*Note for the Teacher: This calendar with supporting resources is provided as a guide and can be adapted to the needs of you and your students. For example, having Student Teams meet with Community professionals is preferable, but optionl for this project.
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Day 1
Students will view the BLOSSOMS video lesson, “Flaws of Averages”, and participate in classroom activities presented in that lesson. Teacher preparation for presenting this lesson can be found in the Video Teacher Guide segment at 12:05 and also in the written Teacher Guide and other resources available on the website. Homework for students can be found below. (If time permits, teacher could begin discussion of the concepts presented in the video lesson, using Teacher Notes listed for Day 2.)
- Instructions to download or stream BLOSSOMS videos (PDF format, Word format)
- Homework for Day One (PDF format, Word format)
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Day 2
In a whole class discussion and following up on their homework, students will review all three major concepts introduced on Day 1 in the BLOSSOMS video lesson, including: 1) The average is not always a good description of the actual situation; 2) The function of the average is not always the same as the average of the function; 3) The average depends on your perspective. Teacher Notes for this discussion are included below, along with a power point presentation to assist students in understanding the second “Cookie” concept. Teacher will assign Longterm Homework Assignment on Averages below which will be due on Day 5 of this PBL. Tonight's homework can be found below.
- Teacher Notes for Day 2 (PDF format, Word format)
- “Cookies” Power Point Presentation (PDF format, PPT format)
- Longterm Homework Assignment on Averages (PDF format, Word format)
- Day 2 Homework (PDF format, Word format)
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Day 3
Following up on the homework, teacher will lead class in discussion of how important it is to understand what went into calculating a given average before trusting it. Next students will read short article (below) about life expectancy averages from Massachusetts and Boston, which should lead into a discussion of how using averages can be misleading in presenting a comprehensive and insightful picture of a group or community. At this point, the teacher will introduce the Driving Question of this PBL: “How to better understand averages: what information are they giving us and in what ways may they be misleading us?” Students will learn that during this PBL they will be working in teams of four to collect and analyze data on a topic from their community—a topic that would be distorted if only presented as an overall average. One aim of this project will be to make them more knowledgeable and skeptical consumers of statistics. Teacher should tell students that they will learn more about the actual project in a few days. For the next class, students must be prepared to hand in the number of hours they slept the night before. Homework reading assignment is listed below.
- In-Class Reading Assignment for Day 3 (PDF format, Word format)
- Homework Reading Assignment for Day 3 (PDF format)
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Day 4
Today’s class will open with the teacher creating a Histogram Diagram of sleep data provided by students and then discussing that histogram with the class. This will be followed by a review of the homework reading assignment and a discussion of Histograms and Distributions. See Teacher Notes for Day 4 below. Before moving on, it will be important to make sure students understand these two concepts. Next the class will go through examples of Histograms and Distributions found in the Illustrative Histograms and Distribution document below. They will compare and contrast the information provided by an average versus that provided by the entire distribution. Hopefully students will learn to identify whether an example is an effective use of averages or not. Remind students to be prepared to discuss their Longterm Homework Assignment on Averages during the next class.
- Teacher’s Notes for Histograms and Distributions for Day 4 (PDF format, Word format)
- Illustrative Histograms and Distributions for Discussion for Day 4 (PDF format, Word format)
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Day 5
The teacher will remind students of the Driving Question of this project as presented in an earlier class and of the fact that they will be working in teams of four. Teams will be established in a randomized structured way as described here in the BLOSSOMS PBL Tools. Once teams are established, team members will discuss their Longterm Homework Assignment on Averages examples in their groups and will come together for a whole class reporting out. Students will receive a blank Team Contract form, and their homework will be to give some thought to what they want included in their team’s contract, particularly the 4-6 Team Agreements and what the team should do if they slip out of their agreements.
- Blank Team Contract (PDF format)
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Day 6
Today students will spend time developing new skills that will help them work more successfully in their teams as they prepare to start their projects. We suggest using team contracts, which are documents that state what teams will agree to and what will happen if they do not keep to these statements. Have teams start their team contracts for the upcoming project. Also, to help keep students on task and on time, we suggest using a task log, a live task list that makes it easy for teams (and the teacher) to know what has been done, what is in process, and what has just started. You can read more about this useful tool here. Teacher Notes for introducing these two tools can be found below.
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Day 7
Today students will meet with their teams and will be randomly assigned one of the topics listed on the Suggested Personal Data Projects document below. Over the next 7 days, they will record the requested data for each student on the team. After 7 days, they will work together in class to create the histogram of results and show average, median, mode and 5% tails. Each team will present results to the class. What insights have they gained from the broad distribution of their data, in addition to the average? This assignment will not require much time in class beyond gathering the data since most of the work will be done after the 7th day of data collection. Students should be told that in the next class they will be introduced to their longterm projects. This 7-day project is a warm-up for the longer one!
