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##### Mathematical Processes

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**Competency 018**Mathematical Processes**Competency 018**Mathematical Processes**Competency 018**Mathematical Processes • Logical Reasoning: In logic, three kinds of logical reasoning can be distinguished: deduction, induction, and abduction. Given a precondition, a conclusion, and a rule that the precondition implies the conclusion, they can be explained in the following way: • Deduction means determining the conclusion. It is using the rule and its precondition to make a conclusion. Example: "When it rains, the grass gets wet. It rains. Therefore, the grass is wet." Mathematicians are commonly associated with this style of reasoning. • Induction means determining the rule. It is learning the rule after numerous examples of the conclusion following the precondition. Example: "The grass has been wet every time it has rained. Therefore, when it rains, the grass gets wet." Scientists are commonly associated with this style of reasoning. • Abduction means determining the precondition. It is using the conclusion and the rule to support that the precondition could explain the conclusion. Example: "When it rains, the grass gets wet. The grass is wet, therefore, it may have rained." Diagnosticians and detectives are commonly associated with this style of reasoning.**Competency 018**Mathematical Processes Logical thinking exercises help kids learn the process of elimination or deductive thinking. Most problems give a variety of conditions and you must use an "if"-"then" approach. It's important that you read the whole problem, and choose the best hint or clue before starting to solve the problem. When practicing logic with reasoning making a chart or drawing a picture are good strategies. Now here is an everyday problem to solve using Logical Reasoning. Alvaro, Rodrigo, and Alejandro go to Pecos’s Pizza's, where each one chose one of three kinds of pizza: sausage, cheese, or pepperoni. Using the following clues, who ordered which kind of pizza? A. Rodrigo eats anything that is spelled with a double letter. B. Alvaro loves pizza, but he can't eat anything with too much dairy in it. C. Alejandro said he would settle for whatever kind was left. Now using Logical Reasoning fill out the table below by putting an X in the kind of pizza each person would want.**Competency 018**Mathematical Processes**Competency 018**Mathematical Processes 4 steps to solve a problem: Understand -- Before you can solve a problem you must first understand it. Read and re-read the problem carefully to find all the clues and determine what the question is asking you to find. Plan -- Once you understand the question and the clues, it's time to use your previous experience with similar problems to look for strategies and tools to answer the question. Try It -- After deciding on a plan, you should try it and see what answer you come up with. Look Back -- Once you've tried it and found an answer, go back to the problem and see if you've really answered the question. Sometimes it's easy to overlook something. If you missed something check your plan and try the problem again.**Competency 018**Mathematical Processes 4 steps to solve a problem: try the QDPA. Question (Pregunta): Que te dic que la pregunta, que quieres saber? Data (Datos): Cuales son los datos que te da el problema? Plan: Que tienes que hacer para resolver el problema. Busca pistas, palabras claves, usa razonamiento logico si es posible. Answer (Contesta): Lleva a cabo el plan y piensa si tu respuesta es razonable.**Competency 018**Mathematical Processes Problem solving: Solving a problem involves more than just numerical computation; logical reasoning and careful planning also play important roles. These are some problem solving strategies:**Competency 018**Historical Development of Mathematics Muchas culturas han ayudado ha desarrollar los conceptos matemáticos que utilizamos hoy en día. Ha sido un proceso largo y acumulativo que ha permitido desarrollar procesos que permiten la solución a problemas que incluyen cómputos. Entre estas civilizaciones tenemos: Hindu Greeks (astrónomos) Algebra y geometría Egyptians and Babylonians Sistema de numeración Concepto de cero**Competency 018**Historical Development of Mathematics Aztecs Conceptos de ingeniería, arquitectura, calendario Arab Sofisticado Sistema algebraico, Precursores del sistema de numeración actual Mayans Sistema de numeración y el concepto de cero, astronomía y ingeniería**Sample Question**• Ms. Hernandez plans to buy carpeting for her living room floor. The room is a rectangle measuring 14 feet by 20 feet. She wants no carpet seams on her floor, even if that means that some carpeting will go to waste. The carpeting she wants comes in 16-foot-wide rolls. What is the minimum amount of carpeting that will have to be wasted if Ms. Hernandez insists upon her no-seams requirement? • 40 square feet. • 60 square feet. • 80 square feet. • 100 square feet.