# Exploring with Slopes Author: Tyler Styons Unit Title: Exploring with Slopes                                   Grade: 8th Subject: Math Estimated Duration: 6 - 50 min class periods Unit Activities: Acivity 1 - Robots vs. Astronauts Activity 2 - How to Control a Robot Activity 3 - Slope Intercept Form Activity 4 - Mission Launch Activity 5- Mission Complete Date: July 22, 2015
###### The Big Idea (including global relevance)

The Big Idea in this Unit is the topic of Robotics, specifically those used in space exploration. Students will explore basic concepts in terms of how robots are used in space exploration and how robots are controlled once they reach space. Students will demonstrate an ability to use what they know about slope and the equations of lines in order to control their robot.

###### The Essential Questions:
• How can effective mathematical models be used to direct a robot to move on its own?
• When exploring in outer space what would be more effective, a human or a robot?
• What designs of robots are used when exploring Outer Space?
###### Justification for Selection of Content:
• Students previously scored poorly on standardized tests, end-of term test or any other test given in the school or district on this content.
• Misconceptions regarding this content are prevalent.
• Content is suited well for teaching via CBL and EDP pedagogies.
• The selected content follows the pacing guide for when this content is scheduled to be taught during the school year. (Unit 1 covers atomic structure because it is taught in October when I should be conducting my first unit.)
###### Misconceptions:

The misconceptions for this unit lie in that student’s inability to plot points on a coordinate grid. If the students do not have this basic ability they will not be able to plot the points in the Excel workbook to model the robot’s path or the location of the obstacles.

###### The Hook:

The first day of the unit will be discussing the topic of space exploration and the pros and cons of human exploration versus robotic exploration. Students will be given the following website to examine to start a discussion of the costs and benefits of both forms of exploration:

http://www.racetomars.ca/mars/article_robots.jsp

From here students should be asked to decide which of these would be the best based on classroom generated criteria.

###### Unit Lessons and Activities:

1 Day = 1 50 Minute Class Period

Lesson 1 (4 Days): In this first lesson, students will develop a basic understanding of why we might choose robots to explore space instead of humans. We will begin to develop the idea that there are mathematical ways that we can program robots and describe their path. We will ultimately arrive that the slope intercept form of equations and the four ways slope is defined will help use describe the path

Activity 1: Robots vs. Astronauts. (1 Day)

Students will explore articles that outline the pros and cons of sending both humans and robots to space. Once the students arrive that there are several reasons why a robot might be better, students will generate questions about robotic space exploration. This will eventually lead to the discussion of controlling the robotic movement.

Activity 2: How to Control a Robot? (1 Day)

As a class, students will discover the need to give very specific directions when describing the movement of such an expensive piece of machinery. NASA has developed an introductory activity to play as a class to illustrate to students the importance of precision in directions. Follow the link to find the activity: http://www.nasa.gov/audience/foreducators/robotics/home/ROVER_nf.html#.VaXAoflVikp

Students will be introduced to the concept of programming and will arrive at the point that equations and descriptions of slope will be helpful when giving directions.

Activity 3: Slope Intercept Form and Slopes (2 Days)

Students will be exposed to many forms of practice with Slope Intercept form and the four different types of slope.

Lesson 2 (2 Days): The second lesson will revolve around the students using their knowledge of the slope intercept form of equations along with the descriptions of slope to program the robot to follow a certain path. Students will be able to test their solution using an Excel tool to graph the path of the robot to ensure that it will not hit any obstacles.

(While this Unit/Lesson could focus around the Excel graphing tools and the EV3 programming software, for my purposes the Excel tool will be premade so that the students will simply have to insert their ordered pairs. Similarly with the EV3 programing, the instructor should have already developed the “line follower” programing so students can make their on the floor with electrical tape and the robot will follow the path. The “programming” for the students comes in the form of slope intercept equations and being able to identify the various types of slopes that a line can have)

Activity 1: Mission Launch (1 Day)

Students will be given all of the parameters of the challenge. Students will begin to design the paths of their robot on paper and then they will move to the Excel Workbook to test their initial results culminating in finding the total distance that their robot traveled.

Activity 2: Mission Complete (2 Days)

Students will have finished their first paths and determined the total distance traveled by the robot. Students will explore alternatives to this initial paths, select the best solution based upon finding the equations that allows for the most distance to be covered, and will ultimately program the robot to travel along the proper path, avoid all obstacles, and hopefully explore as much of the planet’s surface as possible.

