STUDENT LEARNING GOALS ADDRESSED BY THE PROJECTILE MOTION MODEL Graphing data Describing trends revealed by data Applying basic trigonometric functions to a real problem Determining mathematical models that describe the relationships between data points Interpreting the contextual meaning of graphs Using analyzed data to confirm, modify, or reject hypotheses Using computer models to extend understanding of scientific concepts Understanding two dimensional motion

STANDARDS MET BY THE PROJECTILE MOTION MODEL National Science Education Standards Content Standard Description Unifying Concepts and Processes All students should develop understanding and abilities aligned with the following concepts and processes: Systems, order, and organization Evidence, models, and explanation Constancy, change, and measurement Evolution and equilibrium Form and function Science as Inquiry All students should develop: Abilities necessary to do scientific inquiry Identify questions and concepts that guide scientific investigations Design and conduct scientific investigations Use technology and mathematics to improve investigations and communications Formulate and revise scientific explanations and models using logic and evidence Recognize and analyze alternative explanations and models Communicate and defend a scientific argument Understandings about scientific inquiry AAAS Benchmarks Topic Description 1B-Scientific Inquiry Hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of data (both new and previously available). 2B-Mathematics, Science, and Technology Mathematics provides a precise language for science and technology - to describe objects and events, to characterize relationships between variables, and to argue logically. 9B-Symbolic Relationships In some cases, the more of something there is, the more rapidly it may change. Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation. 11A-Systems Understanding how things work and designing solutions to problems of almost any kind can be facilitated by systems analysis. In defining a system, it is important to specify its boundaries and subsystems, and identify what its input and its output are expected to be. The successful operation of a designed system usually involves feedback. The feedback of output from some parts of a system to input of other parts can be used to encourage what is going on in a system, discourage it, or reduce its discrepancy from some desired value. The stability of a system can be greater when it includes appropriate feedback mechanisms. 11B-Models The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation. A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning. Computers have greatly improved the power and use of mathematical models by performing calculations that are very long, very complicated, or repetitive. Therefore computers can show the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and testing of devices and structures and in the simulation of complicated processes The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that the model is the only "true" model or the only one that would work. 11C-Constancy and Change Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change. Maryland Core Learning Goals in Science Goal/Expectation Description Goal 1 The student will demonstrate ways of thinking and acting inherent in the practice of science. The student will use the language and instruments of science to collect, organize, interpret, calculate, and communicate information. 1.2 The student will pose scientific questions and suggest experimental approaches to provide answers to questions. 1.4 The student will demonstrate that data analysis is a vital aspect of the process of scientific inquiry and communication. 1.5 The student will use appropriate methods for communicating in writing and orally the processes and results of scientific investigation. 1.6 The student will use mathematical processes. Goal 5 The student will demonstrate the ability to use scientific skills and processes to explain and predict the outcome of certain interactions which occur between matter and energy. 5.1.2 The student will use algebraic and geometric concepts to describe an object's motion. National Council of Teachers of Mathematics Standards Expectation Description Mathematical Models All students should be able to use mathematical models to represent and understand quantitative relationships: Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts Draw reasonable conclusions about a situation being modeled Analysis of Change All students should be able to: Analyze change in various contexts Approximate and interpret rates of change from graphical and numerical data Problem Solving All students should be able to solve real world problems: Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Maryland Core Learning Goals in Mathematics Goal/Expectation Description Goal 1 The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra. 1.1 The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology. 1.2 The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

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