Proportional Views Of Multiview Figures - Illinois State Board Of Education
Proportional Views of Multiview Figures Unit: Orthographic and Multiview Projection Problem Area: Multiview Projections Lesson: Proportional Views of Multiview Figures Student Learning Objectives. Instruction in this lesson should result in students achieving the following objectives: 1 Explain the reasons that proportional views are created for multiview drawings. 2 Draw proportional multiview drawings from coded plans or orthographic drawings. 3 Create proportional views of multiview orthographic drawings as a technical drawing or a CAD drawing. List of Resources. The following resources may be useful in teaching this lesson: “Creative Building,” The LEGO Group. Accessed Sept. 25, 2008. http://creative.lego.com/en-us/games/default.aspx . Giesecke, Frederick E., et al. Technical Drawing, 12th ed. Prentice Hall, 2003. Illinois Drafting Educators Association. I.D.E.A. Curriculum. Accessed June 18, 2008. http://www.idea-online.org/curriculum.html . Lesson: Proportional Views of Multiview Figures Page 1 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
“Image: Table of Architecture, Cyclopaedia, 1728,” Wikipedia. Accessed Sept. 25, 2008. http://en.wikipedia.org/wiki/Image:Table of architecture, Cyclopaedia, 1728, volume 1.jpg . Madsen, David A., David P. Madsen, and J. Lee Turpin. Engineering Drawing and Design, 4th ed. Cengage, 2007. Rowlett, Russ. “How Many?: A Dictionary of Units of Measurement,” University of North Carolina at Chapel Hill. Accessed Sept. 25, 2008. http://www.unc.edu/ rowlett/units/index.html . List of Equipment, Tools, Supplies, and Facilities ü Overhead or PowerPoint projector ü Visual(s) from accompanying master(s) ü Copies of sample test, lab sheet(s), and/or other items designed for duplication ü Materials listed on duplicated items ü Computers with printers and Internet access ü Classroom resource and reference materials Terms. The following terms are presented in this lesson (shown in bold italics): architectural scales coded plan engineer’s scales fractions measurement scales metric scales proportion ratio scale drawings scale factor symmetry Interest Approach. Use an interest approach that will prepare the students for the lesson. Teachers often develop approaches for their unique class and student situation. A possible approach is included here. Begin a discussion by asking, “How have technical drawings developed throughout the years?” In previous lessons, students have learned about the standards of technical drawing with respect to orthographic projection or multiview projection drawing, but initial drawings have been simple, full-size drawings that easily fit on the paper or computer screen on which they are drawing. Lesson: Proportional Views of Multiview Figures Page 2 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
Using a computer projection device or copies of the Table of Architecture Cyclopedia 1728, have the students analyze this nearly 300-year-old architectural drawing. http://en.wikipedia.org/wiki/Image:Table of architecture, Cyclopaedia, 1728, volume 1.jpg Ask the students to compare the drawing to first-angle and third-angle multiview projections presented in earlier lessons. Then have the students explain how the drawing is reduced to fit on paper. Introduce the concepts of ratio, proportion, and measurement scales. Ask students to explain why some parts of the drawing are larger or smaller than others. Discuss the importance of the different mathematical concepts that make proportional multiview drawings necessary for business and industry. Discuss the restrictions that pencil and paper drawing impose and the limitless nature of CADD. SUMMARY OF CONTENT AND TEACHING STRATEGIES Objective 1: Explain the reasons that proportional views are created for multiview drawings. Anticipated Problem: What is a scale drawing, and why is it necessary to create scale drawings? When is it necessary to identify the scale of a drawing, and what affect does the scale of measurement have on printed drawings? I. Mathematical concepts that influence and affect technical drawings A. Proportion and symmetry are important basic concepts related to all design. 1. Proportion is the harmonious relationship between the parts and the whole— balance. All good design has proportion, but not all design has symmetry. 2. Symmetry is the relationship between equal proportions related to vertical or horizontal features of an object. It has to do with a correspondence in size, shape, and relative position of parts on opposite sides of a dividing line, median plane, or center line or axis. 3. A lack of proportion is defined as asymmetry. B. Fractions express amounts that are numerically less than a whole number. 1. The numerator is the part of the fraction above the line that indicates the number of pieces or parts. 2. The denominator is the part of the fraction below the line (signifying division) that indicates the number of whole parts. 3. When dividing the numerator by the denominator, a percentage is expressed as a decimal. Lesson: Proportional Views of Multiview Figures Page 3 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
