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 and the 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?
Layup is a very basic basketball skills maybe everyone layup but there is a way of layup is not everyone that is wrong step layup.
air max 90
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
kd shoes
Layup is a very basic basketball skills maybe everyone layup but there is a way of layup is not everyone that is wrong step layup.
lebron soldier 10
NBA players in addition to playing badly, and also an art cells, for two consecutive years in the NBA finals two teams join forces with the warriors and knight, but only two dancers, two teams played neck and neck, dancing is close, take a look at
kyrie shoes
Recently, the Fansided to knight main rotation player in the first two rounds of the playoffs, the performance of the Owen only C +, love there is only a B.
kyrie 3 shoes
Yesterday, the wall on the right side 45 live a miserable life in the three points must win.The shooting location is Owen puts up the location of the many times.Today was asked Owen saw wall dead there is what feeling
adidas tennis hu
With three points to beat John wall, the day before yesterday the wizards will competition into the tiebreak wars, 8:00 tomorrow the wizards will be tie-break at Celtic and rival.
curry 3 shoes
NBA players in addition to playing badly, and also an art cells, for two consecutive years in the NBA finals two teams join forces with the warriors and knight, but only two dancers, two teams played neck and neck, dancing is close, take a look at
supreme yeezys
Recently, the Fansided to knight main rotation player in the first two rounds of the playoffs, the performance of the Owen only C +, love there is only a B.
Nike CR7
“I don’t think eastern conference finals will be a long war, knight’s strength is too strong. The celtics nobody with lebron, they even Owen this level of star all have no, they are really no one can stop the knight.
canada goose
Layup is a very basic basketball skills maybe everyone layup but there is a way of layup is not everyone that is wrong step layup.
russell westbrook shoes
Layup is a very basic basketball skills maybe everyone layup but there is a way of layup is not everyone that is wrong step layup.
yeezy shoes
Obviously, the right to occupy a team-high 21.6 shots of Michael Owen, but failed to hit as James scores, this let a person feel, Owen has become a “cancer” of the knight.But many fans also feel,
kyrie irving shoes
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
kyrie 3 eybl
“I don’t think eastern conference finals will be a long war, knight’s strength is too strong. The celtics nobody with lebron, they even Owen this level of star all have no, they are really no one can stop the knight.
kyrie 4
Yesterday, the wall on the right side 45 live a miserable life in the three points must win.The shooting location is Owen puts up the location of the many times.Today was asked Owen saw wall dead there is what feeling
new balance running shoes
Knight finally written pledge to fulfill a military order!Owen Jefferson suspected the contradiction, huang zhan anger: don’t win playoff team and the team retired showdown between the more and more intense, will the rockets in just eliminated the spurs tomorrow will come and warriors in the first fight
nike air max 97
According to The Fear of The Sword, The knight’s point guard deron Williams is a fan of MMA (mixed), compared to The basketball game, deron prefer to watch The ultimate fighting championship.Deron Williams recently said in an interview, he retired from the NBA
air max 90
Knight finally written pledge to fulfill a military order!Owen Jefferson suspected the contradiction, huang zhan anger: don’t win playoff team and the team retired showdown between the more and more intense, will the rockets in just eliminated the spurs tomorrow will come and warriors in the first fight
yeezy shoes
With three points to beat John wall, the day before yesterday the wizards will competition into the tiebreak wars, 8:00 tomorrow the wizards will be tie-break at Celtic and rival.
adidas porsche design
For Jordan and gregg popovich comments James never hit back, but just yesterday in the knight’s basketball stadium set aside a James training video, far look like illusions emerged both Owen, a carefully look just know is James
adidas supreme yeezys
The noises and stressful the playoffs.”We are eager to match.”Owen said.Knight should first game will be on Thursday in east, and before them
adidas ultra boost
The noises and stressful the playoffs.”We are eager to match.”Owen said.Knight should first game will be on Thursday in east, and before them
air jordan 32
Because Michael Owen at the side of huang zhan, so his nickname called small report.The earliest Owen left the impression of the world, is probably the flashy passing movements and dazzling breakthroughs, remember in the rookie challenge, he drew down two slipped past knight
nike zoom vaporfly
“I don’t think eastern conference finals will be a long war, knight’s strength is too strong. The celtics nobody with lebron, they even Owen this level of star all have no, they are really no one can stop the knight.
