## The Luxor Hotel Contract

### Wanda MartinSanta Rosa District Schools

#### Description

Given square feet of the base, volume, and the volume formula, students will determine slant height the Luxor Hotel so that they can find surface area. Then they will create a model to scale, including the mirrored glass, which is on each triangular face of the hotel. Your (students') company has just been asked to submit a bid, accompanied with a scale model, for the Luxor Hotel in Las Vegas. You have been asked to cover the exterior of the building with mirrored glass tile. In your excitement at being offered such a prestigious opportunity, you failed to gather all necessary information. Because you cannot reach the architect and you have a deadline to meet, you have to determine what you need to know from the information you have so you can complete your task.

#### Objectives

The student uses concrete and graphic models to explore and derive formulas for surface area and volume of three-dimensional regular shapes, including pyramids, prisms, and cones.

The student solves and explains real-world problems involving surface area and volume of three-dimensional shapes.

The student constructs and uses scale drawings to recreate a given situation.

The student determines and justifies the measures of various types of angles based upon geometric relationships in two- and three-dimensional shapes.

The student draws and builds three-dimensional figures from various perspectives (for example, flat patterns, isometric drawings, nets).

#### Materials

-Computer with Internet access
-LCD projector
-SmartBoard (optional)
-Plain paper
-Poster board
-Silver-sided poster board
-Foam-core board (or other sturdy foundation material)
-Labels
-Glue sticks
-Tape
-Scissors
-Rulers
-Yard sticks
-Protractors
-Folders
-Copies of Check List and Rubric for each group
-Hat (or other small container) from which students draw mirrored glass dimensions

#### Preparations

1. Ensure that there is a computer with Internet access and an LCD projector for displaying PolyMod and Internet sites .
2. A SmartBoard is nice (but not necessary) because it can be written upon, and the entire board can be printed as documents for students to use for reference.
3. Download PolyMod software and become familiar how to use it. It is a simple program to manipulate.
4. Bookmark the Weblinks below for easy access.
5. Gather enough materials, poster board, silver-sided poster board, foam-core board, scissors, glue sticks, etc., for each group of students.
6. Make enough copies of the Check List and Rubric for each group of students. A manila folder for each group is nice for organization and keeping with incomplete models.
7. Prepare strips of paper with various dimensions and cost/ft2 for mirrored glass, which students will draw from a hat.

#### Procedures

Students should have prior knowledge of:
• solving equations
• Pythagorean Theorem
• area – for polygons
• surface area – for prisms
• volume – for prisms
• conversions
• ratios and proportions

Day 1
1. Divide student into groups of two or three. Ability grouping works very well with this project.

2. Introduce the project:
Your (students’) company has just been asked to submit a bid, accompanied with a scale model, for the Luxor Hotel in Las Vegas. You have been asked to cover the exterior of the building with mirrored glass tile. In your excitement at being offered such a prestigious opportunity, you failed to gather all necessary information. Because you cannot reach the architect and you have a deadline to meet, you have to determine what you need to know from the information you have so you can complete your task.

3. Groups decide upon a name for their company.

4. Show students the online photographs of the Luxor Hotel (see Weblinks below).

5. Distribute the manilla folders containing the Checklist and Rubric.

6. Have groups complete the company name and student names on folder, Checklist, and Rubric (see Associated Files: Check List and Rubric).

7. Review the Checklist and Rubric with the class (see Associated Files: Check List and Rubric).

8. Collect folders.

Day 2
9. Have students sit with their groups.

10. Distribute the folders.

11. Show students the online site, “Tell me about the structure of the pyramid and the beam.”

12. Discuss the company’s predicament of how they do not have sufficient information to place a bid (they have base square feet and volume, but no slant height).

13. Discuss volume of polyhedrons, and introduce the formula for the volume of a pyramid.

14. Show the online photographs of the Luxor Hotel and discuss the information addressed in the online site “Tell me about the structure of the pyramid and the beam,” (see Weblinks below).

15. Allow students to take appropriate notes from the online site “Tell me about the structure of the pyramid and the beam,” (see Weblinks below).

