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Modeling and Prototypes Presentation 4.4.1 Explanation © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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The Unit Big Idea The Engineering Design process is a systematic, iterative problem solving method which produces solutions to meet human wants and desires. © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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The Lesson Big Idea At various intervals of the engineering design process, conceptual, physical, and mathematical models evaluate the design solution. © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Modeling As learned in the engagement there are three different ways to represent our world Written & Spoken Mathematical Graphical © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Modeling During design process, check for proper design to note areas of needed improvements Conceptual, physical, and mathematical models evaluate the design solution Usefulness of models can be tested by comparing predictions to observations in the real world © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Conceptual Models Conceptual models Allow designs to quickly be checked and critiqued Design may be refined and improved. Technical sketching is a design tool used to create conceptual models © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Conceptual Models Several types of technical sketching © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology Isometric Oblique Perspective Orthographic (note: already discussed in exploration)

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Isometric 3D drawings of objects using true measurements © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology Front & side drawn at a 30 o to horizontal For more info, search for “isometric drawing”

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ISOMETRIC GRID

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Oblique Drawings 3D drawings with the width represented as a horizontal line. Side view of object drawn at 45 o from horizontal For more info, search for “oblique drawing” 45˚ © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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OBLIQUE GRID

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VERY IMPORTANT POINT!!!!!

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Perspective 3D drawings of objects where lines converge on one or more points. Intended to be close to the human eye in observation. © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology Can be 1, 2, or 3 point. For more info, search for “perspective drawing”

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Physical Models Mock ups or prototypes. Prototype is a working model to test a design concept through observation and adjustment Mock up simulates the look of an object and not functional. © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Mathematical Models Find a mathematical relationship that behaves same way as objects or processes under investigation Mathematical modeling simulates how a system might behave. Express mathematical ideas precisely © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Mathematical Models Create representations to organize, record, and communicate ideas Symbolic algebra to represent and explain mathematical relationships Computers improved power and use of mathematical models by performing long, complicated, or repetitive calculations © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Example of Mathematical Modeling Designer wants to create hot air balloon designs without creating physical models Algebraic formulas represents increases or decreases of lift based on inside volume or temperature Calculations are communicated on spreadsheets or computer based simulations © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Creating a Mathematical Model Determine Output you would like to achieve for the mathematical model What data/information is available Research for other mathematical models already created you can use. © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Creating a Mathematical Model Identify relationships among variables (science concepts, such as Ohm’s Law) Create equation that relates variables Check accuracy of model against a similar system or over time © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Properties of 2 & 3 Dimensional Objects Engineers and designers must understand basic properties of 2D & 3D objects 2D objects, must be able to calculate area 3D objects, must be able to calculate volume and surface area Properties help determine modifications related to function and marketability © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Calculating Area Area is the amount of surface of a 2D object. Formulas are below. Rectangle: A = length x width Triangle: A = base x ½ (height) Circle: A = ∏ x radius 2 © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Calculating Volume Volume is amount of space a 3D object takes up. Formulas below. Rectangle Box: V = length x width x height Pyramid: V = Area of Base x 1/3 Perpendicular Height Sphere: V = Diameter 3 x.5236 Cylinder: V = Diameter 2 x Length x.7854 © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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Calculating Surface Area Surface area, the measure of how much exposed area a 3D object has. Formulas below Rectangle Box: SA = (H x W x 2) (H x D x 2) (D x W x 2) Pyramid: SA = (Perimeter of Base x ½ Slant Height) + (area of base) Sphere: SA = Diameter 2 x 3.1416 Cylinder: SA= (Diameter x Length of curved surface x 3.1416) + (area of bottom + area of top) © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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All Models Important that they function as close to the real world as possible They must be continually checked and refined during the design process. More than one of the three types is often used for the same product © 2011 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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TOP FRONT RIGHT SIDE

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TOP FRONTRIGHT SIDE ORTHOGRAPHIC PROJECTION

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ISOMETRIC OBLIQUE PERSPECTIVE ORTHOGRAPHIC PROJECTION MOCK UP PROTOTYPE

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Unit 4 Lesson 4 TEST UNIT 4 OPEN NOTE TEST ON TUESDAY MARCH 24. YOU WILL NEED YOUR WORKSHEETS FROM LESSONS 1-4 AND YOU WILL HAVE TO COMPLETE A DRAWING.

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