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You are reading an older version of this FlexBook® textbook: CK-12 Modeling and Simulation for High School Teachers: Principles, Problems, and Lesson Plans Go to the latest version.

Activity: Roomba Introduction (45 minutes)

Ask students to raise their hands if they have chores at home. Have students name those chores and record them on the board. Ask students to raise their hands if they would like it if they didn’t have to do those chores anymore. Ask them if they can think of things that might make that possible. Accept all reasonable answers and record them on the board. Students will likely mention robots. Ask students if they have heard of the Roomba (an autonomous robotic vacuum cleaner). If students are familiar with the Roomba, have a few volunteers describe what the Roomba is and what it does.

Play a short portion of "Examining Roomba’s Motion" found on the Roomba DVD (if available, run Roomba in the classroom, or you can find the video on Youtube: http://www.youtube.com/watch?v=hcgPARH6lzk) to demonstrate the Roomba.

Tell students that they will be working as teams of engineers to compete to design iRobot's next generation of Roombas. Ask students to explain what an engineer is. One explanation is that "engineers are the men and women who design, build, test, repair, and establish many products used in today’s world." Ask students if they know anyone who is an engineer or if they can think of any specific types of engineers (automotive engineer, biomedical engineer, sound engineer, etc.).

If time allows, project the Discover Engineering website http://www.discoverengineering.org/.. Click the "What’s Engineering?" tab, followed by the "Career Profiles" tab. There are many different types of engineering jobs listed under "Select a Career." Clicking on any of them provides a brief description. Another useful feature on the website can be accessed by choosing the "Cool Stuff" tab and then choosing the "Engineers" button. This showcases areas that might be of interest to your students, such as "Cars, Cars, and Cars!" and "Waterslide Action." Each of these areas includes a description and a list of the multiple types of engineering careers that are related to each area. Visiting this website will begin to show students the wide range of engineering career possibilities available. A possible homework/class work extension would be to have students continue to explore this website or others like it.

Activity: Engineering Design Process (45 minutes)

Ask students to share the results of any additional exploration of engineering websites. Give an example like "designing a car" and ask students to name as many types of engineers that might work on that as they can think of.

Remind students that in the last class, you told them that they would be working as teams of engineers to compete to design iRobot's next generation of Roombas. Ask students what steps they think they will need to take in order to "attack" this challenge. Record student ideas on the board.

Tell students that engineers use something called the Engineering Design Process (EDP). Break students into teams of 2-4 and pass out handouts containing EDP steps (see "Resource Pages" located at the end of this lesson). Instruct students to work as a team to put the steps in an order that makes sense to them. Groups may arrange the steps in various orders. Circulate and discuss why they made the choices they did. Offer alternatives.

Working as a team, students should label a piece of lined paper "Engineering Design Process Steps and Reflection" and list the steps in the order that they think is correct. Underneath the steps, they should write a paragraph explaining why they put the steps in the order they did. As a class, discuss the order of the steps. Lead them to see that there are multiple possibilities and not one "correct" answer. A good engineering design process, like the scientific method, doubles back on itself and works more in a cycle, rather than a series of linear steps.

Project "Steps of the Engineering Design Process" (see "Resource Pages") on a screen using an overhead or LCD projector. Cover the steps, revealing one step at a time for discussion. Ask the class to generate an example that could use this process, and apply it to each step.

Project "A Visual Representation of the Engineering Design Process" (see "Resource Pages"). Tell students that this figure represents the steps you just discussed, but it shows them occurring in a circle, or cycle. Ask students to make connections with other things they have learned about in science. Students may mention the water cycle, life cycles, etc. If students mention the scientific method, let them know that you will be returning to that idea.

Project "ANOTHER Visual Representation of the Engineering Design Process" (see "Resource Pages"). Students should notice that this EDP is different from the 8 steps they had to work with. Explain to the students that the EDP is similar to the scientific method. EDP is not the only way to solve an engineering problem, but a good proven approach. Also point out that the steps don’t necessarily follow a single path — often, scientists and engineers will go back and redo steps as they learn more about their problem and the limitations of their projected solution.

Discussion question: Why do you think understanding the engineering design process is an important tool for engineers?

Activity: Identifying the Problem and Constraints (45 minutes)

Remind students that they will be working as teams of engineers to compete to design iRobot's next generation of Roombas. Now that they have had a short course in the Engineering Design Process, they are ready to begin the challenge.

