As evident from this video, there are many mysteries revolving the Great Pyramids. Generations have been fascinated by these pyramids and studied them immensely. Yet, there are still unanswered questions. Mathematicians are working to solve some of the mysteries using mathematics. You and your group will act as a researcher of the Great Pyramids and use mathematical analysis to solve some questions! Modifications

This webquest had been modified from the original in many ways to better facilitate increased comprehension and task completion.

1. The tasks have been presented in much more detail, making it a step by step activity instead of an open ended one. 2. The websites have been updated to be more interactive and less wordy so that students are better able to identify the important information. Descriptions of the websites have been given as well. 3. A graphic organizer has been added to help visual students better understand how to accomplish this activity. 4. A list of vocabulary words has been provided to aid students in their understanding of the material. 5. A worksheet has been created that helps students stay organized in their research. 6. Examples and hints have been provided in the worksheet to guide students in their mathematical analysis. 7. The Webquest in general has been made more visual rather than text based. This was done by incorportating more images as well as video. Advance Organizer

You are to become an mathematical expert about the Great Pyramid, the Khafre Pyramid and the Menkaure Pyramid.

1.Research the topic: Learn about the pyramids to get an understanding of why they are so facinating.

2.In your research group, each pick one pyramid to study in-depth: a.The GreatPyramid b.The Khafre Pyramid c.The MenkaurePyramid

3.Find the measurements (in feet) of your assigned pyramid: a.Height b.Width

4.With your group, write down the formulas for: a.Area of pyramid base b.Volumeof pyramid c.Lateral area of pyramid excluding the base

5.Using your measurements and formulas find the following for each pyramid: a. Area of pyramid base b.Volume of pyramid c.Lateral area of pyramid excluding the base

(This image can help you visualize the type of pyramid you are working with)

6.Compare your findings between all three pyramids using ratiosfor: a.Height b.Width c.Area of Base d.Volume e. Lateral Area

8.Create scaled down pyramidsout of any material. Ideas include: a.Construction paper and tape b.Wood and glue c.Styrofoam d.Blocks

(The above picture is a 2D image that can be used to build your 3D model)

9.Meet with your group to put the information together to present to the class. Presentation should include: a.List of your measurements b.Formulas used c.Results of mathematical findings d.Description of how you made your model e.Any interesting facts you found in your research

Use this worksheet to help you stay organized in your research and to find some hints for how to do this activity:

Use the following to help you visualize exactly what you need to do for this activity.
Start at the smiley face!

Q&A

Here is a partial outline of the questions for your webquest task to help you get started.

Area Questions 1. These pyramids are: (Triangular/Square/Pentagonal) 2. The shape of the base of a pyramid is a s _ _ _ _ _ . 3. The area of that shape is represented by (_) x (_) . 4. The width and length of a pyramid are approximately equal? (True of False) 5. The width of the Great Pyramid is: 6. The width of the Khafre Pyramid is: 7. The width of the Menkaure Pyramid is: 8. The area of the base of the Great Pyramid is: 9. The area of the base of the Khafre Pyramid is: 10. The area of the base of the Menkaure Pyramid is:

Volume Questions 1. The volume of a pyramid is represented by: (1/3) x (_) x (_) . 2. The height of the Great Pyramid is: 3. The height of the Khafre Pyramid is: 4. The height of the Menkaure Pyramid is: 5. The volume of the Great Pyramid is: 6. The volume of the Khafre Pyramid is: 7. The volume of the Menkaure Pyramid is:

Lateral Area Questions 1. Lateral area is the s _ _ f _ _ _ area of the pyramid not including the base. 2. One side of the pyramid is the shape of a t _ _ _ _ g _ _ . 3. There are f _ _ _ faces of a pyramid. 4. The surface area of one face of the pyramid is represented by: (1/2) x (_) x (_) . 5. The lateral area of a pyramid is represented by: 4 x (1/2) x (_) x (_) . 6. The lateral area of the Great Pyramid is: 7. The lateral area of the Khafre Pyramid is: 8. The lateral area of the Menkaure Pyramid is:

Websites

Use the following websites to help you in your research!

Measurements National Geographic Scroll over the pyramid images to see their names and click on the one you want to learn about. Measurements are provided in feet. This interactive website is also a good resource to learn about the history of each pyramid. Pyramid Measurements This website provides easy to find measurements of the Great Pyramid in terms of meters.

Formulas World of Math This link provides you with all the geometry formulas you will need for this assignment. Navigate the menu options to find your desired formula. For example, click "Volumes" to find the formula for the volume of a pyramid.

Construction of Scale Models PBS Pyramids This site provides you with information and examples about how to scale down a pyramid into model size. (Additional information can be found on your worksheet: Geometry Webquest Worksheet).

