Joseph+W.+Pluskota

Population Problem for the New School |||| Related Lessons: 11 |||| Unit: Exponential and Logarithmic Functions || __ACT Readiness__ Instructional Objectives: In this troubling economy, several community members have challenged the demand for the new high school built in our community. In fact, the 2011-2012 school year is our new high schools inaugural year. Students will be faced with challenge of assessing not only the current population needs of our community, but the future population needs of our community to determine whether the new school was necessary despite a troubling economy. Students will complete all research and synthesize this information with what they have learned in the classroom about exponential growth and decay. This exercise will allow students to use mathematical concepts such as exponential growth, expressions and equations as well as make comparisons, contrasts and interpret data. By the end of their research students will have to determine the direction of the population in our community. The following are the intended outcomes of the lesson: To effectively prepare for this lesson, I will need the following: Students will choose their own partner for the project in an effort to support cooperative learning efforts and retain interest in the project. Over the course of the unit, students will meet as a class to review prior concepts in support of the project. The class will hold an open forum for each group to discuss their ideas regarding approach to the project further benefiting those groups who have not yet realized the same connections. Additionally, students during both small and large group will discuss “big picture” items and flesh out various concepts and techniques that can be applied to the project. || The first day of the will involve a prerequisite bell-ringer. After viewing the results of this informal assessment, I will be able to better assess whether students should continue on with the lesson. If the results are lower than expected, I will have to take more time to ensure students recall the information needed to be proficient in exponential growth/decay modeling. The first day will also include a presentation of the project as well as a class discussion about the final product and the project expectations. Prior to selecting a partner and beginning research, students will be required to complete an exit slip. Those who do not understand the guidelines of the project will be retaught the expectations prior to selecting a partner. Those who do comprehend what the task entails may proceed to choose a partner and start research. Upon completion of the first day, students will continue to research historical population figures and projections on day 2. They will use the historical figures to create a scatter plot and determine the line of best fit. Students will also post the source of their information on the social bookmarking site. Prior to moving on to the next lesson, all students/partners must submit a graph and give justification to the class for the websites posted. I will facilitate such discussion for the benefit of the class. Accommodations: While students select their own partner, students will be placed in cooperative learning groups during activities with other students of varying skill sets to collaborate about their thoughts. Students will benefit from the insight of their peers, regardless of skill-set, as they informally assume roles as facilitators, planners and support roles according to their own interests. Those who act as facilitators will enhance their leadership skills while planners will increase their creativity and support roles will benefit from working with those of higher skill-sets. Students will be able to take these skills back to their individual partners to develop the final project. Extensions: Students who may not have access to this technology at home to complete homework will be allowed extra time to complete the exercise during school hours. Passes to the media center to complete this task may need to be issued. Back-Up Plan: I need to play the role as a facilitator who continuously monitors partner progress and may need to intervene with partners to help expedite the work. This intervention may mean that I extend this lesson an additional day. In the event this intervention is unsuccessful on a large scale, I will reconsider the scale to adjust the scope and sequence of the project so that students may gain from the benefits of problem-based learning. || LESSON REFLECTIONS AND NOTES: Following notes parallel the bullet points from above on how student progress will be evaluated: In summary, I believed I focused on the success of my students with the new technology (research and social bookmarking) that I was introducing as opposed to the existing technology that they have been using (graphing calculators). This caused students some confusion that could have easily been avoided for most if we had worked more in-depth with the technology in prior sections. I have made a note of this in my lessons for the next year when my class approaches this unit. Over all, I think the students have a good start to the project and will continue to learn effectively using the technologies in the following lessons. ||
 * = PBL Daily Lesson GAME Plan = ||
 * Lesson Title:
 * Exponential Growth
 * Exponential Decay ||
 * Grade Level:
 * ==GOALS== ||
 * Content Standards:
 * Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts.
 * Analyze and draw conclusions based on information from figures, tables, and graphs.
 * Identify characteristics of graphs based on a set of conditions or on a general equation such as //y// = //ab//x-h + //k.//
 * Solve problems integrating multiple algebraic and/or geometric concepts. ||
 * ISTE NETS-S
 * Research and information fluency.
 * Critical thinking, problem-solving, & decision-making.
 * Digital citizenship.
 * Technology operations and concepts.
 * Research historical population data and projections of our community.
 * Graph population projections of our community.
 * Make a conjecture; determine if the projection is exponential growth or decay. ||
 * ==ACTION== ||
 * Before-Class Preparation:
 * Ensure there are no restrictions on student log-in and passwords for laptop carts.
 * An informational flyer for parents to inform them about the project
 * A permission slip attached to the informational flyer so that students are able to participate in the project.
 * A list of community resources including people to contact.
