Author:
William Allred, Carrie Robledo
Subject:
Mathematics
Material Type:
Activity/Lab
Level:
High School
Tags:
Area, Linear Equations, Minimizing Cost, Minimizing Distance, Slope
License:
Creative Commons Attribution Non-Commercial Share Alike
Language:
English

Education Standards

Math I: Corralling the Sheep - Exploring Linear Equations

Math I:  Corralling the Sheep - Exploring Linear Equations

Overview

Students are given 4-5 coordinate points, that will represent the sheep.  First, they are tasked with creating a fence around the sheep. The students will use the endpoints of each piece of fence to compute the slope, y-intercept, domain and equation of the line. They will then code the rover to draw their lines. Finally, the students can calculate the area/perimeter of their fence and calculate the cost to build the fence. The students will then be challenged to minimize the area, perimeter and cost of building their corral, recalculate the equations of their lines, stating their new slope, y-intercept, and domain.

Instructor Directions

Engineering Design Process

Project Description

Name of ProjectCorralling the Sheep - Exploring Linear Equations
Subject AreaMath 1
Targeted StandardsNC.M1.A-CED.1 -  Create equations in one variable that represent linear relationships and use them to solve problems.NC.M1.F-LE.5 - Interpret the parameters a and b in  a linear function f(x)=ax+bNC.M1.G-GPE.4 - Use coordinates to solve geometric problems involving polygons algebraically
  • Use coordinates to compute the perimeter of polygons and areas of triangles and rectangles
  • Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral
Driving Question / Problem / ActivatorCan you create a fence around given coordinate points (sheep) that will minimize the area of the polygon?
Project SummaryStudents are given 4-5 coordinate points, that will represent the sheep.  First, they are tasked with creating a fence around the sheep. The students will use the endpoints of each piece of fence to compute the slope, y-intercept, domain and equation of the line. They will then code the rover to draw their lines. Finally, the students can calculate the area/perimeter of their fence and calculate the cost to build the fence. The students will then be challenged to minimize the area, perimeter and cost of building their corral, recalculate the equations of their lines, stating their new slope, y-intercept, and domain.
Estimated Time1-2 class periods (1.5 hours each)
Materials / Resources (including link to slideshow if available)*Assignment worksheet, including rover code*large grid paper*Skinny dry erase marker*Ti Innovator hub and rover*Ti 84 Plus CE calculators*Cotton balls for sheep
TagsLinear EquationsSlopeMinimizing distanceAreaMinimizing cost

Project Outline 

AskStudents will create and write linear equations, with restricted domains, to create a polygon that encompasses given coordinate points.
ImagineStudents will draw their corral on paper and identify their potential endpoints to use.
PlanStudents will then begin calculating the features of their equations, including slope, y-intercept, and domain.
CreateStudents will write their equations, program them into the rover, and correctly input the key features into the program. The rover will draw the lines that have been entered.
ImproveStudents will be challenged to minimize the amount of fencing they use, area of their corral, and cost of their materials.
Closure / Student ReflectionsStudents will reflect on how the key features are related to the endpoints of the lines, and how the area/perimeter are affected by changing the features of each line.
Possible Modifications / ExtensionsTeachers could add restrictions to make the task more challenging, including requiring the students to include a pair of parallel lines, giving the students a budget to adhere to or giving the students a specific shape for their corral.

Evaluation (Pre/Post)  

Insert Links to Google Forms

 

Pretest Link:

Post-test Link:

 

Credits or Modified From

Texas Instruments: Leveraging TI Innovator Rover in the Math Classroom

 

Additional Resources / Help for teaching this lesson

 

Pretest Link:

Posttest Link:

 

Sample Pictures / Video

 

  
  

 

 

Teacher Comments of what worked / did not work well

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