Interesting Facts Pyramid Facts Everything you want to know about the Great Pyramid can be found here in great detail. Much of the information is about the mystery of the pyramids and how advanced they are for their time. PBS Explore Another fun and interactive site to explore. This site focuses on the three pyramids you are studying and can educate you about their facts. Information includes a brief history, dates, some measurements and construction details. Vocabulary List

Area[air-ee-uh] The quantitative measure of a plane or curved surface; two-dimensional extent.

Face [feys] Geometry: any of the bounding surfaces of a solid figure: a cube has six faces.

Lateral Area[lat-er-uhl air-ee-uh] The surface area of a 3D figure excluding the area of any bases.

Pyramid[pir-uh-mid] Geometry:A solid having a polygonal base, and triangular sides that meet in a point.

Ratio[rey-shoh, -shee-oh] The relation between two similar magnitudes with respect to the number of times the first contains the second.

Volume[vol-yoom] The amount of space, measured in cubic units, that an object or substance occupies. Illinois Learning Standards

This Webquest activity is intended for secondary geometry students. This project incorporates the use of technology by having students use the Internet to get resources and by having them present their findings using a computer program such as Powerpoint. In this Webquest they will work in teams and also develop communication skills by presenting their findings to the class.

In addition, this activity meets the following ISBE standards:

9.A.5Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.

Standard met when students solve for the area and volume in real world situations.

9.B.4Recognize and apply relationships within and among geometric figures.

Comparing the two sizes of pyramids helps them recognize the relationships between them.

9.B.5Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models).

Standard used when students build the scale models of the pyramids.

9.D.4Analyze and solve problems involving triangles using trigonometric ratios.

Such techniques must be used when solving for the lateral area of the pyramids.

Skylar, Ashley A., Kyle Higgins, & Randall Boone (2007). Strategies for Adapting WebQuests for Students with Learning Disabilities. Intervention in School and Clinic, 43, 20-28.

Geometry WebquestClick on one of the following to jump to that section:Introduction

Modifications

Advance Organizer

Graphic Organizer

Questions

Websites

Vocabulary List

Illinois Learning Standards

References

Introduction

As evident from this video, there are many mysteries revolving the Great Pyramids. Generations have been fascinated by these pyramids and studied them immensely. Yet, there are still unanswered questions. Mathematicians are working to solve some of the mysteries using mathematics. You and your group will act as a researcher of the Great Pyramids and use mathematical analysis to solve some questions!

Modifications

This webquest had been modified from the original in many ways to better facilitate increased comprehension and task completion.

1. The tasks have been presented in much more detail, making it a step by step activity instead of an open ended one.

2. The websites have been updated to be more interactive and less wordy so that students are better able to identify the important information. Descriptions of the websites have been given as well.

3. A graphic organizer has been added to help visual students better understand how to accomplish this activity.

4. A list of vocabulary words has been provided to aid students in their understanding of the material.

5. A worksheet has been created that helps students stay organized in their research.

6. Examples and hints have been provided in the worksheet to guide students in their mathematical analysis.

7. The Webquest in general has been made more visual rather than text based. This was done by incorportating more images as well as video.

Advance Organizer

You are to become an mathematical expert about the Great Pyramid, the Khafre Pyramid and the Menkaure Pyramid.1.Research the topic: Learn about the pyramids to get an understanding of why they are so facinating.2.In your research group, each pick one pyramid to study in-depth:a.The GreatPyramidb.The Khafre Pyramidc.The MenkaurePyramid3.Find the measurements (in feet) of your assigned pyramid:a.Heightb.Width4.With your group, write down the formulas for:a.Area of pyramid baseb.Volumeof pyramidc.Lateral area of pyramid excluding the base5.Using your measurements and formulas find the following for each pyramid:a.Area of pyramid baseb.Volume of pyramidc.Lateral area of pyramid excluding the base(This image can help you visualize the type of pyramid you are working with)

6.Compare your findings between all three pyramids using ratiosfor:a.Heightb.Widthc.Area of Based.Volumee.Lateral Area7.Scaledown actual pyramids to model size8.Create scaled down pyramidsout of any material. Ideas include:a.Construction paper and tapeb.Wood and gluec.Styrofoamd.Blocks(The above picture is a 2D image that can be used to build your 3D model)

9.Meet with your group to put the information together to present to the class. Presentation should include:a.List of your measurementsb.Formulas usedc.Results of mathematical findingsd.Description of how you made your modele.Any interesting facts you found in your researchUse this worksheet to help you stay organized in your research and to find some hints for how to do this activity:Geometry Webquest Worksheet.doc

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Graphic Organizer

Use the following to help you visualize exactly what you need to do for this activity.

Start at the smiley face!