 * A social bookmarking site to share useful websites. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * Day 1 |||| * Review prerequisite knowledge; exponential growth and exponential decay.
 * Present the problem to the students.
 * Class discussion about the problem.
 * Divide students into groups.
 * Begin research (if time allows). || * Exponential bell-ringer activity.
 * Project handout with community resources.
 * Class laptop cart. ||
 * Day 2 |||| * Continue research.
 * Plot population trends on graphing calculators or emulation software on the computers.
 * Social bookmarking site to be updated at the end of class or for homework. || * Class laptop cart.
 * Interactive whiteboard for plotting exemplars on graphing software and to review bookmarking site. ||
 * Note student groupings, environmental modifications needed, etc.:
 * ==MONITOR== ||
 * Ongoing Assessment(s):
 * ==EVALUATE AND EXTEND== ||
 * Student progress will be evaluated in the following ways:
 * Students will be assessed on pre-requisite knowledge from the exponential growth and exponential decay bell-ringer. The bell-ringer will serve as a formative assessment before students are allowed to continue with the current lesson.
 * Students will be assessed on project knowledge from the class discussion with an exit slip covering pertinent project information. The exit slip will serve as a formative assessment before students are allowed to select a partner and conduct research.
 * Students will submit an electronic copy of their population graphs; including their individual growth/decay projection synthesized with pre-requisite knowledge determining a line of best fit. The graph submitted will serve as a summative assessment with respect to the information found via research. This information will be cross-referenced with their contributions to the social bookmarking website.
 * Students will journal their findings and submit a copy of their contribution to the social bookmarking website prior to consolidation of resources with the rest of the class.
 * Students performed well on the bell ringer that assessed pre-requisite exponential growth and exponential decay. The formative assessment was based on traditional mathematics assessment methods that typically focus on theoretical understanding an application.
 * As suspected, there were students who did not fully comprehend the full scope of the project. This can be attributed to a few things such as: students arriving late to class with excused passes, students absent from school during the lessons covering the pre-requisite knowledge, and students who have historically displayed a deficiency in intrinsic motivation.
 * Creating the graphs using emulator software on the laptops was difficult for some students. I believe that spending extra time working with scatter-plot graphs during the pre-requisite knowledge lesson(s) or during this project would have alleviated some of the ambiguity and anxiety experienced. I am making a note to include a day (or a portion of a lesson) from the pre-requisite knowledge lesson so that working with these types of graphs during the project will not be so cumbersome. By adding this extra time, students will benefit from the spiral-effect of experiencing this type of data representation and use of technology.
 * While delayed because of the graphing emulator software exercise, the social bookmarking aspect went well. Students were able to research effectively and post their resources on the social bookmarking website. There was incredible dialogue about the resources when we reviewed them together in class.

Recommendations for the New School and its Population |||| Related Lessons: 11 |||| Unit: Exponential and Logarithmic Functions || __ACT Readiness__ Instructional Objectives: In this troubling economy, several community members have challenged the demand for the new high school built in our community. In fact, the 2011-2012 school year is our new high schools inaugural year. Students will be faced with challenge of assessing not only the current population needs of our community, but the future population needs of our community to determine whether the new school was necessary despite a troubling economy. Students will complete all research and synthesize this information with what they have learned in the classroom about exponential growth and decay. This exercise will allow students to use mathematical concepts such as exponential growth, expressions and equations as well as make comparisons, contrasts and interpret data. After the first lesson, students will need to collaborate to determine if the school is needed or the school is not needed. Students will also have to determine how the community can use the space until it is fully utilized. The following are the intended outcomes of the lesson: To effectively prepare for this lesson, I will need the following: Students will keep their partner from the prior day(s) lesson. By keeping their partner for the project, this strategy will continue to support cooperative learning efforts and retain interest in the project for the student. Similarly, over the course of the unit students will meet as a class to review prior concepts in support of the project. The class will hold an open forum for each group to discuss their ideas regarding approach to the project further benefiting those groups who have not yet realized the same connections. Additionally, students during both small and large group will discuss “big picture” items and flesh out various concepts and techniques that can be applied to the project. || After each evening, I will be checking the discussion boards of each Wiki. Students will have a minimum posting requirement as well as a time spent logged into the Wiki. Those students who procrastinate will be easily identified as well as those who are contributing the most to their group. The intention is to effectively monitor what not only happens in the classroom, but what happens outside of the classroom as students work on this project at home. Accommodations: While students select their own partner, students will be placed in cooperative learning groups during activities with other students of varying skill sets to collaborate about their thoughts. Students will benefit from the insight of their peers, regardless of skill-set, as they informally assume roles as facilitators, planners and support roles according to their own interests. Those who act as facilitators will enhance their leadership skills while planners will increase their creativity and support roles will benefit from working with those of higher skill-sets. Students will be able to take these skills back to their individual partners to develop the final project. Extensions: Students who may not have access to this technology at home to complete homework will be allowed extra time to complete the exercise during school hours. Passes to the media center to complete this task may need to be issued. Back-Up Plan: I need to play the role as a facilitator who continuously monitors partner progress and may need to intervene with partners to help expedite the work. This intervention may mean that I extend this lesson an additional day. In the event this intervention is unsuccessful on a large scale, I will reconsider the scale to adjust the scope and sequence of the project so that students may gain from the benefits of problem-based learning. || LESSON REFLECTIONS AND NOTES: ||
 * = Online Collaboration Daily Lesson GAME Plan = ||
 * Lesson Title:
 * Exponential Growth
 * Exponential Decay ||
 * Grade Level:
 * ==GOALS== ||
 * Content Standards:
 * Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts.
