Designs Around the World

Transcription

1 Math Concepts Integers Fractions/Ratios Decimals Computation Estimation Collect/Classify Data Display Data/Graphs Patterns/Predictions Lines/Relationships Angles 2D/3D Geometrical Shapes Linear Measurement Perimeter/Circumference Area Volume Pythagorean Theorem Symmetry/Reflections Tessellations/Translations Weight/Mass Time Money Math in the Middle... of Design Designs Around the World Acropolis Alhambra aqueducts asymmetrical bilateral symmetry Cartesian plane Colosseum Columns Corinthian Doric Ionic Tuscan Egyptian Cubism excavation Moor frieze gang nailer Golden Rectangle Islamic mosques Mayan Indians M.C. Escher Parthenon reconstructionist resize Key Terms Roofs gable gambrel hipped shed mansard rotational symmetry Sierpenski Triangle Styles Italianate Romanesque Federal Colonial French Provincial Spanish Greek Revival Victorian/Gothic Palladian tabby tessellation/tiling translation Triangles isosceles equilateral scalene trusses vertex Video Fieldtrips Visit an art museum to see works by artists who use designs that have mathematical influences. Objectives Promote the idea that ancient to modern day cultures/civilizations have used mathematical and geometric elements in developing structural and decorative designs Develop a geometric sense of classical designs through creating 2D/3D designs Compare and contrast structural and decorative designs Math in the Middle... of Design Lesson 1 - Designs Around the World Page 1

2 Activity 1 - Building Replicas Architects, designers, and engineers frequently use three dimensional building models for project development.whether planning for a theme park or an office complex. Find pictures of drawings of famous buildings and structures such as the Parthenon, the Empire State Building, the Eiffel Tower, Notre Dame Cathedral, or the Egyptian or Mayan pyramids. Choose one that you would like to recreate as a model. From reference materials or other sources of information, find the actual dimensions or determine relatively close measurement figures for the chosen structure. Determine a reasonable model building scale, in either metric or customary units, such as 10 yards (of actual) converts to 1 inch (of model). Convert the actual dimensions to model dimensions. A scale drawing on graph paper should be made to develop a working building plan. Using available materials.such as craft sticks, straws, sugar cubes, toilet/paper towel rolls, construction paper, craft paper, cardboard, poster board, boxes, etc.build the model from the scale drawing. The structure should be built on a sturdy base such as corrugated cardboard. Markers or water-based paints can be used to add details and decorations. Landscape details, such as trees, rivers, etc., can be made and added to make a more realistic setting. If the model will be used for display purposes, then background information should be attached. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 2

3 Name: Date: Activity 1a - Building Replicas Attach a picture of a famous building in the space below. Name of building: Estimated dimensions: Math in the Middle... of Design Lesson 1 - Designs Around the World Page 3

4 Name: Activity 1b - Building Replicas Date: Determine which view of the building to create a scale drawing. Develop an appropriate scale for the drawing, and use the area below to make the scale drawing. View of building: Scale used: 1 square represents Math in the Middle... of Design Lesson 1 - Designs Around the World Page 4

5 Activity 2 - Resizing Designs Photographers, textile designers, and interior designers are among many of the occupations that deal with the enlarging or reducing of images, pictures, and patterns. Using graph paper, a pencil, a straightedge, and coloring implements, develop a design from the center of the paper. To make a larger version of the original design, use graph paper with larger squares. To make a smaller version, use smaller grid graph paper. From the center of the original design, count the units (number of squares) to the outside edges of the design. Using the same unit measurements from the center to the edge, recreate the design on the second sheet of graph paper. Once the design has been resized, then color the newer version to match the original. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 5

6 Name: Activity 2 - Resizing Designs Date: Develop a design in grid #1. Resize the design either smaller or larger. Grid #1 Grid #2 Grid #3 Math in the Middle... of Design Lesson 1 - Designs Around the World Page 6

7 Activity 3 - What Is It? Lines and shapes are fundamental elements of art as well as geometry. Identifying and analyzing geometrical elements is necessary in developing an understanding of how they relate and support in the development of designs and structures. Find photographs or drawings of interiors/exteriors of famous buildings or take pictures of buildings or homes that are nearby. Look for and identify the geometric elements that appear in each view...such as parallel/perpendicular lines; concentric circles; right, obtuse, acute, and straight angles; various polygon shapes; solid geometrical shapes; vertices; edges; and faces. List the elements that are found. Use the information to determine which elements are used more or less than others and how the elements are used either in the construction or decoration of the interior/exterior of a structure. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 7

