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Volume III: Physical Problem-Solving

Physical Problem-Solving: Using Kinematics and Kinesthetics to Improve Mathematics
Jonathan Stephen Fantazier
Pittsburgh CAPA 6-12

The title of this unit may be misleading. It uses ten-dollar words to share a two-cent idea, which is that middle and high school students may best learn some math skills by relating these skills to physics and physical activity. In particular, the skill set that generally falls under the curriculum of an Algebra 1 course, and which is fundamental to all subsequent mathematics study, can be better attained and retained by students who are able to connect it with their own physical identities and physical actions, and comprehensions of the physical universe.

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I Dare You to DANCE!
Merceda Gomez
Pittsburgh Gifted Center

Did you ever wonder how breakdancers can execute power moves such as windmills and flares? Have you ever been intrigued by the double full handsprings done in rhythmic gymnastics? If you answered "yes" to any of these questions, then this course should interest you.

Physics, Math, and the art of creativity in performance-based Humanities all act as the backbone and foundation for a variety of dance forms from Ballet to Krump. Daring dance forms have recently swept the nation: throughout the media and the streets, in theaters and in homes, these intriguing dance moves and techniques are ever present.

I Dare You to DANCE is an interdisciplinary course designed for 3rd-4th grade students at the Pittsburgh Gifted Center; however it can be used with and modified for students of all ages in all types of classroom settings. I Dare You to DANCE will allow students to enhance their interest in and knowledge of dance. It will also show students how Science and Math play a major part in many of the extracurricular activities that they take part in on a daily basis.

During the course, we will study the following daring dance forms: Hip-Hop dance such as Breakdancing & Krump, Ballet, Trapeze & Aerial Silk Acrobatics, Rhythmic Gymnastics, and Figure Skating.

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Physics in Physical Education?? You bet!
Cindy Haigh
Pittsburgh CAPA 6-12

The intended student audience for this unit is for 8th graders of all learning levels. The Standards and Objectives addressed in this paper are from the curriculums of multiple content areas: Physical Education, Math and Science. Plus, the focus of science in the 8th grade is Physics! The genre is football, with an emphasis on offensive strategies. The lessons provide hands-on activities to explore specific motor skills and concepts. They are: quarterback wait time and passing; wide receiver running of five different pass patterns; accuracy and timing of both the quarterback and receiver to achieve success in the catch zone – the designated empty space at the end of each pass pattern.

The lessons follow the steps of the scientific method. A pre-test poses a question for students to think about and then make a prediction (a hypothesis) about it – writing why a particular hypothesis was made. Each student has his/her own data collection answer sheet for recording data and doing calculations. Students will then work in small groups to collect data by performing experiments from five different task cards. They will be measuring distance and time to then calculate speed. Students will use the Pythagorean Theorem to calculate distance using coordinate position reference points. Each student will then draw conclusions about his/her hypothesis, which occurs during a post-test.

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PS, I Love You (PS stands for physics of sports)
Adam Holy
Pittsburgh Gifted Center

While enjoying sports, people can learn about science. In this course, we will explore the physics behind sports including football, baseball, golf, soccer, basketball, billiards, bowling, tennis, ping pong, marbles, and others. You will participate in hands-on activities, view videos, design gear, and explore the science that underlies each particular sport. You may also choose a particular sport and research the physics of that sport in greater detail. Who thought physics could be fun?

Sports in today's society plays a significant role in many people's lives, whether they play for pleasure, health, or professionally, or watch for entertainment. The development of both mental and physical elements of children's lives is something that cannot be truly measured but can account for limitless memories and aid in maturation of each child's character. To be able to unify sports in the classroom would aid in comprehending concepts that otherwise may be difficult for students to grasp and offer a hands on engaging approach to learning physics through sports.

There is no one size fits all way to teaching science to any student no matter the age or skill level they are at. Teaching physics concepts through sports is one approach that would seemingly be something that interests students and therefore make a connection to students. This would in turn make learning meaningful, engaging, and hopefully obtain the ultimate goal, retention of the big idea or concept you are teaching.

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Learning Physics- Walking to Historical Landmarks
Stephanie Johnson
Pittsburgh Faison Primary

This unit will explore math and physics all at the same time. It has a theme such as the Great Race the reality television program. The students will walk to different landmark destinations. At each destination they will learn about the history of the place. They will also be burning plenty of kinetic energy as they walk. Data will be collected on this journey based on the steps that the students will be taking. The steps will be monitored by a timing device called a pedometer. Walking provides several things including exercise and a way to transport you from one destination to the other.

The math that I teach has a large portion of routines that are done on a daily basis. I teach a combination math core curriculum of Everyday math and Envision. The one that I am referring to is called Everyday Mathematics. I have a first grade self contained class in an urban area. My students are interested in new ways of learning. The walking routines that will be done will connect nicely with the core math curriculum. Walking is a routine that we do daily. It takes us to where we desire to go and it is a convenient way to transport you. Energy is important in physics and this unit provides a way for a student to learn it in an interactive way; walking and exploring landmarks at the same time.

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Physical Physics Abstract
Elyse L. Karpa
Pittsburgh Faison Intermediate School

As the title suggests, this unit will involve applying general physics terminology and principles in a physical education setting. Introducing many of the beginning physics terms and general principles in the physical education class will give the students prior exposure to the physical science/physics curriculum making it easier for them to excel in those classes. This on-going unit is designed for middle school physical education classes, but can be modified to the elementary or high school level as well. The physical education teacher will be able to use this unit with any sport or activity he/she introduces to the students throughout the school year. The simplicity of the sample lessons will make it easy and interesting for the students and teacher. These lessons can be tailored by the teacher to fit the students needs. This unit will also facilitate a cross-curricular experience that is sure to assist the students in not only furthering their science experience, but enjoy the physical education classes as well.

