Walking the Line: Using Motion Sensors to Graph Slope - Part 1


Traci Seto - Joseph Kerr Middle School

Subject Area - Math (Algebra)
Grade Level - Middle School

Overview: To make the abstract concept of the relationship between motion and slope more concrete, students will connect the everyday, physical activity of walking to a graphing activity.

Objectives:

  • Students will make connections of slope (rate of change) of a line to motion of an object (distance vs time).

Procedure:

  • Set up motion detector, overhead or document camera, and teacher workstation. Explain the hardware set up to students and give a brief explanation on how the motion sensor works. Pass out Student Worksheet 1.
  • Explain possible student walking conditions:
    1. Start at the CBR (motion sensor) and walk away at a slow steady rate.
    2. Start at the CBR and walk away at a fast steady rate.
    3. Start at opposite end of room and walk towards CBR at slow rate.
    4. Start at the CBR and walk away at a slow steady rate at 3 meters stop for 2 seconds then walk at a faster rate to the end.
    5. Start at the CBR and walk away at a fast steady rate, at 3 meters stop for 2 second then walk at a slow rate to the end.
    6. Start at the CBR and walk away at a fast steady rate turn around at 4 meters and walk back towards CBR at a slow rate.
    7. Start at the CBR and walk away at a slow rate speeding up over the 5-meter walk.
  • Ask for student volunteers to demonstrate one - or a combination - of the above walking conditions. For each walk:
    • have students describe the walk in words
    • have students make a prediction about the graph and share their prediction
    • have student volunteers walk according to the conditions in the teacher section.
    • observe the graph of the motion and sketch the graph on the worksheet
    • copy the data points information for student table
    • calculate the slope (after the data has been collected of all walks)
  • After students have made and shared predictions for each walk, project (on overhead or document cam) and discuss the graph.
  • Use trace function to get 4 representative data points. Data points should be significant graph events (places where slope is changing). Note: slopes can be calculated after all of the motion information has been collected.


Note: This lesson has been adapted from a workshop by Gail Standiford for CMETS Middle Grades Summer Institute 2002.

Materials:

  • TI83+ Teacher’s edition with overhead panel and motion detector
  • Computer with TI Graph Link 83+ (optional)


Lesson Resources:


Standards

ISTE NETS:

  • Collaborate with peers, experts, and others using telecommunications and collaborative tools to investigate curriculum-related problems, issues, and information, and to develop solutions or products for audiences inside and outside the classroom.
  • Select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems.


Common Core Standards – Mathematics

  • Grade 7 - Analyze proportional relationships and use them to solve real-world and mathematical problems
  • Grade 8 - Understand the connections between proportional relationships, lines, and linear equations.
  • Algebra I - Create equations that describe numbers or relationships; represent and solve equations and inequalities graphically.


California Content Standards for Mathematics

7th Grade

  • Algebra and Functions 1.5 - Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
  • Algebra and Functions 3.3 - Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.


Algebra I

  • Algebra 6.0 – Students graph a linear equation and compute the x- and y- intercepts.