###### Description of Challenge

Through knowledge of linear equations, effectively program the path of a robot to traverse across adverse terrain. Once the robot is put into motion, the team will not be able to alter the robot it any way.

Before the robot can be used, students must use some sort of mathematical modeling to simulate the path of the robot to be sure that no obstacle will be hit. (This will be done in an Excel Spreadsheet that will graph the path of the robot based on ordered pairs that the students will put into a table. In this same table they will also have to input the obstacles to ensure that the path of the robot will not cross these obstacles.

There will be a cost related to the distance that the robot will travel. The challenge will be to use the least amount of battery power to move the robot from one point to another. (Students will be able to use the EV3 Data Logging Software to record the distance that the robot traveled.

An extension to this would be for the instructor to have various missions. The above challenge could be one mission however to reinforce the concept of the slope intercept form of writing a line, students could be given multiple locations that they must reach from and initial point (y-intercept) and then write equations to reach each of the locations.

###### List of Constraints Applied
• Students will be given the location of the obstacles that the robot must not hit.
• They will have to design a path that must use all of the 4 types of slope (positive, negative, undefined, and zero).
• Students will have to generate a mathematical model to simulate the path of the robot before it travels.
• Understanding that the students up to this point have only studied linear equations the robots will only be able to move in a series of straight lines across the terrain.
• If the robot crashes into an obstacle then this is an automatic mission failure.
• Each movement the robot makes will correspond with a certain dollar amount therefore students will want to design the most efficient path in order not to waste movements.
• Anticipated Guiding Questions
• Once robots get to the planet how do they move?
• When robots move how are they able to avoid obstacles on in the terrain?
• What are ways that we can model the path a robot will take before it actually moves?
• Are there certain words that we can use to describe the path that the robot will travel on?
• Is there a mathematical way that we can describe the path of the robot?
• What is the slope of the line and how is it used in the slope – intercept equation?
• What is the y – intercept and how is it used in the slope – intercept equation?
• How does the slope of a line correspond to the movement of the line?
• What are the four ways that we can define slope?
###### How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.

Students will test or implement their initial path by testing their path through the Excel model. Students will plug the values of the path in the model that will be created in the spreadsheet to make sure that there will be no conflicts with the obstacles. Students will then be able to test this path by using the robot that will travel along the Cartesian coordinate grid that is on the floor. The data collection software will be able to track how far the robot traveled and thus students will be able to determine how much of the surface the robot traveled. From this data, students can redesign their path to try and cover as much of the planet’s surface as possible.

The evidence that the solution worked will be that the students are able to use the model to accurately predict the path of the robot as well as the robot actually performing the task of navigating the obstacles on the coordinate grid on the floor.

In completing the challenge, students will have several opportunities to redesign the path that their robots take. Depending on the academic level of the students, there are several opportunities to extend the challenge. In designing a path, students will be required to gather information on how the robots can move (in in a linear motion as these are the types of equations the students are familiar with), and identify the alternatives of the various paths the robots can take. While the students will have the initial challenge of defining the path of the robot and exploring how cost relates to the distance traveled, the opportunity to involve programming into the actual challenge can be incorporated.

###### How will students present or defend the solution? Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.

The students will present their solution in the form of the excel workbook that they will create as well as the path that the robot takes. They will also be charged with presenting the math that not only will define the path of the line, but also the measurements of how much distance the robot was actually able to be explored.

###### What academic content is being taught through this Challenge?

At the most basic level students will have to use their understanding of the coordinate grid to identify and label points on the graph. The academic content that is being taught through this Challenge is a student’s ability to use the slope intercept form to define a line.

###### Real world applications:

While the concept of space exploration is a concrete activity, the idea of space is a somewhat abstract notion. By using the EV3 robot to actually travel along the path that the students create will result in a more concrete experience.

Activity 4 and 5

###### Societal Impact:

The issue of robotics that is robotics in a general sense not just in the area of space exploration, is a growing field in today’s society. Robots perform many tasks that were formally

Activity 4 and 5

###### What careers will you introduce (and how) to the students that are related to the Challenge? (Examples: career research assignment, guest speakers, fieldtrips, Skype with a professional, etc.)

This Unit could be paired up with any career involved in mechanical engineering as they would be involved with the actual construction of the robot. There are also many opportunities with field trips to iSpace that could be used to also explore the concept of space exploration.

###### Unit Academic Standards - CCSS

CCSS.MATH.CONTENT.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

CCSS.MATH.CONTENT.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

 Common Core State Standards -- Mathematics (CCSS) Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Model with mathematics Attend to precision