8 Name: Activity 3 - What Is It? Attach pictures of structures in the boxes below. Identify the geometrical elements used in the design. Structure #1 Date: Structure #2 Geometric Elements Geometric Elements Which elements were used more often? Math in the Middle... of Design Lesson 1 - Designs Around the World Page 8

9 Activity 4 - Different Styles for Different Profiles Throughout modern history, architects and builders have been affected by a variety of cultural influences. Ancient, as well as more recent building elements, are used in the development of structural and decorative design. Find pictures or illustrations of buildings or structures that focus on the following: columns (Corinthian, Doric, Ionic, Tuscan, or Egyptian), roofs (flat, gable, gambrel, hipped, shed, or mansard), windows (Gothic, stained glass, fanlight, Palladian, Italianate, four over four, or six over six), or overall style (Greek Revival, Victorian/Gothic, French Provincial, Spanish, Italiante, Romanesque, Federal, or Colonial). Examine the physical characteristics of the different styles. Compare/contrast the attributes of the various elements. Find local buildings that were constructed using the different design styles. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 9

10 Name: Date: Activity 4 - Different Styles for Different Profiles Study pictures of the different architectural elements and complete the items below. Likenesses Columns Differences Likenesses Roofs Differences Likenesses Windows Differences Likenesses Overall Style Differences Math in the Middle... of Design Lesson 1 - Designs Around the World Page 10

11 Activity 5 - Complete the Picture Symmetry provides a balance for a structure or a picture by weaving geometry, art, and culture in the development of a visual composition. Using magazines, calendars, sample books, catalogues, etc., cut out samples/pictures of designs or items that are decorated with designs. Some possible design pictures would include quilts, flower arrangements, automobile wheel covers, flooring, wallpaper, or fabric. Look for all of the lines of symmetry (bilateral and rotational). Choose a picture with a bilateral line of symmetry...either vertical or horizontal and cut off half of the picture. Glue the remaining half to a piece of drawing paper so that the original line of symmetry is in the middle. Using a pencil, lightly sketch the reflection of the original half of the picture. Color the reflection with markers or colored pencils to best recreate the color of the original half. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 11

12 Name: Activity 5 - Complete the Picture Date: Glue half of a picture along the horizontal or vertical line of symmetry. Sketch the reflection to complete the picture. Color to match the original. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 12

13 Activity 6 - Simply Symmetrical Spatial visualization skills are important to seeing the reflective characteristics in two and three dimensional designs. Working individually or with a partner, construct a design on one geoboard using one to three rubber bands. Decide on which side of the geoboard design to have a bilateral line of symmetry. Using a second geoboard with the necessary rubber bands, construct the reflection of the original geoboard design across the line of symmetry. If additional geoboards are available, reflections for the other three sides of the design could be constructed. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 13

14 Name: Date: Activity 6 - Simply Symmetrical Original Geoboard Design X X X X X X X X X X X X X X X X X X X X Geoboard Reflection X X X X X X X X X X X X X X X X X X X X Draw the original design in the middle. Construct reflections in each of the 4 directions. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 14

15 Activity 7 - Piecing Together Greek Art Archaeologists rarely discover a vase or piece of ancient pottery that is totally intact. They must often rely on puzzle-solving abilities to determine the original design/decorative aspects of the archaeological find in piecing together a vase or developing a reconstructed one. Using reference materials, museum gift shop catalogs, or personal knowledge of vase/pottery design, find a shape that is visually appealing. Fold a piece of construction or drawing paper in half. With the fold line becoming the vertical line of symmetry for the vase, draw one half of vase. Cut the folded sheet of paper and open it to discover the whole vase. Geometric shapes and designs were frequently used to decorate vases. Use various geometric styles and colors to decorate the vase. Cut the vase in at least ten jagged sections similar to broken pieces. Remove 3-5 pieces and have an excavation partner put the remaining pieces together. Have the partner sketch what the original vase would have looked like. Compare the sketch to the actual vase with all of the pieces put together. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 15

16 Name: Date: Activity 7 - Piecing Together Greek Art: Sheet for Vase Designer Student 1: Vase Designer 1. Cut out rectangle below. 2. Fold in half along vertical line of symmetry. 3. Cut along outside edges to make the vase shape. 4. Open to see whole shape. 5. Decorate using geometric type designs. 6. Cut apart into at least 10 pieces. 7. Remove 3-5 pieces. 8. Turn over pieces to Student 2. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 16

