FOREWORD. Robotics is Everywhere! What is a robot? Can you think of some examples? Write them here: How is Math Involved in Robotics?

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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 Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

2 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 P a g e

3 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. Definition One whole number is divisible by another if, after dividing, the remainder is zero. If one whole number is divisible by another number, then the second number is a factor of the first number. 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. Example 18 is divisible by = 2 with a remainder of 0. 9 is a factor of is divisible by is Divisible by 3: = 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 P a g e

4 DIVISIBILITY RULES: Divisible If: Examples: by: Yes No 2 The last digit is even (0,2,4,6,8) The sum of the digits is divisible by =12, and 12 is divisible by =10, but 10 is NOT divisible by 3 4 The last 2 digits are divisible by is divisible by is NOT divisible by 4 5 The last digit is 0 or is NOT divisible by 5 6 The number is divisible by both 2 and is even, and 1+1+4=6 and 6 is divisible by =11, but 11 is NOT 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 Double 2 = 4, and 67 4 = 63, and 63 is divisible by Double 5 is 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 - # Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

5 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 P a g e

6 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 Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

7 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 degrees 30 cm x = 360 degrees 30 cm 15 cm = 720 degrees 3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

8 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: Dependent Variable: Control Variable: driver motor running for 360 encoder value follower motor (the output shaft) encoder value 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: 100% 50% 25% Write down encoder value of the follower motor for each Trial Median value Average (after discarding 2 outliers) Error margin (+ / -) 3322 Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

9 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 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 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 Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e

10 EXPERIMENT 2 Now, we will use your chassis to do the test. Let s do a simple experiment. Build simple robot with a non- 1:1 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: Dependent Variable: Control Variable: Time in seconds Distance in cm Gear Ratios Test 1 a. Create a configuration with gear ratio of. b. Program it to run for 5 seconds. c. Run it for 10 times, and measure the distance it travels for each time. d. Plot it on the graph. 100% 50% 25% Write down the distance in centimeter for each Trial Median value Average (after discarding 2 outliers) Error margin (+ / -) Test 2 a. Modify the gear ratio to gearing it up. b. Program it to run for 5 seconds c. Perform the same experiment as above. Test 3 a. Modify the gear ratio again to gear it down. b. Program it to run for 5 seconds c. Perform the same experiment as above Rt. 22 West, Building 15 - #1503, Branchburg, NJ P a g e