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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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)

8. 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”

9. 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

10. 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”

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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