Ask for student volunteers to explain the general steps of the Engineering Design Process (accept any reasonable answers).

Hand out the "EDW: Engineering Design Worksheet" (see "Resource Pages"). Tell students that they will get another blank copy when it is time to submit it, so they should feel free to mark up the first copy but be sure to make the final copy presentable. Give students 5 minutes to decide on a team name. Students should record their team name and their names under "Project Engineers." The job title could be something like "Roomba Redesign."

Students should then work in their groups to define the problem. When groups have come to a consensus about the problem, ask a member from each group to share. The problem is basically to improve the current Roomba design.

At this point, tell the students that you have received an email memo from a fictional institution called Robotics University (see "Resource Pages") which outlines the specific design criteria and goals. Project the memo or hand out paper copies to each group. Have the students summarize the design criteria and goals on their "Engineering Design Worksheet." Their goal should be to design software so that the Roomba will finish cleaning a room more efficiently.

Activity: Qualitative Roomba Observations (30 minutes)

The next step on the "Engineering Design Worksheet" is "Research the Problem." Start by asking students to share ideas in their groups about how they think the Roomba works. They should choose a recorder to make notes about their ideas on paper. After the groups have discussed, someone from each group should share the group’s ideas with the class.

Ask the class how they could research the Roomba and display answers on the board. Answers should include using the Internet, contacting iRobot, and observing the Roomba at work. If time allows, have the students do some Internet research about the Roomba and how it works. (This could also be done as additional research after the classroom observation.) Students should suggest observing the Roomba in action. Tell students that you will be playing a video clip of the Roomba vacuuming on a grid titled "Examining Roomba’s Motion" http://www.youtube.com/watch?v=hcgPARH6lzk. (If possible, have a Roomba in the classroom for the students to observe.) Remind students that all good scientists keep accurate records of their work. Hand out Roomba observation reports to each student. Discuss the difference between qualitative (non-numerical) and quantitative (numerical) data. Tell students that they will be able to watch the Roomba more than once. Ask them to focus on collecting qualitative data about the Roomba during the first viewing. Tell them they will be turning in individual observation reports with their proposal. Then inform them that they will also have to compile the most relevant data into a group report. Give the students time to share their observations with their group members. The final group report will be completed near the end of the activity.

Activity: Explore NASA Website and View AskNASA Video (60 minutes)

Ask students if they have ever heard of the highly rated hit TV show AskNASA. Tell them that you have found out that today’s episode features a scientist who may be able to help them with the Roomba Design Engineering Challenge.

Before projecting the AskNASA video, ask students what they know about NASA. Many will associate NASA with the Space Shuttle and trips into space. Use the discussion to introduce/review the concepts of aerospace and aeronautic design. According to the Merriam-Webster Online Dictionary, aerospace is "space comprising the Earth's atmosphere and the space beyond," and aeronautics is "1: a science dealing with the operation of aircraft, and 2: the art or science of flight." Display these definitions on the board and discuss them. Ask students what they could do to find out more about NASA. Hopefully, someone will suggest going to the NASA website. Display it for the entire class (or, if you have the capabilities, direct all students to the website).

Go to: http://www.nasa.gov

Point out to students that the NASA website contains a lot of information and features, and that they will have the opportunity to explore them at a later time. Let them know that there is a section just for students and that it would be a good place for them to start.

Click on the "For Students" tab near the top of the page.

Show students that the resources are arranged in grade clusters. Point out the SEARCH feature in the upper right hand corner of the page and type in, "What is NASA?"

The link that comes up (http://www.nasa.gov/audience/forstudents/k-4/stories/what-is-nasa-k4.html) is geared toward K-4, but it gives a good quick overview. From there, type "What does NASA do?" into the SEARCH box.

This takes you to an overview (http://www.nasa.gov/about/highlights/what_does_nasa_do.html) and is a good jumping off point for discussion, as students may be unfamiliar with many of the terms and projects that it discusses. Use the NASA website to highlight some of NASA’s work and contributions. Encourage the students to do some exploring on their own for homework, of if there is additional time at the end of class.

Now that students are a bit more familiar with NASA, tell them that it is time to watch the following video, titled "AskNASA" http://www.youtube.com/watch?v=UMaCNekJobE&feature=related. Tell them that you would like them to focus both on the Roomba-related suggestions made by Sharon Padula, as well as the information she shares about her own line of work.

