Analytical Fun with Math and Robotics – Track 1
FOREWORD
Instructor, think about the following:
 Who came up with robots?
 Who invented the first robot in the world?
 When was the first robot built?
Robots / Sum up to 3 words: Sense, Think, Act
Robotics is Everywhere!
What is a robot? Can you think of some examples? Write them here:
Definition
Examples: (NOT Terminator, R2D2, C3PO!!! )
How is Math Involved in Robotics?

Calculating motor power and torque

Gear ratios – speed versus torque

Minimize cost while maximizing performance

Etc.
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
DAY 1 – INTEGERS: THE BASIC
Q1. What is an Integer?
DISCUSSION: In what ways do we classify, or group, numbers?
Erin, “classify, or group, numbers?
Please clarify…
Adding, Subtracting, or Multiplying a group of integers always results in an integer!!
Multiplication is just repeated addition. Raising an integer to a power is just repeated multiplication.
(Both of these are simply fast ways of counting).
A Multiple of an integer is the product of that integer with any integer. For any integers m and n,
their product m*n is both a multiple of m and a multiple of n.
Q2. What is a “perfect square”? Can you list all of the perfect squares less than 100?
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
When an integer n is divisible by another integer d, we say that d is a divisor of n, or that d divides n.
Divisors are also known as factors.
Example
Definition
One whole number is divisible by another if, after dividing, the
remainder is zero.
18 is divisible by 9
18 ÷ 9 = 2 with a remainder of 0.
If one whole number is divisible by another number, then the
second number is a factor of the first number.
9 is a factor of 18
18 is divisible by 9 .
A divisibility test is a rule for determining whether one whole
number is divisible by another. It is a quick way to find factors
of large numbers.
1356 is Divisible by 3:
1+3+5+6 = 15. 15 is divisible by 3.
i.e. Pass the divisibility rule of 3.
Q3. What does it mean when we say that an integer m is divisible by another integer n?
Basic Math Symbols used in this workshop:
Since / Because
So / Therefore / Henceforth
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
DIVISIBILITY RULES:
Divisible
by:
2
3
If:
4
The last 2 digits are divisible by 4
5
The last digit is 0 or 5
Examples:
Yes
128
381
3+8+1=12, and
12 is divisible by 3
1312
12 is divisible by 4
175
6
The number is divisible by both 2 and 3
114
The last digit is even (0,2,4,6,8)
The sum of the digits is divisible by 3
4 is even, and 1+1+4=6 and
6 is divisible by 3
7
Double the last digit and
Subtract it from the rest of the number
and
the answer is: 0, or divisible by 7
672
Double 2 = 4, and
67 – 4 = 63, and
63 is divisible by 7
No
129
217
2+1+7=10, but
10 is NOT divisible by 3
7019
19 is NOT divisible by 4
809
9 is NOT divisible by 5
208
3+0+8=11, but
11 is NOT divisible by 3
905
Double 5 is 10,
90–10 = 80, but 80 is NOT
divisible by 7
More on divisibility rules may be introduced, depending on group’s progress.
Q4. Gave 2 examples to demonstrate the divisibility rules for the following numbers? And why.
Yes
No
#2#3#4#5#6#7-
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
CHALLENGE MATH PROBLEMS
a) What is the largest integer whose cube is less than 10,000?
b) How many integers 1-9 are divisors of the five-digit number 24,516?
c) The diameter of a circle is a whole number. The area of the circle is between 100 and 120 square
units. What is the number of units in the circle’s diameter?
ROBOTIC EXERCISES:
Create your Dancing Robots to dance in synchrony to music. In these lessons, you will learn that there is a
linear proportional relationship between:
 Speed and power
 Speed and wheel diameter
 Wheel diameter and distance traveled
Important: Must perform design work for each dance move and write a flowchart for each move!
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
DAY 2 AM - DISCOVERING PRIME AND COMPOSITE NUMBERS
Before you are given a lesson on this, you will spend sometime to review yesterday work.
A prime number is a natural number has ONLY 2 factors – 1 and itself.
Q1. What is a prime number? What is a composite number?