Q&A

Here is a partial outline of the questions for your webquest task to help you get started.Area Questions1. These pyramids are: (Triangular/Square/Pentagonal)

2. The shape of the base of a pyramid is a s _ _ _ _ _ .

3. The area of that shape is represented by (_) x (_) .

4. The width and length of a pyramid are approximately equal? (True of False)

5. The width of the Great Pyramid is:

6. The width of the Khafre Pyramid is:

7. The width of the Menkaure Pyramid is:

8. The area of the base of the Great Pyramid is:

9. The area of the base of the Khafre Pyramid is:

10. The area of the base of the Menkaure Pyramid is:

Volume Questions1. The volume of a pyramid is represented by: (1/3) x (

_)x(_) .2. The height of the Great Pyramid is:

3. The height of the Khafre Pyramid is:

4. The height of the Menkaure Pyramid is:

5. The volume of the Great Pyramid is:

6. The volume of the Khafre Pyramid is:

7. The volume of the Menkaure Pyramid is:

Lateral Area Questions1. Lateral area is the s _ _ f _ _ _ area of the pyramid not including the base.

2. One side of the pyramid is the shape of a t _ _ _ _ g _ _ .

3. There are f _ _ _ faces of a pyramid.

4. The surface area of one face of the pyramid is represented by: (1/2) x (_) x

(_) .5. The lateral area of a pyramid is represented by: 4 x (1/2) x (_) x (_) .

6. The lateral area of the Great Pyramid is:

7. The lateral area of the Khafre Pyramid is:

8. The lateral area of the Menkaure Pyramid is:

Websites

Use the following websites to help you in your research!MeasurementsNational Geographic

Scroll over the pyramid images to see their names and click on the one you want to learn about. Measurements are provided in feet. This interactive website is also a good resource to learn about the history of each pyramid.

Pyramid Measurements

This website provides easy to find measurements of the Great Pyramid in terms of meters.

FormulasWorld of Math

This link provides you with all the geometry formulas you will need for this assignment. Navigate the menu options to find your desired formula. For example, click "Volumes" to find the formula for the volume of a pyramid.

Construction of Scale ModelsPBS Pyramids

This site provides you with information and examples about how to scale down a pyramid into model size. (Additional information can be found on your worksheet: Geometry Webquest Worksheet).

Interesting FactsPyramid Facts

Everything you want to know about the Great Pyramid can be found here in great detail. Much of the information is about the mystery of the pyramids and how advanced they are for their time.

PBS Explore

Another fun and interactive site to explore. This site focuses on the three pyramids you are studying and can educate you about their facts. Information includes a brief history, dates, some measurements and construction details.

Vocabulary List

Area [

air-ee-uh]The quantitative measure of a plane or curved surface; two-dimensional extent.

Face [feys]

Geometry: any of the bounding surfaces of a solid figure: a cube has six faces.Lateral Area [

lat-er-uhlair-ee-uh]The surface area of a 3D figure excluding the area of any bases.

Pyramid [pir-uh-mid]

Geometry:A solid having a polygonal base, and triangular sides that meet in a point.Ratio [

rey-shoh, -shee-oh]The relation between two similar magnitudes with respect to the number of times the first contains the second.

Volume [

vol-yoom]The amount of space, measured in cubic units, that an object or substance occupies.

Illinois Learning Standards

This Webquest activity is intended for secondary geometry students. This project incorporates the use of technology by having students use the Internet to get resources and by having them present their findings using a computer program such as Powerpoint. In this Webquest they will work in teams and also develop communication skills by presenting their findings to the class.

In addition, this activity meets the following ISBE standards:9.A.5Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.Standard met when students solve for the area and volume in real world situations.

9.B.4Recognize and apply relationships within and among geometric figures.Comparing the two sizes of pyramids helps them recognize the relationships between them.

9.B.5Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models).Standard used when students build the scale models of the pyramids.

9.D.4Analyze and solve problems involving triangles using trigonometric ratios.Such techniques must be used when solving for the lateral area of the pyramids.

References

Dictionary.com. Retrieved Nov. 10, 2009, from http://dictionary.reference.com/.Great Pyramid of Giza. Retrieved Nov. 10, 2009, from http://en.wikipedia.org/wiki/Great_pyramidMath is Fun. Retrieved Nov. 10, 2009, from http://www.mathsisfun.com/.Mathwords. Retrieved Nov. 10, 2009, from http://www.mathwords.com/.MathWorld. Retrieved Nov. 10, 2009, from http://mathworld.wolfram.com./.Measurements of Great Pyramid. Retrieved Nov. 10, 2009, from http://www.gizapyramid.com/measurements.htmNational Geographic. Retrieved Nov. 10, 2009, from http://www.nationalgeographic.com/NOVA Online.Retrieved Nov. 10, 2009, from http://pbs.org/wgbh/nova/pyramid/explore/Skylar, Ashley A., Kyle Higgins, & Randall Boone (2007). Strategies for Adapting WebQuests for Students with Learning Disabilities.

Intervention in School and Clinic, 43, 20-28.The Math League. Retrieved Nov. 10, 2009, from http://www.mathleague.com/Top of Page