Catapults
by Elise Briseno, Leah Coutorie, and Charelle Smith
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Intro PaperProject Description , Driving Question, Goals, Objectives, Rationale, Background Information, AssessmentsDescriptionWe are striving to achieve the attention and motivation of young mathematical students to excel and enjoy their math course. We are proposing a project that we believe will engage our students beyond that of a traditional classroom environment. We strive for communication, cooperation, and motivation. Although the traditional classroom environment is beneficial to students, we believe that our approach will greater benefit all students’ understanding and attitude toward learning mathematics in a different way- a more physical way. Mathematics should be engaging and exciting for students and we will achieve that. We have found that our own students’ lack of enthusiasm, when it comes to mathematics, is deterring their ability to understand and explain concepts. We wish to bring outside resources and applications to our classroom and students. This will strengthen students’ knowledge of mathematics by providing extensive hands-on activities. Our project revolves around concepts found in algebra, geometry, and physics. The lessons in the project pinpoint background concepts that students need to learn to better apply these subjects in the real world. With these lessons and activities the students will not only work with these concepts, but apply them to a physical problem. Although we have resources in our limited time to offer the students, the execution of the project allows us to incorporate background knowledge and to reinforce that knowledge. Driving QuestionWhat type of catapult can you build to throw water balloons at your teacher? Overall Goals of ProjectThe proposed project will expand and entertain the ideas and approaches to learning mathematics. The goals we have established for ourselves are teaching the material in an open questions environment with correct and informative communication, controlling and over-viewing the students in their groups, and communicating in various ways (teaching styles) the algebra, geometry, and physics behind the catapult project. The first goal is achieved throughout our collaborated and open-questioned designed lesson plans. The environment of our classroom has been established throughout the school year and the students’ behavior has already been address. The groups consist of mixed ability students so that the groups themselves must interact and communicate efficiently and productively to achieve their goals of completing the project. The skill of mathematical communication is the main goal in having our students work together and learn together. The students will achieve a new vocabulary for mathematics and use it to communicate amongst themselves and their teachers. We hope to establish this skill in our students since future mathematics and occupation rely heavily on correct and understood mathematical concepts and ideas. Our second goal will be accomplished by using proximal distance and group leaders to control the students’ volume and keep them on task. The most effective way to control our students is by having an already established classroom environment which we will achieve prior to the catapult project. We also rely on our proximal distance to groups to (1) keep an eye on the students and how they are proceeding throughout their work, (2) be available to the groups if they need assistance, and (3) evaluate the students’ understanding and applications to the new mathematics they have been learning. All our goals are based in our teaching styles and how effectively and efficiently we communicate the concepts needed for the catapults in algebra, geometry, and physics. Even though there are three of us, we plan to be completing the catapult project and assignments around the same time. We all have different teaching styles that benefit each of us, but working as a teaching group we have adopted some approaches to different mathematically concepts that we believe will benefit our classroom. Collaborating together we can use each others’ quizzes and assignments formats, different classroom management skills, and have a daily and weekly checkpoint with our groups to insure time is use adequately and timely. Our goals as established above are achieved by recording the progress of the students’ individual assignments and collaborative teamwork. We had integrated a weekly time log system that will be completed by each week’s leader of all the groups. The time log will be a list of achieved and ongoing goals that the students will meet. In addition to this, there is a weekly journal entry due that will explain the groups’ progress, the divisions of members’ roles, and any problems the students are having within their projects. These steps are accomplished by the students to build communication and responsibility. However, we, as the teachers, must also have a system for evaluation that measures the progress of our students. We plan to use the students’ time logs and journal entries for a quarter of their grade, but rely more heavily on the assignment of the smaller group and individual activities. The hands-on activities will incorporate how much and how well a student can communicate mathematics to their classmates and teachers by working problems and writing their logic behind each step. The responses the students give to our open-ended questions are an effective way to establish a base to what information they are absorbing. The students will be given additional problems that compose of both conceptual and procedural examples for the weekends to be their only ‘homework’ grades because we strive to communicate the concepts and skill within the school weekdays. These homework problems allow us to see the progress of our students’ understanding and knowledge of the past week. The problems become a form of post-assessment for the topics already covered. Overall, the evaluation of our students amounts to the work they show and communicate to their peers and instructors verbally and written. Project ObjectivesStudents will be able to: List and arrange ideas and concept they have about catapults. Draw a representation of a water balloon with different axes. Use and give steps to using a calculator properly. Give a linear regression and quadratic regression equation. Give and represent the path of water balloons with various axes. Properly use calculators. Find geometric and algebraic patterns from given data. Observe and understand projectile motion. Explain the two components of projectile motion Formulate a quadratic equation that represents that parabolic path of an object. Use the quadratic function to position a catapult to hit given targets. Enter, graph, and analyze data in Excel Answer questions about the processes Answer questions about the significance of their data Recall trigonometric properties Use these properties to solve problems Apply this knowledge to further problems Discuss their findings RationaleOur project involves having students