Classroom Robotics – Mathematics Day 3 Pg. 1
Rel04032012
Classroom
Robotics –
Mathematics
Day 3
Overview
Today students will use the gears in their kits to better
understand gear ratios. They will also learn how gear ratios
affect the force and distance in the Work formula.
Workshop Objectives:
Students will be able to…

Utilize ratios to mathematically model the effect of gears
Suitable Ages: 11+
Time Needed: 1 hr 15 min
In this packet
Teacher’s Guide
Fun with Gears Worksheet
Classroom Robotics – Mathematics Day 3 Pg. 2
Rel04032012
TEACHER’S GUIDE
Activity Goal
Today students will use the gears in their kits to better understand gear ratios. They will also learn how gear ratios
affect the force and distance in the Work formula.
Objectives
Students will be able to…
 Utilize ratios to mathematically model the effect of gears
Materials


Copies of Fun with Gears Worksheet
Copies of Gear Train and Row of Gears Builds
Set Up
Go through the lesson plan and make any necessary copies.

Lego kits
Classroom Robotics – Mathematics Day 3 Pg. 3
Rel04032012
Procedure
Time
5 min
Action
1. Break the students into groups, giving each building guides, a
lego kit and worksheets.
Materials Needed
Copies of Fun with Gears
Lego kits
Building guides
2. Give students time to work on worksheets.
60 min
3. Go through the answers of the worksheet with the students.
10 min
<75
minutes
We encourage and welcome your feedback!
Please fill out the feedback form based on your experience and observations and forward
it to <NETID>@utdallas.edu at the Science and Engineering Education Center.
Classroom Robotics – Mathematics Day 3 Pg. 4
Rel04032012
Fun with Gears Worksheet
Name ________________________________________________
Class ________________________
This lesson is about gear ratios. A ratio is a fraction. For our purposes we will be dealing with this fraction:
𝐷𝑟𝑖𝑣𝑒 𝐺𝑒𝑎𝑟
= 𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜
𝐹𝑜𝑙𝑙𝑜𝑤 𝐺𝑒𝑎𝑟
To do the problems below you will need to understand how to multiply fractions and cancel like numbers.
Multiplying fractions is much easier than adding and subtracting fractions. All you need to do when multiplying
fractions is to multiply the numerators together and multiply the denominators.
1 3
3
So if you want to know what is ½ of ¾ just multiply: ∗ =
2
4
8
A nifty rule can be used to make multiplication easier, cancellation. If a numerator is the same as a denominator you
can simply cancel them.
8
12
96
Therefore:
∗ = = 1 If you just cancel like terms you can get the same answer without multiplying; the 8s
12
8
96
cancel and the 12s cancel leaving 1 in the numerator and 1 in the denominator which is one.
8 12 1
∗
= =1
12 8
1
Simplify the following:
1.
30
=
90
2.
40
=
24
3.
8
24
=
Try the following problems. Simplify your answers.
3
1. ∗ 12 =
4
2.
1
3
1
∗ =
2
4
5
5
12
3. ∗
4.
40
24
∗
=
24
8
=
2
5
3
8
5. ∗ =
6.
7
12
∗
12
21
8
5
4
2
=
7. ∗ =
8.
5
2387
∗
2387
7
=
Build the Row of Gears models from the Fun with Gears Build LDD Model. Place a mark on one of the teeth of each
of the gears. Rotate the 40 tooth gear one rotation.
Classroom Robotics – Mathematics Day 3 Pg. 5
Rel04032012
1. How many times did the 8 tooth gear spin? __________________
2. How many times did the 24 tooth gear spin? __________________
3. If this was a transmission and the 40-tooth gear is the drive gear, what would the
40 tooth gear be connected to on your robot? ____________________ Which gears are
follow gears? ______________ What part of the robot are they connected to? ____________
4. What is the gear ratio from the 40-tooth gear to the 8 –tooth gear? (use the formula above)
What is the gear ratio from the 40-tooth gear to the 24-tooth gear?
To determine the overall gear ratio you multiply the first gear ratio by the second gear ratio.
𝐷𝑟𝑖𝑣𝑒1
𝐹𝑜𝑙𝑙𝑜𝑤1
∗
𝐹𝑜𝑙𝑙𝑜𝑤1
𝐹𝑜𝑙𝑙𝑜𝑤2
= 𝑇𝑜𝑡𝑎𝑙
What is the total gear ratio? ____________________________
The middle gear is called an Idle Gear. What does it add to the transmission?
Work out the following gear ratios. If the motor makes the drive gear turn through one rotation, how many
rotations will the wheels go through if they are attached to the axle of the follow gear? (Hint: If you have
trouble visualizing these, just put the gears on a beam.)
1)
Drive gear
10
Follow gear
5)
Follow gear
10
5
10
Ratio
Will the wheels go faster (F) or slower (S)
than the motor? ____________
Ratio
2)
6)
15
Drive gear
20
F or S ________________
20
Ratio
Ratio ________________
F or S? ______________
F or S _______________
15
Classroom Robotics – Mathematics Day 3 Pg. 6
Rel04032012
3)
7)
10
10
30
30
Ratio
Ratio ________________
F or S? ______________
F or S _______________
4)
8)
10
40
10
40
Ratio
Ratio ________________
F or S? ______________
F or S _______________
Gear Train
Build the gear train from the Fun with Gears Build LDD. Place a mark on one of the teeth for each
gear to determine rotations.
Classroom Robotics – Mathematics Day 3 Pg. 7
Rel04032012
1) If you spin the 40-tooth gear one time how many times do the others rotate?
First 8-tooth _______ 24-tooth ___________ Second 8-tooth _________
2) If you spin the second 8-tooth one time how many times do the others rotate?
24-tooth ___________ First 8-tooth _______ 40-tooth ____________
3) How much force does it take to turn the second 8-tooth gear with the 40-tooth gear?
4) How much force does it take to turn the 40-tooth gear with the second 8-tooth gear?
Motor
# of Rotations:
__1_
30
10
Wheels
Axle
20
10
If the servo turns forward, will
the wheels be turning forward
or backward?
__________________
____x ____=____ What direction do the
Times middle gears turn?
Faster _____________________