 * Analyze and draw conclusions based on information from figures, tables, and graphs.
 * Identify characteristics of graphs based on a set of conditions or on a general equation such as //y// = //ab//x-h + //k.//
 * Solve problems integrating multiple algebraic and/or geometric concepts. ||
 * ISTE NETS-S
 * Creativity and innovation.
 * Communication and collaboration.
 * Research and information fluency.
 * Critical thinking, problem-solving, & decision-making.
 * Digital citizenship.
 * Technology operations and concepts.
 * Create a Wikispaces page to present their population projections.
 * Collaborate online using Wikispaces to determine the best line-of-fit for their exponential population projections.
 * Collaborate online using Wikispaces to discuss optional uses for excess space and the duration of the use of that space.
 * Collaborate online about the best way to represent their intended message on the Wikispaces page they create. ||
 * ==ACTION== ||
 * Before-Class Preparation:
 * Ensure there are no restrictions on student log-in and passwords for laptop carts.
 * An informational flyer for parents to inform them about the project.
 * A permission slip attached to the informational flyer so that students are able to participate in the project.
 * Create a Wiki for students to share useful insights about what they have found using the information from the prior lesson. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * Day 1 |||| * Work with students on how to properly access the Wikispaces account, upload files, and post discussion on each page being developed.
 * Have groups set up their individual page (if time permits). || * Class laptop cart.
 * Interactive whiteboard for review of Wikispaces. ||
 * Day 2 |||| * Have groups set up their individual page.
 * Students begin construction of their Wikispaces page and collaborate on the best line-of-fit.
 * Students research and collaborate on alternate uses for the new space.
 * Students determine a timeline for the use of space at the new school (if time permits). || * Class laptop cart. ||
 * Day 3 |||| * Students complete timeline for the use of space at the new school.
 * Students consolidate their ideas and to prepare to tell the story.
 * Students complete construction of their Wikispace page. || * Class laptop cart ||
 * Note student groupings, environmental modifications needed, etc.:
 * ==MONITOR== ||
 * Ongoing Assessment(s):
 * ==EVALUATE AND EXTEND== ||
 * Student progress will be evaluated using a rubric in the following ways:
 * Students will have to satisfy a time limit for contributing to the Wiki.
 * Students will need to satisfy a minimum requirement of postings to the Wiki in which they are participating.
 * Students will need to have collectively determined the best line-of-fit for their exponential population projections.
 * Students will need to have determined optional uses for excess space and the duration of the use of that space.
 * Student will need to have consolidated the group’s intended message on the Wiki in a progressive, logical manner (aesthetics and uniformity).
 * Students will need to have strictly adhered to the district’s internet usage policies and professionalism standards.