build catapults in order to sharpen their algebra, geometry, and physics skills and understanding. The main goal is to have students apply concepts within these subjects to situations that are not usually seen inside the classroom. We plan to introduce this project idea with a short five-minute video we have designed and shot ourselves. The video gives an artistic and visually stimulating view on the high school project, which we believe will grab the attention of our students. Throughout the six week period that this project covers, the students will be engaged in several benchmark lessons that pinpoint exact concepts that will be helpful in building and using catapults. These lessons will help the students to collect, record, and analyze data. In turn the students will work together and apply their information in constructing a working catapult. The students will have the information on how far their particular catapult can propel items, such as water balloons at a given object. The students will learn about quadratic functions in order to help them recognize parabolas and the movement an object makes when being launched. They will also be able to solve these functions to find theoretical and realistic solutions to problems presented. With these solutions the students will be able to provide graphical representations of problems and situations solved. And of course, at the end of the session the students will be provided water balloons and a target to execute their hard work over the six-week period. Background InformationOriginally designed by the Greeks in 399B.C. and perfected by the Romans by 350 B.C. the catapult was the main factor in the conquering for Roman territory. The giant piece of artillery was used against cities’ citadels, castles, and walls. However, catapults are more associated with the time of the Dark Ages, weaponry of knights and villagers. We are trying to associate the catapult with modern entertainment, as in the Punkin’ Chunkin’- a contest to catapult a pumpkin as far as possible. Since pumpkins are not an ideal tool for the students to hurl at the teacher, we decided to have the students use water balloons instead. The water balloons are noticeably smaller than pumpkins and therefore the students will have to scale down their catapults to accommodate the difference. We will have the students design and create their own catapults in groups of three. Under the stipulations that the catapult must fit within four square feet and must be able to launch water balloons at completion, they will research the different types of catapults online and make note of the directions and materials they will need. The teacher will then furnish these tools and monitor as the students build own their own. We will provide websites for them to visit in order to find such information. One of the sites is icatapults.freeservers.com/plans.htm. This site gives explanations of different types of catapults and offers descriptions and directions for how to build them. Another site is http://www.smithtown.k12.ny.us/msteched/catapultproject.htm. This site gives a short history of catapults, catapult vocabulary, and directions for how to build one. There is also http://www.knightforhire.com/catapult.htm that gives the students ideas of the different types and directions as well. It also has even more links for the students to explore. Finally, there is http://www.rochesterschool.org/pages/school/middle_school_catapults.htm that shows other students posing with their catapults that they built for a school project. This will give them ideas of the final product. The students will give a presentation of their creations processes at the end of the term and finally get to launch their catapults with water balloons at the teachers. For the students to effectively know the physics behind catapults and motion, we have included a lesson over projectile motion and how it ties to catapults. All information in these lessons over the physics came from the following websites: http://library.thinkquest.org/2779/History.html and http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html Assessments and Final Product1.) Minute Paper - This assessment will be used at the beginning of the project (first or second day of class) to test the students’ prior knowledge of the subject. It will also give the students the chance to tell the teacher what they have had trouble with conceptually in the past. 2.) Categorizing Grid - We will integrate this assessment into the second day of lesson 5. The students will use excel to make a grid that categorizes the different concepts they learned and to differentiate between the different types of catapults. 3.) Concepts Maps - During the first week of class after the first lesson, the students will make a concept map that will help them with a plan to design, build, and use their catapults. 4.) One Sentence Summary - At the end of each benchmark lesson, the students will provide the teacher with a one sentence summary of what they learned that day. 5.) What’s the Principle? - This assessment will be incorporated into project plan as a section wrap up of the entire project. The teacher will give the students different problems and the students will have to provide the correct principles that best apply to those problems. 6.) Direct Paraphrasing - During the course of the benchmark lessons, the teacher will use this as an attention grabber. The students will randomly have to paraphrase what the teacher is presenting to them that day. 7.) Course-Related Self-Confidence Surveys - Given the first day of class, the students will take a survey that tests how confident they feel with the concepts that have been presented to them about math. 8.) Double-Entry Journals - The students will keep an ongoing 2-sided journal that will include the topics/concepts/problems they come across in the project everyday on one side; and on the other side the students will provide their thoughts and concerns that will aid the teacher in helping them with the project. 9.) Goal-Ranking and Matching - This assessment will also be used the last day of the project in such a way that the students will rank the different parts of the entire project in order of least to most important to them. 10.) Punctuated Lectures - These will be used during the lessons as a tool to allow the students to reflect on what was just learned and how they are behaving. 11.) Teacher Designed Feedback Forms - These will be given at the end of the first week of lessons to see how students relate to the way that the teacher relays the lessons. The questions will be non-biased and focus only on the techniques of the classroom. 12.) Chain Note Feedback - The students can/will turn in anonymous feedback cards throughout the 6 week period that conveys how they feel about the course and work that is being done. The cards will be available at all times. 13.) Exam Evaluations- After each exam that the students take, they will be able to evaluate the format/wording and let the teacher know if/where they had had trouble. Calendar
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