17 Name: Date: Activity 7 - Piecing Together Greek Art: Sheet for Vase Reconstruction Student 2: Vase Reconstructionist 1. Piece together vase. 2. Visualize what the whole vase would have looked like. 3. Sketch the design on sheet Retrieve missing pieces from Student Compare reconstructed sketch to the original. 6. Attach the original to the back of this sheet. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 17

18 Activity 8 - Hard Decisions The ancient Romans were noted for such architectural building components and structures as arches, aqueducts, roads, and the Colosseum. One of their favorite building materials was concrete which was made by combining small rocks and various finely ground minerals with water. For today s homeowner who needs to use a concrete product for a home improvement project, the local hardware or home improvement store offers a variety of choices that weren t available to the ancient Romans. Using newspaper/magazine advertisements, shopping fliers, or a trip to the store, find concrete and concrete repair related products. Gather information about price, weight, mixing, anchoring, strength, uses, finishing, setting time, etc., about concrete mixes and repair products. Determine what tools and equipment would be needed for mixing a concrete product and what the clean-up procedure would be for the tools. Gather information on other home/building related products that are made with concrete, such as garden pots and blocks for buildings and patios. Find out about dimensions, weight, price, uses, color choices, etc. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 18

19 Activity 8 - Hard Decisions Find pictures, catalog, or newspaper information about concrete/ concrete repair products. Place in the boxes below. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 19

20 Name: Activity 8 - Hard Decisions List school related products made with concrete Date: List home related products made with concrete. State the color. Estimate the dimensions and the weight. 1. Product Color Dimensions Weight Math in the Middle... of Design Lesson 1 - Designs Around the World Page 20

21 Activity 9 - Classical Cubes Roman builders used bricks and stones to build the arches needed for the aqueducts, bridges, and other structures. Study pictures of arches and plan the best way to approach the project. Using sugar cubes and white glue, build a sugar cube arch on a letter-sized piece of cardboard. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 21

22 Name: Activity 9 - Classical Cubes Sketch the planned arch in the space below. Estimate the number of cubes for the plan. Count the number of cubes actually used. Date: Estimated number of cubes in the plan Actual number of cubes used Math in the Middle... of Design Lesson 1 - Designs Around the World Page 22

23 Activity 10 - Making a Modern Frieze Ancient Greek sculptors would use a decorative strip along the upper part of a wall called a frieze. Modern day interior designers and home improvement hobbyists continue to use a frieze type device, wallpaper border, to decorate interior spaces. Study pictures in home interior related books to study designs and combination of designs for wall/room decoration...or... Visit a hardware, home improvement, or interior decorating store to look at available wallpapers/borders or sample books. Using an 18-inch piece of adding machine tape and colored pencils/markers, make a frieze sample for a favorite room. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 23

24 Name: Date: Activity 10 - Making a Modern Frieze Use the vertical strips below to make two different frieze designs that a wallpaper border design could be based on. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 24

25 Activity 11 - Tessellating Tiles Islamic artists used complex geometric designs in decorating the art forms found in mosques, paintings, and textiles. The use of mathematical ornamentation through circles, polygons, and symmetry are important features of Islamic art. M.C. Escher was greatly influenced by the geometric structure of Moorish wall tilings, which influenced him in the creation of the animated images appearing in his tessellating designs. One of the most important parts of a tessellation is a translation. Using a square or rectangle, draw a simple design on one side of the shape. Cut out the design shape. Slide the shape to the opposite, parallel side and attach with a small piece of tape. If a more complex design is desired, the same steps can be repeated for the remaining two sides. Use the pattern piece to develop a tessellating design on a piece of construction paper. Finish the design by either coloring with pencils/markers or giving animated features to the pattern pieces before coloring. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 25

26 Name: Activity 11 - Tessellating Tiles Date: Choose a square or rectangle at the bottom of the page. Cut out. Draw a simple design on one interior side of the shape. Cut out the shape. Slide the cut-out portion to the opposite side. Tape. Use the newly made tessellation shape to develop a tessellation design in the space below. Trace around the tessellation shape and keep repeating. Color. Add facial features, if desired. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 26

27 Activity 12- Arches By Any Other Name...Are They The Same? From Roman aqueducts to passageways in Islamic mosques or English churches, arches have been used to support weight and span distances. In the modern, commercial era, the most famous arches serve as a worldwide recognized advertising logo for McDonalds. Before becoming part of an advertising sign, the arches were actually a structural part of the building. Study local buildings and structures for the use of arches in construction. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 27

