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Shapes and Designs Inv. 1.3: Tiling Activity

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REVIEW OF DIRECTIONS: 1.) Log on to: OR find this on my math website.www.PHSchool.com 2.) There is an “Enter Code” box in upper left hand of screen. 3.) Enter “amd” in 1st box and “3103” in 2nd box and hit Enter. 4.) Click on “Shapes and Designs” 5.) Click on “Tessellations” 6.) Click on “instructions” and read how to move shapes around. Use the computer to work through Problem 1.3 (page 15 in your book. See also page 9, 10 and 14.)

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NOTE: If you have NOT gone through Problem 1.3 on your own, using your own worksheet, you MUST do this before going any further in this PowerPoint! Click here to go to my web site Go to my website on the Northstar Home Page for a copy of the worksheet. Thank you!

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A. 1. The only possible shapes and tiling patterns. Remember, you weren’t supposed to use B in your sketch here!! A D B

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Regular Triangle or Equilateral Triangle Square Regular Hexagon (Page 9, 10, and 14 show all of the names, shapes, and their letters. Also see your polygon flip book for names.) A. 2. Regular Polygons that tile: Shape A, Shape D, and Shape B. B A D

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B. Possible Sketches using a combination of two or more different shapes. A A D B B F

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A D A B B F In addition to the three examples above, there are 5 other patterns that will tile around a point: 1.square, equilateral triangle, equilateral triangle, square (B,A,B,A) 2.square, regular hexagon, square, equilateral triangle (B,D,A) 3.regular dodecagon, regular hexagon, square (Y,D,B) 4.regular dodecagon, regular dodecagon, equilateral triangle (Y,Y,A) 5.equilateral triangle, equilateral triangle, equilateral triangle, equilateral triangle, regular hexagon (A,A,A,A,D)

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C. 1. Draw in the point where the vertices of the polygons meet. Here or Here

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C. 2. The following polygons fit around these points. Two regular hexagons and two equilateral triangles. Pattern: D,A,D,A Two regular hexagons (D) and two equilateral triangles (A). Pattern: D,A,A,D D,A,A,D D,A,D,A

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C. 3. No, not always. As you can see, this same tiling has two different pattern orders, depending on where you choose the point. (D,A,D,A) (D,A,A,D) DD A A D A A D

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Well Done! Please see me if you have any questions.

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