Project the AskNASA video for the entire class.

At the conclusion of the video, have a class discussion about what the students learned in the video.

Activity: The Traveling Salesman Problem (30 minutes)

Remind the class that they are essentially working on an optimization problem. Ask students to share ideas about what it means to optimize something. The Merriam-Webster Online Dictionary defines optimization as "an act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically: the mathematical procedures (as finding the maximum of a function) involved in this." Stress to the students that engineers, including aerospace engineers, use optimization in their work all the time. For example, when engineers at NASA are designing or attempting to improve existing designs of aeronautic products, they want to optimize as many aspects of the products as they can.

For example:

  • When designing a new rocket, NASA engineers optimize its structure to be as light as possible, while simultaneously able to withstand all the structural loads it will encounter during a flight into space.
  • When a rocket takes off the ground and travels toward space to get into orbit around Earth, its trajectory is optimized to deliver the maximum amount of payload into space.

A good example of an optimization problem is a famous scenario called "The Traveling Salesman Problem." In this scenario, a traveling salesman has to stop in a certain number of cities. The task is for him to visit each city exactly once in the shortest possible tour.

Seems like it could be pretty easy, right? (Draw the following on the board.) Let’s say you have to visit two cities and they’re 10 miles apart. Well, you obviously travel from point A to point B. Easy. Now add city C. If city C was somewhere on the straight path between A and B, you wouldn’t have a problem, but what are the chances of that happening? So let’s say City C is down here, below the path. Well, now you have a few options. Hand out the "STSP: Simple Traveling Salesman Problem" and review the directions with the students. Each individual student should work independently.

What are your possible paths? (A to B to C [or C to B to A], A to C to B, C to A to B). Note that the problem has been studied by researchers from mathematics and many branches of science, including chemistry, physics, and computer science.

Activity: Traveling Salesman Problem Simulator (30 minutes)

Direct students to the Traveling Salesman website:

http://www.tsp.gatech.edu/games/tspOnePlayer.html

Students have a choice of using the TSP simulator individually or in a head-to-head competition. Students should begin by using the single-player setup. The idea is to optimize the trajectory of the salesman by connecting the dots using the shortest length path. They can start by clicking on any dot, and then continue to click them in the order they want. Once the loop is complete, the simulator will tell them how close they are to the optimized (shortest) path. Students can also click "o" to see the optimized path. Students can experiment with this simulator by generating new puzzles that are more or less complicated. Each student should print at least one of their paths with the optimal path overlaid for their binder. (More advanced students should be able to verify the percentage difference from the optimal path by comparing the optimal length to their path length.) Class should end with discussion of the Traveling Salesman Problem and how it relates to the optimization problem of the Roomba.

Embedded Activity: Averaging Line Length Estimates (15 minutes)

Draw a horizontal line on the board (at least 24 inches long, up to as long as your board space allows). Ask students to estimate the length of the line in inches and record their estimate on a sticky note. Collect the estimates and display them on the board. Ask students to make observations about the estimates (lowest, highest, repeats, clusters). Discuss the fact that they can’t all be correct. Then tell the students that all of the students working together will do better at estimating the length of the line than if you had just asked one or two of them to try. Have students use the class data to calculate the mean. Ask for student volunteers to announce the mean. Get a few students to verify it. Then ask for volunteers to measure the line you have drawn on the board. Have two or three students measure the line to the nearest inch. The measured length should be pretty close to the calculated one. Explain to students that scientists use this technique of compiling data to come up with an average all the time. (In fact, it is a good optimization technique.)

Activity: Quantitative Roomba Observations (45 minutes)

Now that students have completed a qualitative analysis of the Roomba, and heard from a NASA engineer about the process of optimization, they should have some understanding that the best option they have for improving the Roomba’s cleaning is to optimize its trajectory. However, in order to optimize its trajectory, students must have a more quantitative understanding of its current trajectory. In order to accomplish this, students will need to measure the Roomba’s speed, length of time when stopping to change direction, graph its motion, and use a simulator to compare the efficiency of the Roomba’s path as it moves around the room, and the efficiency of the students predicted, more optimized path.

Students need stop watches, rulers, and graph paper to complete these measurements.