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Take me out to the Ballgame
Barbara C. Kengor
Pittsburgh Gifted Center

Take me out to the Ballgame is a curriculum written to teach basic physics principles to primary students. Using the game of baseball as a theme all of the activities centered around the laws of motion, force and energy as they apply to the sport. The unit is organized into the parts of a baseball season; the draft, spring training, the regular season, the play-offs and ends with the World Series. The classroom activities consist of experiments and hands-on explorations. These activities are organized into nine innings.

Each inning begins with background information needed by the student to complete the assigned work. Each inning contains directions for a student activity or experiment. The unit ends with a culminating activity for the World Series which ties in all the concepts and skills used in the curriculum.

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The Physics of Motion and Sports
Eric Laurenson
Pittsburgh Allderdice High School

The physics of sports is a great way to motivate students to learn physics concepts and the mathematical formulations that are involved in simple physics. However, before I engage the students with the external applications of physics principles, I intend to start at the beginning and first address the physics of the human body. In sports we utilize the physics of the motion of the body to perform feats that demonstrate the principals of physical laws. We will be able to address actions such as walking, running and jumping, which are the prerequisites for many sports. We will also consider the mechanics of throwing, which covers the majority of other favorite sports. Once I have addressed the basic physical principles of how the body is able to move, I intend on concentrating on some non-contact sports such as skiing, (until you hit the ground). Then we will consider contact sports, such as football and hockey and baseball, golf and soccer (if you are the bat, club or ball), which address the fundamental concepts of impulse, momentum and forces. I will also consider sports such as football, baseball, soccer and basketball, which also investigate the aspects of projectiles, collisions, momentum and energy. Sports offer a wealth of relevant examples that engage the imaginations of physics students and exemplify physics concepts in action while drawing on students vast amounts of pre-knowledge. It is possible that I may provide students with background knowledge for a plethora of sports and allow them to explore the sport that most interests them. There are books on all of the sports listed so it should not pose any difficulty for students to find readable material for the sport that interests them the most. These sports could act as a culminating explanation and project of the physics of Newtonian mechanics.

My unit will be an ongoing exploration of the fundamental link between sports and physics. I have always drawn on my student's prior knowledge of physics, particularly in sports, to indicate the vast amount of physics we know as humans. Sports are the obvious applications of incredibly complex physics knowledge. This unit is intended for all physics students. I will teach it to my first year physics students as well as my second year, AP B physics students. This unit is engaging both at the conceptual and mathematical levels. However, I believe that these concepts can be simplified to teach it to all levels of physics students.

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Science Across the Curriculum: Developing Critical Thinking Skills Through an Interdisciplinary Approach
Ronni Rossman
Pittsburgh Murray ALA

This curriculum was written to specifically be incorporated into the Pittsburgh Public School curriculum. Specific ideas have been provided for 6th, 7th, and 8th grades. The 6th grade centers on archaeology. The 7th grade centers on Egypt. The 8th grade centers on the Industrial Revolution. Although these are specific to the Pittsburgh Curriculum, the ideas can easily be adapted to be used in other curricula, as well as adapted to be used in Pittsburgh in the upper level grades as well. The lesson plans provide an overview of a multi-disciplinary approach that includes social studies, literature, mathematics, and science classes. The specific daily curriculum in this unit has been designed for 6th - 8th grade.

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Mathletics: Mathletes in Action
Tammy Rullo
Pittsburgh Gifted Center

Currently, I am a third/fourth grade humanities teacher at the Pittsburgh Gifted Center. Last year I taught math as well, and so I have been privileged to instruct most of the students in a variety of courses. Each student in our school is identified as gifted based on a particular strength in either math, humanities (including writing, reading, social studies, and art), or science. Most of our students have amazing talents in two or all three of the areas and find it difficult (or not as enjoyable) to focus on just one content area. We are encouraged to team teach to reach each student in a plethora of ways. In addition, many gifted students have difficulty finding the time, with all of their interests, to keep active or to just experience "playtime".

Pittsburgh has long been known for its amazing sports teams and for its love of athletic competition. With the Pittsburgh Steelers win of the Superbowl and the Penguins Stanley Cup victory last year, combined with the 2010 Winter Olympics and the World Cup, students are even more excited about our city sports and those they are perhaps just discovering. The purpose of this unit is to integrate that enthusiasm for sports into math and writing.

In this unit students will be introduced to concepts of kinetic and potential energy, the relationship between energy and work, and how these tie in with the sport of snowboarding and skateboarding. I think this unit is ideal to capture the challenge needed for advanced and gifted students; to address all the strength areas for our students including math, science, and humanities; and allow students to have fun and keep fit while learning.

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Physical Matheletics: Understanding Algebra Through Volleyball
Sylvia Scott
Pittsburgh Oliver High School

This curriculum unit focuses on linear and quadratic equations, with an emphasis on quadratics a concept of Algebra II that students have a difficult time understanding. The intent of this unit is to get students to feel comfortable in learning and applying the concepts so that they feel confident in applying them in future real world situations. We will examine the concepts of linear and quadratic equations, and in doing this explore the physics concepts of force, momentum, and projectile motion using associated topics of Algebra II through the sport of volleyball. Engaging students into learning the concepts of mathematics has always been challenging. Many students convince themselves that they cannot "do" math and become content to not even try to do or understand the math. At the most basic level of this course, students will establish linear equations from the path of the ball as it flies through the air. Students will also examine the path of the ball, as one player sets it to another, and the curve of the ball caused by the force of gravity. In examining the parabolic curve created from setting the ball, the student can also begin to study the fundamental concepts of physics.

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Chatham University
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Jointly sponsored by Carnegie Mellon University, Chatham University and the Pittsburgh Public Schools.
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