16. Have students place materials inside folders and collect folders.

Day 3
17. Have students sit with their groups.

18. Distribute the folders, calculators, and plain paper.

19. Use the PolyMod software to demonstrate the pyramid (it is helpful to construct the 3-D portions of the pyramid by drawing them on the projection), and guide students through the construction of the Luxor Hotel showing the height, square footage of the base, and the volume formula.

20. Have students work through #1 and #2 on the Check List (see Associated Files: Check List) and allow groups to investigate the PolyMod software as an aid to designing their pryamid.

21. Circulate among groups and give help when needed.

22. Have students place materials inside folders and collect folders and calculators.

Day 4
23. Have students sit with their groups.

24. Distribute the folders, calculators, and plain paper.

25. Refer to the PolyMod demonstration of the Luxor Hotel showing the height, square footage of the base, and the volume formula.

26. Manipulate the software to show the 3-D diagram and the net for the pyramid. Allow groups to investigate the PolyMod software as an aid to finding the relationship of height in a polyhedron, and designing their net for the pyramid.

27. Allow students to “discover” the answers for #3 through #7 on the Check List (see Associated Files: Check List).

28. Circulate among groups and give help when needed.

29. Have students place materials inside folders and collect folders and calculators.

Day 5
30. Have students sit with their groups.

31. Distribute the folders, and calculators.

32. Have students answer #8 through #11 on the Check List (see Associated Files: Check List).

33. Circulate among groups and give help when needed.

34. Have students place materials inside folders and collect folders and calculators.

Day 6
35. Have students sit with their groups.

36. Distribute the folders, calculators, and plain paper.

37. Have students answer #12 and begin #13 (as groups begin #12 distribute the poster board, ruler, and protractor) on the Check List (see Associated Files: Check List).

38. Circulate among groups and give help when needed.

39. Have students place materials inside folders and collect folders and calculators.

Day 7
40. Have students sit with their groups.

41. Distribute the folders, calculators, poster board, rulers, protractors, and scissors.

42. Have students complete #13 on the Check List (see Associated Files: Check List).

43. Circulate among groups and give help when needed.

44. Have students place materials inside folders and collect folders and materials.

Day 8 -9
45. Have students sit with their groups.

46. Distribute the folders, calculators, poster board, foam-core board, rulers, protractors, scissors, glue sticks, etc.

47. Have students complete #14 on the Check List (see Associated Files: Check List).

48. Circulate among groups and give help when needed.

49. Have students place materials inside folders and collect folders and materials.

Day 10
50. Have students sit with their groups.

51. Distribute the folders, calculators, poster board, foam-core board, rulers, protractors, scissors, glue sticks, etc.

52. Have students complete #15 on the Check List (see Associated Files: Check List).

53. Have students place materials inside folders and collect folders and materials.

#### Assessments

Evidence:
Students, working in groups of two or three, complete Check List and create a scale model of the Luxor Hotel.

Criteria:
Check List (see Associated Files: Check List)
Individual formative assessment occurs as teacher circulates and signs off on Check List while students develop and complete the project.

Rubric (see Associated Files: Rubric).
• Sketches, Nets, and Patterns - Sketches, nets, or patterns are clear and easy to understand and include all dimensions

• Mathematical Procedure - Used correct formula, correct method, correct information, and calculated correctly

• Explanation - Explanations are detailed and clear

• Model - Model is constructed from net drawn exactly to scale (determined in Check List, see Associated Files: Check List), and mirrored glass (silver-sided poster board) is applied to surface.

• Completion - All items are completed.

Free software for demonstrating polyhedrons and nets
PolyMod Software

This site provides necessary information from the link, “Tell me about the structure of the pyramid and the beam.” (located to the right of the photograph)
“Tell me about the structure of the pyramid and the beam.”

Photograph of the pyramid for view of mirrored glass.
Front View Photograph of Luxor Hotel

#### Attached Files

Check List.     File Extension: pdf

Rubric.     File Extension: pdf