Begin by reviewing the concept of speed. Speed is equal to distance over time. Students can use the "Calculating Speed" clip on the DVD or on Youtube http://www.youtube.com/watch?v=X_KGRdwzG7Q. Students should begin by making a scale drawing of the grid on graph paper. Each square in the video is 18 inches by 18 inches. Students should watch the video and trace the straight line path of the Roomba on their graph paper and determine the length of the path. Now, students should repeat the stopwatch to measure the time it takes the Roomba to travel that path. Students should watch the clip and measure the time at least three times. Students should use each of these times to calculate the Roomba’s speed, and then average their answers. Each team should then report out their average measured speed. Each team’s speed should then be averaged together to get a more accurate speed for the Roomba.

Use the "Predicting Time" video clip to measure how much time the Roomba takes to change direction when it stops at a boundary. Again, make several measurements and calculate an average so that the value used by the class is more accurate.

(Note to teachers: There may be other portions of the video clips where the Roomba is traveling a straight line path that would be appropriate for calculating the average speed of Roomba. These can be used for comparison. For more advanced students, there is a clip of the Roomba traveling a straight path along the hypotenuse of a triangle. Students should use the Pythagorean theorem to calculate the distance traveled and then calculate the speed.)

Activity: Using a Simulator to Predict Time (60 minutes)

Materials: graph paper with Roomba grid, stopwatch, Excel Simulator

Now students enter their measurements into the simulator and use them to predict travel time for the Roomba’s trajectory. Students begin by observing the Roomba in the following clip http://www.youtube.com/watch?v=NmhrVBM5GO4 titled "Estimating Time." (Note to teachers: you may want to use just a portion of this clip when you begin. The entire clip runs nearly 2.5 minutes, and it might be difficult for students to track the entire trajectory.)

Students need a copy of the grid layout for the Roomba. (See resources at the end of this document.) There are two things students should do as they are tracking the Roomba’s trajectory:

1. They should check off how many times the Roomba enters a given box. Simply tallying each time it enters a box will be easier than trying to trace out the entire trajectory.

2. They should make a tick mark in an exterior box any time the Roomba stops along the perimeter to change direction.

Once they have completed the observation and recorded their data on their grid sheet, they are ready to use the simulator. Using the average speed calculated in the previous activity, calculate the average time for the Roomba to cross a given square. Enter this into the simulator. Enter in the time observed for the Roomba to change directions. Enter the number of tally marks recorded for each box on the grid. The simulator will then tell the student how long it would take for the Roomba to travel that trajectory. Students should compare results.

Return to the video and use a stop watch to calculate the actual time of travel for the Roomba. Average all times together to get a more accurate answer. Compare the measured times to the times predicted by the simulator. How close are they? What might account for the differences in these answers? (Note to teacher: More advanced students can calculate the percentage difference in these two quantities.) Are these differences acceptable? Will the simulator still help us to create a more optimized trajectory?

Activity: Using the Simulator to Construct a More Optimized Trajectory (60 minutes)

Begin by reviewing students’ qualitative statements that describe the Roomba’s motion. Think about when it needs to make a decision (change of direction) and what kind of choices it has for that change.

Students next observe the "Predicting Trajectory" clip http://www.youtube.com/watch?v=byhhgHUUC1k. They can either use a stop watch or the simulator to measure the length of time for the trajectory. Keep in mind that they are trying to determine the Roomba’s efficiency in vacuuming by determining how long it takes to reach the two marked points.

Students can now work in their teams to develop a more optimized trajectory. Remember, Roomba, will not know when it has crossed a dot, so it cannot not just change direction because it crossed one of the dots. (If you have a Roomba in your classroom, it will be good to show at some point that if you repeatedly start the Roomba at the same point in the grid, it will not take the same trajectory every time.) Students should draw their more optimized path on graph paper, and then use the simulator to predict the length of time each of those trajectories would take. Students should produce at least two different trajectories to examine.

Activity: The Wrap-Up (60 minutes)

Each engineering team will be using a binder to collect all of their evidence and support for their experiment. All handouts, data recordings, and any additional support should be neatly organized and labeled in their binder.

Their binder should also include a one-page summary of their experiment. The summary should identify: 1) the purpose of the experiment; 2) a list of 5 things they learned or skills they developed from working on this project; and 3) a list of at least 2 questions or ideas they would have explored further if they had had fewer constraints on what they were allowed to change in the design (e.g. time and resources). Finally, they should submit a list of at least 3 decision-making statements that might optimize the trajectory of the Roomba.

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