Tell the story. |||| Related Lessons: 11 |||| Unit: Exponential and Logarithmic Functions || __ACT Readiness__ Instructional Objectives: In this troubling economy, several community members have challenged the demand for the new high school built in our community. In fact, the 2011-2012 school year is our new high schools inaugural year. Students will be faced with challenge of assessing not only the current population needs of our community, but the future population needs of our community to determine whether the new school was necessary despite a troubling economy. Students will complete all research and synthesize this information with what they have learned in the classroom about exponential growth and decay. This exercise will allow students to use mathematical concepts such as exponential growth, expressions and equations as well as make comparisons, contrasts and interpret data. By the end of their research students will have only two outcomes possible; the school is needed or the school is not needed. The following is the course of action that students will take depending on the outcome of their research: To effectively prepare for this lesson, I will need the following: Students will keep their partner from the prior day(s) lesson. By keeping their partner for the project, this strategy will continue to support cooperative learning efforts and retain interest in the project for the student. Similarly, over the course of the unit students will meet as a class to review prior concepts in support of the project. The class will hold an open forum for each group to discuss their ideas regarding approach to the project further benefiting those groups who have not yet realized the same connections. Additionally, students during both small and large group will discuss “big picture” items and flesh out various concepts and techniques that can be applied to the project. || As a requirement of each day, students will be required to upload their progress to their Wiki they constructed from the prior lesson. After each evening, I will be checking the Wiki to follow the progress of the partners. This progress check will most likely occur the following morning since students are required to complete their work as homework if they cannot complete each day’s checkpoint. In total, students should have two checkpoints and one final draft of the digital story. Those students who procrastinate will be easily identified as well as those who are contributing the most to their group. The intention is to effectively monitor what not only happens in the classroom, but what happens outside of the classroom as students work on this project at home. To serve as incentive for students to keep on pace, those students who are further than the schedule will be awarded extra credit. Accommodations: While students select their own partner, students will be placed in cooperative learning groups during activities with other students of varying skill sets to collaborate about their thoughts. Students will benefit from the insight of their peers, regardless of skill-set, as they informally assume roles as facilitators, planners and support roles according to their own interests. Those who act as facilitators will enhance their leadership skills while planners will increase their creativity and support roles will benefit from working with those of higher skill-sets. Students will be able to take these skills back to their individual partners to develop the final project. Extensions: Students who may not have access to this technology at home to complete homework will be allowed extra time to complete the exercise during school hours. Passes to the media center to complete this task may need to be issued. Back-Up Plan: I need to play the role as a facilitator who continuously monitors partner progress and may need to intervene with partners to help expedite the work. This intervention may mean that I extend this lesson an additional day. In the event this intervention is unsuccessful on a large scale, I will reconsider the scale to adjust the scope and sequence of the project so that students may gain from the benefits of problem-based learning. || NOTE: It is important to note that the most succinct and accurate sections of the partner’s digital story will be combined to create one final digital story for presentation to the Board of Education. Those students selected (by their peers) to work on the final draft will earn extra credit in the class. LESSON REFLECTIONS AND NOTES: ||
 * = Digital Storytelling Daily Lesson GAME Plan = ||
 * Lesson Title:
 * Exponential Growth
 * Exponential Decay ||
 * Grade Level:
 * ==GOALS== ||
 * Content Standards:
 * Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts.
 * Analyze and draw conclusions based on information from figures, tables, and graphs
 * Identify characteristics of graphs based on a set of conditions or on a general equation such as //y// = //ab//x-h + //k.//
 * Solve problems integrating multiple algebraic and/or geometric concepts. ||
 * ISTE NETS-S
 * Creativity and innovation.
 * Communication and collaboration.
 * Research and information fluency.
 * Critical thinking, problem-solving, & decision-making.
 * Digital citizenship.
 * Technology operations and concepts.
 * 1) If the school is not needed in the capacity it was intended to serve, students will need to determine ways to use the extra space to help offset costs to the community of operating the building. Students will present their findings and suggestions to the Board of Education using digital storytelling.
 * 2) If the school is needed in the capacity it was intended to serve, students will need to present their findings to the Board of Education in support of operating the school with the same intention. Recommendations will be made about how to use the space until the new school reaches its expected population potential using digital storytelling. ||
 * ==ACTION== ||
 * Before-Class Preparation:
 * Ensure there are no restrictions on student log-in and passwords for laptop carts.
 * An informational flyer for parents to inform them about the project.
 * A permission slip attached to the informational flyer so that students are able to participate in the project.
 * Establish a timeline with the Board of Education for one presentation of the recommendations our classes find. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * Day 1 |||| * Show exemplars of digital storytelling to the class.
 * Work with students on how to effectively use digital storytelling software.
 * Have groups start planning their digital story (if time permits). || * Class laptop cart.
 * Interactive whiteboard for review digital storytelling software. ||
 * Day 2 |||| * Students begin construction of their digital story: population problem (complete).
 * Students continue working on their digital story: exponential growth/decay best line-of-fit graphs (if time permits). || * Class laptop cart. ||
 * Day 3 |||| * Students continue working on their digital story: exponential growth/decay best line-of-fit graphs (complete).
 * Students continue working on their digital story: use of school recommendations (complete). || * Class laptop cart ||
 * Note student groupings, environmental modifications needed, etc.:
 * ==MONITOR== ||
 * Ongoing Assessment(s):
 * ==EVALUATE AND EXTEND== ||
 * Student progress will be evaluated using a rubric in the following ways:
 * Students will need to satisfy a minimum time requirement of the digital story.
 * Students will have to include an introduction to the population problem, graphs to support their projections, and recommendations.
 * Students will have to meet all checkpoints in a timely manner as they post their progress on the Wiki.
 * Student will need to have consolidated the group’s intended message in the digital story in a progressive, logical manner (aesthetics and uniformity).
 * Students will need to have strictly adhered to the district’s internet usage policies and professionalism standards.