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Day 8
Today, after collecting data for their Personal Data Projects, teams will be introduced to the main project of this PBL lesson. Building from the analysis of “averages”, teams will select (or be assigned) one of several community-based projects listed below. (See Teacher Notes) Preferably, each team will have a different project. Allowable projects are not limited to the ones listed here. With the teacher’s advice and assistance, student teams can design their own project. Each of the described projects deals with a local community safety issue:
- Fire Safety and Distance to Nearest Fire Hydrants (PDF format, Word format)
- Drivers’ Intersection Safety (PDF format, Word format)
- Smart Traffic Lights (PDF format, Word format)
- Sidewalk Safety (PDF format, Word format)
- Playground Safety (PDF format, Word format)
- A “None-of-the-Above” Project, negotiated with teacher (PDF format, Word format)
The teacher will provide an overview of each project. Then students will return to their team to begin discussing the options and developing a list of the order of their preferred projects. The homework will be for each team member to develop a personal list of project preference order.
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Day 9
Today the teacher will discuss in more detail the focus and requirements of each of the five listed community projects and answer any questions the students may have. After this discussion, teams will meet and finalize their list of the projects in order of preference. It is hoped that each team can be assigned a project before the end of class and that detailed assigned project descriptions can be distributed to all team members. Teams must also collect the data for their Personal Data Projects.
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Days 10-12
After collecting daily data for the Personal Data Projects, these will be the first full three days that teams work on their Community Projects. Teams will need to begin designing their project’s data collection strategy, schedule the needed project activities, assign tasks and responsibilities and begin identifying the appropriate community professional(s) they will want to meet with as part of the projects. During these three days, the teacher as coach and mentor will meet with teams each day to make sure they understand project instructions and assess their progress in moving forward with the work. By Day 10, the teacher should have established a system for student Task Log completion and a regular schedule for teacher reviews of those Logs. Once the teacher feels confident that students have devised an effective data collection strategy, teams should begin scheduling their visits to the field, which will take place most likely during off-school hours. They should initially do a test run of the data collection strategy to make any needed adjustments. They should also be close to identifying the community official that they will want to meet with, so that an appointment can be made. During this 3-day period, the teacher should also distribute and discuss the Project Goals and Project Rubric documents below - explaining what is expected of team members on their Community Safety Project. Students should also receive the document below, The 5 Steps to Data Collection, which should be discussed with them during this 3-day period.
- Flaws of Averages Project Goals (PDF format, Word format)
- Flaws of Averages Rubric (PDF format, Word format)
- The 5 Steps to Data Collection (PDF format, Word format)
- Homework Assignment for Day 12 (PDF format, Word format)
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Day 13
During the first part of class, the teacher will meet with each team to review their homework assignment and to pass out copies of the student handout below, to insure that students are prepared for their in-class histogram assignment the next day. With the remaining class time, teams will share some of the work they have been doing on their Community Safety Projects.
- Student Handout: What is expected during your in-class exercise on Histograms? (PDF format, Word format)
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Day 14
After collecting their final day of data, student teams will work on creating a histogram of their data and identifying the Mean, Median and Mode. Then teams will come together to discuss the results of their data collection, including whether or not the Mean is a good depiction of the results and other interesting observations they have made. For tomorrow's class, teams should be prepared to discuss their Community Safety Project data collection plan with the teacher and also to provide a schedule for that data collection plan to be implemented. They should also have identified the appropriate community professional(s) to meet with about their project and be prepared to reach out to schedule an appointment with the professiona(s) for when their project will be completed.
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Days 15-19
On Day 15, the teacher will meet with each team to review their data collection plan and their schedule for its implementation. Once teacher approval is received, teams will proceed with their data collection implementation over the course of this five-day period. Since much of this work will be completed outside school hours, it is hoped that this window will wrap around a weekend. Each team should do a test run of its data collection strategy first, in case adjustments to that strategy are necessary. On Day 15, the teacher should also check in with teams on their success in identifying an appropriate community professional to contact and offer assistance to students on this if necessary. During this five-day period, the teacher as coach and mentor will meet with each team daily to assess progress and help problem solve. (Task Logs should be completed and regularly reviewed.) Teams should be reminded to refer back frequently to the Project Goals and Rubric as they complete their work.
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Days 20-22
By Day 20, teams should have completed data collection for their Community Safety Project and also scheduled a meeting with an appropriate community professional(s). Over this three-day period, teams will work to assemble and integrate the data, display it in a histogram, compute mean, mode and median, and ultimately make inferences from the data that could benefit the community. Once teams are ready, they can begin writing the 10-page final report along with presentation slides, including histogram and any photos.
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Days 23-25
Guided by their teacher, student teams continue to work on their presentations, following closely the requirements provided in the Goals and Rubrics documents. By day 25, research is wrapped up, slide show is completed, script is edited and in final form, presentation is rehearsed and bibliography is prepared. Distribute Student Reflection handout below.
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Final Event Day
Final Event: Typically the final presentation day of PBL work is a celebration. This Final Event is hosted ideally during a longer period than one class, such as after school where parents, stakeholders, the community, and other school officials are present. This is where students get to showcase their work. If such a time frame is not possible, then hold this public event during normal class times, but try to make sure that stakeholders are present during the class event. It is imperative to have outside connections as part of the audience, watching students present. Or if stakeholders are not possible, invite administration and other adults that are part of the school.
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Day After Final Event
Required products, including completed Student Reflection handout, are passed in. Refer to Flaws of Averages Project Goals document for a complete list of products to be handed in.
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