1 is the only natural number that is neither prime nor composite.
Q2. For a prime number p, find the smallest composite number that has no prime divisors less
than p.
CHALLENGE PROBLEMS
a) What is the largest two digit prime number whose digits are also prime?
b) Is 9409 prime?
c) Find the remainder when the sum of the six smallest primes is divided by the seventh.
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
DAY 3 - FRACTIONS, RATIOS, AND PROPORTIONS
Robotic Exercises: the Dancing Robots unit asks students to create programs that allow a set of physically
different robots to dance in synchrony to music. In these lessons, students will learn that there is a linear
proportional relationship between:
 Speed and power
 Speed and wheel diameter
 Wheel diameter and distance traveled,
Sample 1 - direct proportion:
360 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
15 𝑐𝑚
𝑥=
=
𝑥 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
30 𝑐𝑚
360 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 ∗ 30 𝑐𝑚
15 𝑐𝑚
= 720 degrees
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
EXPERIMENT 1
Let’s do a simple experiment. Build a gear box with two motors attached to it. Make sure you can easily
change the gear ratio at ease.
Hypothesis: _ lower speed will give you more consistent distance _
Independent Variable:
driver motor running for 360 encoder value
Dependent Variable:
follower motor (the output shaft) encoder value
Control Variable:
Gear Ratios
Steps 1: Create a gear box – with this gear system. Attach two motors on both axles as indicated. We call
it driver motor and follower motor.
Step 2: Identify the pairs.
Step 3: Calculate the gear ratio : _______________ . Show your work on the back of this worksheet
Step 4: Program your robot to display the encoder value for both motors . Run your driver motor for 360
encoder value. Fill in the following table with the encoder value for the follower motor:
Write down encoder value of the follower motor for
each Trial.
1
2
3
4
5
6
7
8
9
10
Median
value
Average
Error
(after
margin
discarding (+ / -)
2 outliers)
100%
50%
25%
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
Step 5: Program your robot to run your driver motor for 720 encoder value. Fill in the following table with
the encoder value for the follower motor:
Write down encoder value of the follower motor for each Trial.
1
2
3
4
5
6
7
8
9
10
Median
value
Average
(after discarding 2 outliers)
Error margin
(+ / -)
100%
50%
25%
Step 6: Based on your observation, fill in the following:
Instructor will provide the value of the follower motor. Then you will
calculate the value of the driver motor.
Driver motor
90
180
270
540
Follower motor
Follower motor
Driver motor
Challenge questions: If the role of driver and follower gear switches.
1. When driver motor turns 1 time = follower motor turns _____times.
2. When driver motor turns 360 encoder value = follower motor turns _______ encoder value.
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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Analytical Fun with Math and Robotics – Track 1
EXPERIMENT 2
Now, we will use your chassis to do the test. Let’s do a simple experiment. Build simple robot with a non1:1 gear ratio. Prefer you will create it to allow you to change the gear ratio at ease.
Hypothesis: _Gearing down will yield high accuracy_
Independent Variable:
Time in seconds
Dependent Variable:
Distance in cm
Control Variable:
Gear Ratios
Test 1
a.
b.
c.
d.
Create a configuration with gear ratio of ____________.
Program it to run for 5 seconds.
Run it for 10 times, and measure the distance it travels for each time.
Plot it on the graph.
Write down the distance in centimeter for each Trial.
1
2
3
4
5
6
7
8
9
10
Median
value
Average
Error
(after
margin
discarding (+ / -)
2 outliers)
100%
50%
25%
Test 2
a.
b.
c.
Modify the gear ratio to gearing it up.
Program it to run for 5 seconds
Perform the same experiment as above.
Test 3
a.
b.
c.
Modify the gear ratio again to gear it down.
Program it to run for 5 seconds
Perform the same experiment as above.
3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ 08876  908-595-1010  www.stormingrobots.com
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