adidas nmd xr1
“I don’t think eastern conference finals will be a long war, knight’s strength is too strong. The celtics nobody with lebron, they even Owen this level of star all have no, they are really no one can stop the knight.
curry 4
According to The Fear of The Sword, The knight’s point guard deron Williams is a fan of MMA (mixed), compared to The basketball game, deron prefer to watch The ultimate fighting championship.Deron Williams recently said in an interview, he retired from the NBA
kyrie irving jersey
The noises and stressful the playoffs.”We are eager to match.”Owen said.Knight should first game will be on Thursday in east, and before them
balenciaga triple s Shoes
Recently, the Fansided to knight main rotation player in the first two rounds of the playoffs, the performance of the Owen only C +, love there is only a B.
air jordan shoes
Carey – Owen about injury of varese, said it happened out how knight players want to play games.”I was about to enter a 5 on 5 game, but after three seconds, varese is injured
nike hyperdunk
Because Michael Owen at the side of huang zhan, so his nickname called small report.The earliest Owen left the impression of the world, is probably the flashy passing movements and dazzling breakthroughs, remember in the rookie challenge, he drew down two slipped past knight
ben simmons jersey
Draft of the same year on the bottom rookie will be what?In general the draft should be able to blow the other party, who would have thought them took Owen on the 60th pick small Thomas in the same year, he turned out to be in the position of the challenger?
asics gel kayano 24
He has future franchise corner potential and the team knows it.
Cheap Jerseys
Obviously, the right to occupy a team-high 21.6 shots of Michael Owen, but failed to hit as James scores, this let a person feel, Owen has become a “cancer” of the knight.But many fans also feel,
russell westbrook shoes
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
nike lebron 14
Layup is a very basic basketball skills maybe everyone layup but there is a way of layup is not everyone that is wrong step layup.
nike free
The NBA playoffs now for today, have determined the warriors in the western conference and will compete for a spot in the finals quota, knight still don’t know who his opponent was.However, even in the face of the celtics or the wizards, presumably knight will be
kd shoes store
Carey – Owen about injury of varese, said it happened out how knight players want to play games.”I was about to enter a 5 on 5 game, but after three seconds, varese is injured
kyrie irving shoes
The NBA playoffs now for today, have determined the warriors in the western conference and will compete for a spot in the finals quota, knight still don’t know who his opponent was.However, even in the face of the celtics or the wizards, presumably knight will be
curry 4
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
nike hyperdunk
The NBA playoffs now for today, have determined the warriors in the western conference and will compete for a spot in the finals quota, knight still don’t know who his opponent was.However, even in the face of the celtics or the wizards, presumably knight will be
kyrie irving shoes
School Previous pick 9.
Wholesale NFL Jerseys
We’re better than them.
Wholesale Jerseys China
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
Curry Shoes
I would like to thnkx for the efforts you have put in writing this website. I am hoping the same high-grade blog post from you in the upcoming also. Actually your creative writing skills has inspired me to get my own web site now. Actually the blogging is spreading its wings quickly. Your write up is a great example of it.
Owen said: “Cleveland need game.”Indeed, they rested for too long.In green, and the wizards to after the tiebreak, the beginning of the knight’s eastern conference finals first time has pushed the next Wednesday.
kyrie 4 confetti
Draft of the same year on the bottom rookie will be what?In general the draft should be able to blow the other party, who would have thought them took Owen on the 60th pick small Thomas in the same year, he turned out to be in the position of the challenger?
puma suede
NBA players in addition to playing badly, and also an art cells, for two consecutive years in the NBA finals two teams join forces with the warriors and knight, but only two dancers, two teams played neck and neck, dancing is close, take a look at
kyrie irving shoes
Lifestyle NetworksLast.
cheap jerseys from china
Thanks for your write-up. I also think laptop computers are becoming more and more popular these days, and now are sometimes the only kind of computer utilised in a household. The reason being at the same time actually becoming more and more very affordable, their computing power is growing to the point where they’re as strong as personal computers through just a few in years past.
adidas iniki runner
PBL – Heller | EDT 622
[url=http://www.g268b8eg07l2x19l8u4lx79fzgm6g4y3s.org/]ucisxvwnno[/url]
acisxvwnno
cisxvwnno http://www.g268b8eg07l2x19l8u4lx79fzgm6g4y3s.org/