# 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.