2016 Revised Alabama Course of Study Mathematics.pdf

# Prove and apply trigonometric identities 1 make sense

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Prove and apply trigonometric identities. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

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2016 Revised Alabama Course of Study: Mathematics 74 CONCEPTUAL CATEGORIES: MODELING Modeling links classroom mathematics and statistics to everyday life, work, and decision making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data. A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object like a coin. Even simple models involve making choices such as the decision to model a coin as a three-dimensional cylinder or as a two-dimensional disk. Other situations—modeling a delivery route, a production schedule, or a comparison of loan amortizations—need more elaborate models that use other tools from the mathematical sciences. Real- world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity. Examples of such situations might include the following: Estimating how much water and food is needed for emergency relief in a devastated city of 3 million people, and how it might be distributed. Planning a table tennis tournament for 7 players at a club with 4 tables, where each player plays against every other player. Designing the layout of the stalls in a school fair so as to raise as much money as possible. Analyzing stopping distance for a car. Modeling savings account balance, bacterial colony growth, or investment growth. Engaging in critical path analysis such as turnaround space required for an aircraft at an airport. Analyzing risk in situations such as extreme sports, pandemics, and terrorism. Relating population statistics to individual predictions. In situations like these, the models devised depend on a number of factors, including “How precise an answer do we want or need?” “What aspects of the situation do we most need to understand, control, or optimize?” “What resources of time and tools do we have?” The range of models that can be created and analyzed is also constrained by the limitations of our mathematical, statistical, and technical skills as well as the ability to recognize significant variables and relationships among them.
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