C. Ratio is the relationship in quantity, amount, or size between two or more things (e.g., 1:2). 1. A ratio is the use of division to describe the relationship of numbers or mathematical facts. 2. Fractions relate a numerator with a denominator. 3. A percentage indicates the number of parts per 100. D. A scale factor is a number used as a multiple or a divisor that shows the relationship between the real object and a printed drawing. 1. A scale factor that is greater than one results in a drawing larger than the real size. 2. A scale factor that is less than one results in a drawing that is smaller than the real size. E. Measurement scales are the real units used to measure an object. 1. The International System (SI) is the metric system. The metric system is a decimal system of weights and measures that is based on the kilogram (weight) and the meter (measure). 2. The English Customary System is based on feet (measure) and pounds (weight) and may be expressed as fractions or decimals. Refer students to the following Web site: http://www.unc.edu/ rowlett/units/index.html to review measurement scales. F. Scale drawings use a scale factor to display a large object on a relatively small piece of paper. 1. A scale factor can be utilized to display a small object as larger to view important details. 2. These may be full-scale (the actual size) objects. Use VM–A to assist students in comprehending this objective. Ask students to bring in plans from LEGO models. These plans are the basis for coded plans (scale drawings or proportional drawings). Three- and four-year-old children, with minimal language and math skills, are able to follow the instructions to build the models. Most drawings are scale drawings in that they represent an object that is reduced or enlarged in size. The most common scale drawing is a map—a single view that shows northsouth/east-west or horizontal-vertical distances. Scale drawings are also made for small things (e.g., a printed circuit board or a microprocessor in a computer). The visual skills that help us determine size and proportion are easily learned with practice. Show students the following Web link: http://creative.lego.com/en-us/games/default.aspx . It is a LEGO game that uses some of the principals of coded plans. Lesson: Proportional Views of Multiview Figures Page 4 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
Objective 2: Draw proportional multiview drawings from coded plans or orthographic drawings. Anticipated Problem: What is a plan view, and how can the front and back be differentiated? What is a coded plan, and how are right and left sides determined? What is the relationship between orthographic projection and the plan view? How is the appropriate measurement scale determined? II. It is necessary to define the plan view or top view for an orthographic projection. A. A floor plan in an architectural drawing shows the length and width of a room, not the height; similarly, a plan or top view shows the length and width. 1. When the most important or special-featured side view is determined, it becomes the front view. The next question is: “Can the object be drawn full size in the required format?” 2. The front and side views define the height of the object. So it is necessary to ask: “Can the object be drawn full size in the required format?” a. Architectural scales are used to draw a large building in proportion on a small piece of paper by using feet and inches as measuring units. For example, ¼ inch 1 foot is a typical architectural scale. b. Engineer’s scales may be used to draw small objects large or large objects small by using decimal units based on an inch. For example, 1 inch 1/10 of an inch may be used. c. Metric scales may be used to draw small objects large or large objects small. Usually millimeter is the chosen measure, but the measure may be a multiple or divisor or may be 10 units larger or smaller. d. The following Web link illustrates several styles of scales: http://www.staedtler-usa.com/triangular scales us.Staedtler . B. A coded plan defines three dimensions in one single view. 1. Length and width are defined in the plan view. 2. Height is given as numbered units on each square of the coded plan. a. A coded plan can be used to scale a drawing larger or smaller. b. Each square of a coded plan relates to some predetermined size based on a grid; one square might be ¼ of an inch or 10 millimeters or 6 inches or 1 inch. c. The following question must be asked: “Can the object be drawn full size, or should it be scaled up or down?” C. Side views can also be called elevations. 1. If there is a one on a square, it indicates that the square is a three-dimensional cube that is equal on all surfaces. 2. All elevations show height and length or width. Lesson: Proportional Views of Multiview Figures Page 5 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
