**Project Overview: **For this project, students will be working to create optimal bus routes for the school district. The district has determined that the bus routes are not longer the most effective or efficient based on many factors. Students will be investigating the current bus routes and will create presentations for the school board with their optimal bus routes.

Students will need to consider things such as (but not limited to):

- Location of bus stops in relation to bus riders’ residences
- Time the route will take
- Distance the route will cover
- Number of busses and drivers needed
- Miles per gallon of the busses
- Speed limits
- If the morning route will be the same as the afternoon (early bird classes and extracurricular involvement)
- Time and distance busses travel from the garage

This project is designed to be completed in groups of 3 – 4 students, but can be completed individually if desired.

**Student Learning Goals (Standards): **

Key Knowledge and Understanding (Standards):

HSA.SSE.A.1.a HSA.SSE.B.3 HSA.CED.A.2 HSF.LE.A.1 8.G.B.7

Key Success Skills:

**Prior Knowledge:** This** PBL lesson is intended for an Algebra I course. Students in Algebra i courses have been exposed to the pythagorean theorem and elements of slope prior to this unit. Throughout the unit, students will apply their knowledge of slope, rates of change and pythagorean theorem as well as many other academic skills. Depending on the demographic area and age of Algebra I students, many Algebra I students are beginning to learn to drive, which will allow them to apply their knowledge of gas milage and cost with an academic focus.**

**Project Outline: ****Challenging Problem or Question:**

Students will be given the following prompt at the beginning of the unit:

District 219 is looking to reroute the busses to be more efficient and cost effective. How can the bus routes be altered to accomplish this?

*You may not eliminate the busses unless you’ve created a more efficient route with less busses

andthe stops have to continue to accommodate all students in the same manner as they are currently.*

Students will be assigned their groups so that each group has a mix of mathematical ability and variety of problem solving skills.

After being presented with the prompt, students will watch these two videos as a class.

After the videos, students will complete a chalk talk to begin brainstorming different ideas as to what they may need to know, what to know or already have ideas about what to change with their groups.

Each group will post their mini chalk talk around the room and students will be able to continually contribute to all group’s chalk talks as the unit progresses.

**Throughout the unit:**

Each lesson in this unit will have elements that tie into the overarching PBL question.

- Graphing Linear Functions: Students will discover graphing linear functions through the lense of maps. After graphing linear functions on traditional graphing tools (paper, desmos, etc) they will be given maps to graph on to determine if a given line is a feasible bus route (based on physical streets) Students will be asked the following questions:
- What types of restrictions do you have when designing your bus routes?
- How can you accommodate for those restrictions?

- Rates of Change & Slope: Students will be discovering rates of change and slope by working with data that depicts distance vs time. This will allow students to make connections between data and linear functions. Students will apply these connections to their bus routes as students are trying to optimize the time and distance relationship for their proposal. Students will be asked the following questions
- In what ways is slope related to your bus routes? What does the slope represent for that scenario?
- Would there be a faster way to get to your location given the speed limit?
- How could re-routing the busses make sense based on the data you have collected?

Students will explore may other aspects of linear equations including restrictions on domain and range, parallel and perpendicular lines, systems of linear equations, etc, which will all contribute to students’ bus route proposals.

After each lesson, students will reflect upon the new knowledge they have gained and brainstorm with their group ways in which this new information may impact their design. As students work through the lesson, there will be continual reflection and revision of their bus route proposals. Students will be provided time for reflection and revision every other day so that the process is ongoing in accordance with new information they are learning.

**Presentation**:

At the end of the unit, each group will present their bus route proposal to the class. For each presentation, we will have a class discussion on the pros, cons, and questions and ideas for improvement. Once each group has presented their proposal to the class, groups will be given two more class days to revise their proposals based on their classmates feedback before submitting their proposals to the school board.

*Students have the creative choice to present their projects in whatever way they choose. Students can present using PowerPoints, poster board, etc. Allow students to be creative and original.

**Assessment: **Throughout the unit, it is incredibly important to be formatively assessing students on a regular basis. For this lesson, formative assessment will primarily be done in three different ways:

- Exit slips: Exit slips will be completed after each lesson has been taught to ensure students are learning the appropriate material at an appropriate level. Differentiation and remediation will be provided when necessary for students who are not grasping concepts throughout the unit.
- Observation: As students work on their projects, I will observe and ask questions that pertain to their proposals.
- Progress Checks: At various points in the unit, I will ask students to present what they have so far to me. This allows me to monitor how much progress students are making to ensure that the projects will be completed on time. These progress checks also allow me to check student work, equations and calculations for accuracy as well as appropriateness to the project. I will also be able to ask students questions that they may have not yet considered in their models.

Summative assessment: Students will be assessed on their final presentation and their final product using a structured rubric. Students will have access to this rubric from the beginning of the unit so they are aware of the expectations.

**Teacher Notes: Being aware of the streets in your community is vital to this project. Students at this level do not yet know quadratic functions (although the project could be adjusted to later in the curriculum to include quadratic functions.) Without the knowledge of quadratics, “curvy” streets may be difficult to account for within their bus route models. Students can use online graphing tools with guidance to account for these streets in their neighborhood.**

**Possible Extensions: **

- Involve “math mentors” from upper level math classes (calculus) who can assist Algebra I students with the optimization and function content knowledge they have not yet been exposed to. These students can work with the Algebra I students to expose them to upper level mathematics and motivate them to continue their mathematical learning process.
- Mathematical modeling: Students can extend their proposal for their local community into a model that can make
*any*district’s bus routes the most efficient and effective. - Relate the school bus route model to public transportation. What goes into planning public transportation? How is this similar or different from school bus routes?

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