is used (.6:1) to
demonstrate what happens to speed vs. torque
compared to under drive ratios

450 divided by 150 = 3:1, under

1000 divided by 400= 2.5:1, under

Talk about multiple gears in mesh

Give an example: gear set A-drive gear has 20
teeth, driven has 40, Gear set B drive gear has
30 teeth, driven gear has 40
2:1 x 1.33:1=2.66:1

5. Work through traditional math examples.

Refer to gear and math worksheet

Stress to the student that counting the teeth is
typically the most accurate method to finding the
ratio
6. Students demonstrate their understanding.

The students are given a worksheet with various problems to
solve

Each problem will include solving for the gear ratio, a given
input torque, and a given input speed


The worksheet will consist of six three part
questions of varying difficulty for the groups to
solve

This will further develop an understanding of the
relationship between gear ratios, torque and
engine speed

This will be used to assess each student’s
understanding of the lesson and to identify any
areas that need further instruction ( calculating
multiple ratios, finding output torque, or finding
output rpm)
The students will work in small groups that are monitored by
the instructor
7. Formal assessment.

NOTES:
The students will use this information to disassemble a
transaxle and count the gear teeth to calculate the ratios and
output speed and torque using the lab worksheet