3. In coded plans, each square is one unit. a. One unit may be shown in the English Customary System or in the metric system. b. The scale must be identified so the viewer can visually understand the real size of the object (e.g., proportionally larger, smaller, or real size). D. Visible surfaces are chosen by the drafter to be the principal views of the drawing or projection. 1. Hidden lines are drawn to represent unseen edges and features. 2. Dimensions are not presented in coded plans because the viewer knows the size of each square. 3. Alternative view positions may be determined from coded plans. Use VM–B to review Objective 2. Assign LS–A to help students create examples of multiview drawings from coded plans. Objective 3: Create proportional views of multiview orthographic drawings as a technical drawing or a CAD drawing. Anticipated Problem: How can the appropriate scale for multiview projections be determined? How are coded plans used to create scaled multiview projections? How can an individual scale orthographic projections to explain or present details? III. Critical features of multiview projections A. Only three projection planes are used. 1. Top: This shows the length and width. 2. Front: This shows the length and height. 3. Side: This (right or left) shows the height. a. It is necessary to ask if the drawing will be drawn or printed on paper. b. It is necessary to ask if the drawing will be produced with a CAD system. c. It is necessary to ask if the object is very large or very small. B. With some objects, all views may fit on paper. 1. With paper, the drawing scale must be determined before beginning. 2. With CAD systems, all objects are drawn full size and are scaled prior to printing. C. Drawing measurement scale units for accuracy 1. Fractional inch units: 1/16, 1/32, 1/64, or smaller 2. Decimal inch units: 1/10, 1/100, 1/1000, or smaller 3. Architectural units: 1/16, 1/32, 1/64, or smaller 4. Metric units: 1/10, 1/100, or 1/1000 mm Lesson: Proportional Views of Multiview Figures Page 6 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
D. Construction lines should be created parallel to the edges of the front plane. 1. Construction lines should be drawn thinly and lightly on paper. 2. In CAD, a continuous line and/or a different color or layer should be used. 3. For paper drawings, a scale factor should be selected to measure accurately. 4. For CAD, the object should be drawn true size. E. It is necessary to darken lines that are visible edges and to use appropriate layers for CAD. 1. Edges that are not visible are drawn as hidden lines. 2. Views that show the most important details should be selected; the most important view should be the front view. 3. Center lines are thin and dark in pencil drawings or a different color or layer in CAD. 4. Dimension and extension lines may be used to clarify the drawing. a. Dimension lines should always be parallel to the lines that they are measuring. b. Extension lines project from the object perpendicular to the dimension line. Use VM–C to show students some coded plan solutions that can be made into scale multiview drawings. Students should create drawings by using a CADD system or by using pencil drafting techniques. Typical CADD solutions for four problems are given in VM–D, VM–E, VM–F, and VM–G. Additional drawing activities and coded plans can be accessed at the Illinois Drafting Educators Association Web page: http://www.idea-online.org/curriculum.html . Review/Summary. Use the student learning objectives to summarize the lesson. Have students explain the content associated with each objective. Student responses can be used in determining which objectives need to be reviewed or taught from a different angle. Questions at the ends of chapters in the textbook may also be used in the review/summary. Application. Use the included visual masters and lab sheets to apply the information presented in the lesson. Evaluation. Evaluation should focus on student achievement of the objectives for the lesson. Various techniques can be used, such as student performance on the application activities. A sample written test is provided. Answers to Sample Test: Part One: Matching 1. c 2. a 3. b Lesson: Proportional Views of Multiview Figures Page 7 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
4. e 5. d 6. f Part Two: Short Answer 1. Features of the English Customary System of measure: a) It is based on feet and inches (measure) and pounds (weight). b) It uses the inch and fractions of an inch to describe linear measurements. c) It may be expressed as fractions of an inch (e.g., 1/64, 1/32, 1/16, c, ¼, or ½). d) It may be expressed as decimals (e.g., 0.001). 2. The purpose of a scale drawing is to illustrate multiple views of an object that normally would be too large or too small if drawn to real size on paper. 3. Features of the metric system of measure: a) It is based on a decimal weight (kilogram) and measurement (meter) system. b) When used for technical drawings, it can easily be adapted to large or small sizes because it is based on a decimal system. For example, 1 centimeter equals 10 millimeters; 1 meter equals 100 centimeters; and 1 kilometer equals 1000 meters. Part Three: Completion 1. 2. 3. 4. 5. 6. asymmetry Symmetry English Customary System International System (SI) Engineer’s scales Architectural scales Lesson: Proportional Views of Multiview Figures Page 8 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
Sample Test Name Proportional Views of Multiview Figures u Part One: Matching Instructions: Match the term with the correct definition. a. scale factor b. ratio c. measurement scale d. fraction e. denominator f. numerator 1. The real units that are used to measure an object 2. A number used as a multiple or a divisor that shows the relationship between the real object and a printed drawing 3. The relationship in quantity, amount, or size between two or more things 4. The lower part of a fraction 5. A numerical expression that is less than a whole number 6. The upper part of a fraction u Part Two: Short Answer Instructions: Complete the following. 1. Describe features of the English Customary System of measure. Lesson: Proportional Views of Multiview Figures Page 9 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
