THE PYRAMIDS OF GIZA
Hope Kabore, Maribel Meekins, Celeste Garza Santoyo, Allen John Wacasey

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Giza Complex, Egypt
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Pyramids are a great way to teach about math and world history in one lesson. Everyone is intrigued by these wonders, young and old alike.

HISTORY

The pyramids of Giza are perhaps the only true rival to the Great Sphinx when one thinks of ancient Egypt and its architecture. The Valley of Giza-- with its wonderful monuments-- is truly a marvel of architectural prowess. The three largest pyramids located in the valley consist of the Great Pyramid of Khufu, the Pyramid of Kafhre and the Pyramid of Menkaura. Each Pyramid is a tomb dedicated to a different king of Egypt.
All three pyramids were built during the Third and Fourth Dynasty; these structures resulted from a monumental effort by the king (and his sons). The Pyramid of Khufu has a base which covers roughly a nine acre area (approximately 392,040 square feet). The Pyramid of Menkaura, unlike the other pyramids, has granite covering one tier of its base. The Pyramid of Khafre had a two-tiered base encased in granite.
Unfortunately, like many of the great kings of the Old Kingdom of Egypt, the Pyramids of Menkaura, Khufu, and Kafhre were not finished by the end of each respective king's reign. As an example: in the case of Menkaura, the king died before its construction was completed. The monuments of Giza and the entire Giza Valley stand as a marvelous reminder of the skill executed in the creation of the pyramids, and are truly fabulous to see.


Ratios, Proportions, and Scaling

8th grade Math


TIME: 5 days
TEKS:
Chap. 111.24
(b) Knowledge and Skills
(3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:
(A) Compare and contrast proportional and non-proportional linear relationships; and
(B) Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
(6). Geometry and spatial reasoning.... The student is expected to:
(A) Generate similar figures using dilations including enlargements and reductions
(7). Geometry and spatial reasoning... The student is expected to:
(A). draw three-dimensional figures from different perspectives
(B). use geometric concepts and properties to solve problems in fields such as art and architecture

OBJECTIVES:
  • Given a set of numbers, students will use ratios and proportions to determine their relationship with at least 90% accuracy.
  • Students will use scaling factors to evaluate relationships between physical objects and drawings
  • Given data from the Internet, students in groups of 3 will create a 3D model of a pyramid with at least 90% accuracy.

LESSONS
Day 1 – Introduction to Egyptian Pyramids
· Watch Video 1 from Building the Great Pyramid to introduce them to pyramids and spark their interest. (10 min.)
· Pass out article: A Short Introduction to the Pyramids of Egypt by Jimmy Dunn on the Pyramids of Giza (stop after “128 magical spells of the Pyramid text).
· Have students read silently then share in groups of 4
· Have each group write key facts about the story on poster board and share with the class
· Teacher checks posters for understanding and reads article to the whole class
· Homework: Students research the Pyramids of Giza online at Nova Online – Pyramids The Inside Story and record important facts.

Day 2 – Scale model of the Great Pyramid
· Use NOVA Online Adventure lesson to introduce the concept of ratios, proportions, and scaling.
· Complete guided practice to ensure the concept of scaling and how to use scaling when constructing models is understood.
· Have students in groups of 3 to create scaled down model of the Khafre and Menkaure pyramids.
· Homework: Students will research online and/or at the library plans/drawing of the Giza pyramids to use for their 3D model
Day 3 – Project work day
· In groups of 4, students will select one set of maps/drawing using the information gathered from the homework to use for their model of the Giza complex.
· Students will choose materials, a scale and calculate the appropriate dimensions for their model.
· Teacher verifies measurements and understanding of ratios, proportion, and scaling before building phase
· Students start building
Day 4 – Project work day (Building Phase)
· Students finish building and present work to class and teacher for feedback
· Students finalize models
Day 5 – Presentations
· Each group presents their model
· Students write reflections in their journal about pyramids and concept learned
· Students explain how they were able to use ratio and proportions to scale down a 3-dimensional object.
· Students can complete a self-assessment to see what the student feels they knew before they began the project and what they know after completing the project.
Evaluation:
Daily
· Informal: Observation
· Formal: Formative assessment on work turned in from Day 1 and 2 (graded)
Summative
· 3D Models (graded)
· Project Presentations (graded)
· Reflections (non-graded)
MATERIALS: Paper, graph paper, scissors, glue, ruler, poster board, journals, cardboard, card-stock paper, and markers.

DIFFERENTIATED INSTRUCTION
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Additional differentiation strategies to meet diverse learner needs:
Some students can use calculators. Additional guided practice may be appropriate for struggling learners.
Double check that English Language Learners understand the directions. Include pictures and/or symbols with directions
Provide additional examples as needed.

REFERENCES:
http://www.mnsu.edu/emuseum/prehistory/egypt/architecture/gizapyramids.html
http://www.eyelid.co.uk/Egyptian_Videos/Building-Pyramid1.html
http://www.touregypt.net/featurestories/pyramidintroduction.htm
http://www.pbs.org/wgbh/nova/pyramid/index.html
http://www.pbs.org/wgbh/nova/pyramid/geometry/model.html
http://www.pbs.org/wgbh/nova/pyramid/geometry/print.html