Brief Description of Lesson/Task/Activity: Within the physical science strand of 7th grade science, students focus on the motion of objects. In this task, students will act as a car insurance company representative who is reviewing driving data from a vehicle’s diagnostic port and developing a personalized graph and written analysis for the customer to maximize good driving habits (and lessen the insurance company’s risk). Students will use the initial data and mathematical formulae to develop distance-time and velocity-time graphs through this activity. The real-world and interdisciplinary nature of this activity, as well as its inquiry basis, allows students to build meaningful connections while promoting 21st Century Skills.

Time Frame: 1 class period (60 minutes)

Type of Differentiation for AIGs:

• Extension

Adaptations for AIGs:

• Content
• Process
• Product

Explanation of How Resource is Appropriate for AIGs: AIG students in the middle grades often are advanced in mathematical reasoning skills. As a result, they quickly grasp the concept of line slope in relation to the distance-time graphs in the 7th grade Essential Standards for Science. To challenge these students, it is necessary to provide opportunities for them to use their existing understanding to develop additional graphs, such as the velocity-time graph and discover the relationships between these graphs. The real-world application of this skill, seen in commercials for a common car insurance company, will appeal to AIG students. Explanatory writing is essential in advanced courses (AP sciences, etc.), so any opportunity to develop this skill is beneficial to AIG students. Finally, self-assessment using defined criteria further develops the metacognitive and evaluative/evidentiary reasoning ability of these students.

Needed Resources/Materials:

• Data for the initial distance-time graph
• Graph paper or graphing software
• Formulas for velocity: v=d/t in a given direction  and acceleration: accel = (FV-OV)/(T2-T1), AKA “rise over run” m=(y2-y1)/(x2-x1)
• Guiding questions for graph analysis (see attached)
• Format for Customer Driving Habits Report (see attached)

Sources: Teachers may choose to use existing materials within text ancillaries or from internet sites to generate the vehicle driving distance-time data chart. If the teacher chooses to allow students to use computer graphing software, consider using a site similar to the Kid’s Zone webpage from the National Center for Educational Statistics – http://nces.ed.gov/nceskids/createagraph/ or collaborate with Computer Skills teachers to teach students how to construct a graph from Excel.

Teacher Notes: Some prerequisite knowledge/skills are required. Students should have demonstrated success at interpreting distance-time graphs and calculating the speed of an object using either the speed formula (s=d/t) or the formula to determine the slope of a line (m=y2-y1/x2-x1) aka “rise over run” OR should have sufficient mathematical reasoning skills to use these formulae without significant difficulty if presented with them for the first time.

The teacher may choose to show an internet clip of a commercial for a car insurance company that offers a discount to its customers if they allow the company to track driving data. Explain to students that they will be completing a RAFT activity. They will be assuming the ROLE of a car insurance company representative who is reviewing driving data from a vehicle’s diagnostic port. The AUDIENCE will be the insurance customer (teacher). The FORMAT will be the development of a personalized graph and written analysis for the customer on the TOPIC – the driving habits of the customer. 

The teacher should then review the use of the necessary formulae and the different y-axes on the two types of graphs: distance-time and velocity-time. The teacher should avoid demonstrating more than one data point on each graph type to prevent students from drawing conclusions about the graph relationships prior to the students’ own work. 

Provide students with the data set for the distance-time graph and the guided questions worksheet. After graphing this data, students answer guided questions about the visual representation of the data, such as:

• During line segment AC, what distance was traveled by the driver?
• In how much time did the driver travel line segment AC?
• What was the driver’s speed during line segment AC?
• Was the driver’s speed increasing, decreasing, or remaining constant from line segment AC to line segment CG?
• How does the slope of the line demonstrate this?  

  
Depending on previous student exposure to motion concepts and formulae, the teacher may need to provide an additional explanation of acceleration and how acceleration rates can be determined by examining changes in an objects’ velocity. Acceleration can be positive (an increase in velocity) or negative (a decrease in velocity). By definition, a change in velocity can also be related to a change in direction, but demonstrating that concept mathematically at this level through vectors is not yet appropriate. However, students should be conceptually aware of this aspect of acceleration.

Students should then use the d-t graph to generate the needed information for the velocity-time graph using the distance/time formula or the slope formula. After graphing this data, students should answer guided questions about the visual representation of the data, such as:

• During line segment AC, was the driver experiencing positive acceleration (velocity changes at an increasing rate), negative acceleration (velocity changes at a decreasing rate), or constant acceleration (velocity changes at a constant rate)?
• How does the slope of the line demonstrate this?
• How does constant acceleration on this v-t graph differ from the same graph segment of constant acceleration on the d-t graph?
• How is positive acceleration on this v-t graph similar to/different from the same graph segment of increasing speed on the d-t graph?
• How is negative acceleration on this v-t graph different from the same graph segment of decreasing speed on the d-t graph?

Using the Format for Customer Driving Habits Report, students should explain to the customer the purpose of each of the two graphs and how each represents the data gathered from his/her vehicle’s diagnostic port. Provide each student with a copy of the Driving Habits Report rubric, which should include the following elements:

• the purpose of a distance-time graph
• an overview of the different line slopes and what they represent 
• at least three specific data points and what they mean about the driver’s habits to further elaborate on the overview
• the purpose of a velocity-time graph
• an overview of the different line slopes and what they represent
• at least three specific data points and what they mean about the driver’s habits to further elaborate on the overview

Teacher Notes: The teacher can further elaborate on this real-world task by providing an “exemplary” driver’s set of graphs that show slower acceleration rates, slower deceleration rates, a lower rate of constant speed that would be more likely to be in accordance with posted speed limits, etc. and ensure that the customer’s data points were inconsistent in these areas. The rubric should then be adjusted to include advice to the driver on how to change his/her driving habits to improve his/her insurance rate because of the decreased risk associated with him/her.