2. What is the purpose of producing a scale drawing? 3. Describe features of the metric system. u Part Three: Completion Instructions: Provide the word or words to complete the following statements. 1. A lack of proportion is defined as . 2. is the relationship between equal proportions related to vertical or horizontal features of an object. 3. The is based on feet and inches and may be represented as fractions or decimals. 4. The is another name for the metric system, a decimal-based measurement system. 5. may be used to draw small objects large or large objects small, using decimal units based on an inch. 6. are used to draw a large building in proportion on a small piece of paper by using feet and inches as measuring units. Lesson: Proportional Views of Multiview Figures Page 10 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–A SCALE FACTOR t Purpose: This visual master communicates the mathematical relationships necessary to create proportional views of objects. Different types of drawings require different scales to allow the drawing to be reproduced on paper. As drawings are produced using CADD systems, additional CADD program features allow the CADD drafter to create drawings that meet CAD standards and maintain scale mathematical relationships. t Why are all of the dimensions the same? t What happens when the scale factor changes? t Why would you use a factor greater than one? t Why would you use a factor less than one? t Full size, half size, or double size? t This object has been drawn twice: which is full size? t The object is black. Hidden lines are magenta. Dimension lines are blue. t What about the dimensions on each separate drawing? t Look closely and consider the size and spacing of the dashes in the hidden and center lines in both drawings. Why are they different? Lesson: Proportional Views of Multiview Figures Page 11 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–B MEASUREMENT SCALES t Purpose: This visual master is to communicate technical information and the process necessary to create a variety of different multiview projection drawings. Two different measurement scales of one part are compared in the drawing. The relationship of size and measurement accuracy is an important feature of all types of technical drawings. t Why are the dimension sizes different? t How do you know which measurement scale is being used? t Could these be two different size parts? t How do we know it is not feet and inches? t Instructions: Given the two orthographic drawings, draw the orthographic drawings with their real dimensions using a CADD system. Identify the measurement scales being used. Use blue for dimensions. Use magenta for hidden lines. Use green for center lines. Lesson: Proportional Views of Multiview Figures Page 12 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–C CODED PLAN MULTIVIEW SOLUTIONS t Purpose: This visual master is to communicate technical information and the process necessary to create multiview drawings from coded plans. Coded plans are used to expand visualization skills in creating multiview sketches and drawings. t Part 1: Sketch Solutions t Compare each square on the grid to complete the front and right side views. t Hidden lines are blue. t Dimensions are not necessary. t Note how view position affects the need for hidden lines. Lesson: Proportional Views of Multiview Figures Page 13 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–D MULTIVIEW CADD SOLUTIONS WITH DIMENSIONS EXAMPLE A t Proportional Scaled Multiview Drawing in CADD Using the Factor ½" for the Size of Each Coded Square t Purpose: This visual master is to communicate technical information and the process necessary to create multiview CADD scale drawings from coded plans. Proportional scaled multiview drawings are created in a CADD system. Dimensions are added to the drawing. Lesson: Proportional Views of Multiview Figures Page 14 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–E MULTIVIEW CADD SOLUTIONS WITH DIMENSIONS EXAMPLE B t Proportional Scaled Multiview Drawing in CADD Using the Factor ½" for the Size of Each Coded Square t Purpose: This visual master is to communicate technical information and the process necessary to create multiview CADD scale drawings from coded plans. Proportional scaled multiview drawings are created in a CADD system. Dimensions are added to the drawing. Lesson: Proportional Views of Multiview Figures Page 15 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–F MULTIVIEW CADD SOLUTIONS WITH DIMENSIONS EXAMPLE C t Proportional Scaled Multiview Drawing in CADD Using the Factor ½" for the Size of Each Coded Square t Purpose: This visual master is to communicate technical information and the process necessary to create multiview CADD scale drawings from coded plans. Proportional scaled multiview drawings are created in a CADD system. Dimensions are added to the drawing. Lesson: Proportional Views of Multiview Figures Page 16 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
VM–G MULTIVIEW CADD SOLUTIONS WITH DIMENSIONS EXAMPLE D t Proportional Scaled Multiview Drawing in CADD Using the Factor ½" for the Size of Each Coded Square t Purpose: This visual master is to communicate technical information and the process necessary to create multiview CADD scale drawings from coded plans. Proportional scaled multiview drawings are created in a CADD system. Dimensions are added to the drawing. Lesson: Proportional Views of Multiview Figures Page 17 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