28 Name: Date: Activity 12 - Arches By Any Other Name...Are They The Same? Find buildings that use arches. List them. Identify where the arches are found (i.e. doorways, windows, walkways, etc.) Decide if the purpose of the arch is Structural, Decorative, or Both. BUILDING LOCATION OF ARCH S, D, OR B Math in the Middle... of Design Lesson 1 - Designs Around the World Page 28

29 Activity 13 - Golden Advertisements The Golden Rectangle has been used by architects and builders from as early as the construction of the Parthenon, atop the Acropolis, during the times of the ancient Greeks. The visual appeal of the golden rectangle has continued to be used in a variety of designs. One aspect of design that has a major economic and visual impact is in advertising. Cut out rectangular advertisements from newspaper and magazine layouts. Collect rectangular labels from retail products. Using a ruler, measure a pair of adjoining sides of each rectangular shape. By using the golden rectangle ratio of 1:1.618, determine which ones meet the specifications. Share the information by expressing the results in ratio, fraction, decimal, and percent forms. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 29

30 Name: Activity 13 - Golden Advertisements Date: Cut out rectangular advertisements from magazines, newspapers, etc., and paste in the boxes below. Measure the adjoining sides of each rectangle. Complete the information below each box to determine if the ad is golden. This side = cm This side = cm This side = cm This side = cm = 1 (short side) (long side) Golden? = 1 (short side) (long side) Golden? Math in the Middle... of Design Lesson 1 - Designs Around the World Page 30

31 Activity 14 - Triangles Triangular shapes have been basic elements in construction since the spectacular pyramids of the Egyptians and Mayans. Because of their ability to support great weight and force, triangles are also widely used in bridge construction. Decorative trims such as porch brackets and gable ornaments utilize triangular shapes. Study local buildings or magazine pictures and note the different ways triangular shapes are used in construction. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 31

32 Name: Activity 14 - Triangles Date: Find buildings that use triangles. List them. Identify where the triangles are found (i.e. doorways, windows, walkways, etc.) Decide if the purpose of the triangle is Structural, Decorative, or Both. BUILDING LOCATION OF TRIANGLE S, D, OR B Math in the Middle... of Design Lesson 1 - Designs Around the World Page 32

33 Problems in Designs Around the World Problem 1 - Spanish Flooring in Early America The Spanish, who helped settle northern Florida in the 16th century, used locally acquired materials in construction. Oyster shells and sand were primary flooring materials. If the floor was made with a 12 inch deep layer or oyster shells topped by a 4 inch concrete-like layer of burned oyster shells and sand, what would be the total volume of a floor for a 10 ft by 12 ft room? Problem 2 - Coastal Georgia Tabby Tabby, a building material similar to what the Spanish used, was a combination of oyster shell, lime, sand, and water. This was used in constructing many homes in the coastal area. One coastal home made of tabby had a 22 ft by 12 ft parlor and a dining area of 15 ft by 11 ft. Determine the perimeter and the area of the floor in each area. If the tabby house had ceilings of 9 feet in height, what would the total volume of the rooms be? Problem 3 - Frieze It As part of a kitchen renovation project, a homeowner decided to use a border along the ceiling of the two rooms forming the kitchen. The perimeter of the larger room is 48 feet with the smaller room being 2/3 of the larger. If the border is sold in packages of 15 ft lengths, how many packages would the homeowner need to buy? Problem 4 - Trussed Up Triangles A camping enthusiast plans to build a 40 ft long storage garage for a camper trailer. If roof trusses are to be placed every 2 feet, then how many roof trusses need to be bought? Problem 5 - A Gang of Gang Nailers A type of roof truss design is similar to the beginnings of a Sierpinski Triangle...a triangle with the midpoints of each side connected. With a roof truss, the ends of the boards at each angle are connected by two gang nailers (one for the front and back of each board). If 15 roof trusses are needed, then how many gang nailers are needed in the constructions? Math in the Middle... of Design Lesson 1 - Designs Around the World Page 33

34 Video Challenge Activity Tour your local museum or to find artwork in a library book or on the Internet, and see what mathematical or specifically geometrical shapes and patterns catch your eye. Find a particular painting that really draws your attention, and write a paragraph about what it is within the painting that is so eye-catching. Math in the Middle... of Design Lesson 1 - Designs Around the World Page 34