LS–A Name Coded Plan Problems Purpose The purpose of this activity is to create multiview drawings or sketches following a coded plan. Additional activities include creating CADD drawings from previously drawn orthographic or coded plan drawings. Objectives 1. Complete the multiview sketches on the provided grid sheet by using the coded plans. A coded plan and an isometric drawing are provided for each problem. 2. Sketch the front and right side views for each problem by using the provided information. Materials t paper for sketching or drawing t blank grid sheet t pencil t eraser Procedure 1. Examine the orthographic coded example. 2. Analyze the isometric view example. 3. Create the front and right side views. 4. Use light construction lines, if necessary. 5. Count grid squares in the coded plan or in the isometric example to obtain the height, length, and width. Lesson: Proportional Views of Multiview Figures Page 18 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
6. Darken the object edges. 7. Add the hidden lines where necessary. Do not dimension. 8. Erase or trim the construction lines. Coded Plans and Isometric Views: t Part 1: Sketch each of the coded plans as a top, front, and right side multiview projection on sketch paper. Add hidden lines where necessary. t Part 2: Create a multiview CADD drawing of the figures using ½" for the size of each square. Add hidden lines where necessary, and fully dimension. Lesson: Proportional Views of Multiview Figures Page 19 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
LS–B Name Orthographic/Rectangular Grid Sheet Purpose The purpose of this activity is to create multiview drawings from orthographic drawings or coded plans. Objective Create proportional multiview sketches from coded plans. Materials t paper for sketching or drawing t blank grid sheet t pencil t eraser Procedure 1. Examine the coded plan examples. 2. Determine the front view position. 3. Using the grid sheet, create a three-view, orthographic projection from each coded plan. 4. Add hidden lines where necessary. 5. Using the example in your text, handouts from your instructor, or handouts from the IDEA Curriculum, compare each square on the grid to the rectangular grid. Then use the square size to complete the sketch from the coded squares. Then create a half-size Lesson: Proportional Views of Multiview Figures Page 20 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
orthographic drawing and a double-size drawing using a CADD system for each assigned problem. Lesson: Proportional Views of Multiview Figures Page 21 u www.MyCAERT.com Copyright by CAERT, Inc. Reproduction by subscription only. L600030
Multiview Figures Unit: Orthographic and Multiview Projection Problem Area: Multiview Projections Lesson: Proportional Views of Multiview Figures Student Learning Objectives. Instruction in this lesson should result in students achieving the following objectives: 1 Explain the reasons that proportional views are created for multiview drawings.
Lesson 8: Identifying Proportional and Non-Proportional Relationships in Graphs (Tables to Graphs) Exit Ticket (2 points) For each of the graphs below state whether they represent a proportional relationship and how you know. If the graph does represent a proportional relationship find the unit rate.
TI 30X IIS calculator (or any fraction calculator) . MultiView TI-34 MultiView TI-36X Pro 7 t h G r a d e S u p p l y L i s t 2 0 2 0 - 2 0 2 1 ( b o t h H o n o r s a n d R e g u l a r C l a s s e s ) Personal Supplies . TI-34 MultiView
Orthographic projection is a technique that is used to create multiview drawings. Orthographic projection. is any projection of the features of an object onto an imaginary plane of projection. The . projection plane, projection line, glass box, multiview drawing Created Date:
Orthographic Projection. TOPICS Object representation Glass box concept Line convention Orthographic projection of point, line, plane, surfaceand object. Multiview projection. OBJECT REPRESENTATION Axonometric projection Multiview projection. MULTIVIEW PROJECTION Three principle dimensions
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs Student Outcomes Students decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
G7-M1-Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs Recognizing Proportional Graphs Determine whether or not the following graphs represent two quantities that are proportional to each other. Explain your reasoning. 1. The graph shows that distance in miles is proportional to the time in hours because the points
Lesson 3: Identifying Proportional and Non-Proportional Relationships in Tables Student Outcomes Students examine situations to decide whether two quantities are proportional to each other by checking for a constant multiple between measures of and measures of when given in a table.
32.33 standards, ANSI A300:Performance parameters established by industry consensus as a rule for the measure of quantity, weight, extent, value, or quality. 32.34 supplemental support system: Asystem designed to provide additional support or limit movement of a tree or tree part. 32.35 swage:A crimp-type holding device for wire rope. 32.36 swage stop: Adevice used to seal the end of cable. 32 .
