Engaging Scenario
Current Situation: You are an archeologist in Egypt studying the great pyramids.
Challenge: To create a scale model of the pyramids to take back with you. It must have exact angle and side calculations and be labeled accurately. You must make one for each of the 3 main pyramids using the following website for the vital information.
http://www.pbs.org/wgbh/nova/pyramid/geometry/ Also, write a summary about each pyramid, include its basic measurements, features, and whose tomb it was.
Student’s Role: Archeologist
Product: Submit 3 geometrically similar scale models of Menkaure, Khafre, and Khufu along with a written summary about each one.
Engaging Scenario (Full Description)
You are an archeologist who has been working in Egypt studying the pyramids Menkaure, Khafre, and Khufu. You are collecting data so that you can construct scale models of each pyramid to take back to the museum. It is important that they are geometrically similar and as accurate as possible. With a partner, you will research the pyramids using
http://www.pbs.org/wgbh/nova/pyramid/geometry/, writing down all the important measurements, features, and whose tomb each was. Then, you will use your data to construct a geometrically similar scale model for each pyramid. Lastly, the museum wants a full description about each one. Are you up for the challenge?
Task 1: SQUAREIndicators:
#2 Determine sufficient properties that define 2D or 3D objects
#3b Use triangle angle sum relationships to solve problems.
Essential Question:What special properties define the 2D or 3D object?
How can I find the missing angle on a triangle?
Unwrapped Content Knowledge and Skills:Triangles
Determine properties of 2D and 3D objects
Use triangle angle sum relationships
Solve missing angle problems
Application: Students will produce an archeologist log of all the vital information about each Pyramid.
Instruction, Information, Resources:http://www.pbs.org/wgbh/nova/pyramid/geometry/Important information worksheet for each pyramid for them to complete with all the measurements, facts, and geometric information to be calculated and found
Calculator
Computer
Evidence of Learning: The key parts of the 2D triangles will be found or calculated which put together make all the parts and properties of the 3D pyramid.
Task 1: Archeologist’s LogComplete the log sheet for each of the 3 pyramids using
http://www.pbs.org/wgbh/nova/pyramid/geometry/ to find the basic information (angles, base, height of each side of the pyramid triangles; each pyramid’s history; who it was built for; basic features of each pyramid; geometric features listed under Cross section). Use your knowledge of triangles to solve for any missing information. Show all calculations.
Need Archeologist’s Log for Menkaure, Khafre, and Khufu
Need Internet
Task 2: SQUARE
Indicators:
#1 Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures
#5 Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures
#6 Determine and use scale factors for similar figures to solve problems using proportional reasoning
Essential Question:
What makes triangles similar? What makes triangles congruent?
What is a proportion? How and when can proportions help me to solve triangle problems?
What is a scale factor? How and when can using scale factors help me to solve triangle problems?
Why are the sides/angles of similar/congruent triangles proportional?
Unwrapped Content Knowledge and Skills:Use (proportional reasoning, scale factor)
Describe / Express (relationships between parts/attributes of similar/congruent figures)
Determine (conditions for congruence, scale factor)
Apply (properties of congruent/similar triangles)
Solve (missing length problems)
Application:
Students will create the geometric building plan in order to create their scale models of the pyramids.
Instruction, Information, Resources:Archeologist Log sheets for each pyramid
Scale Model Blueprints worksheets for each pyramid
Calculator
Teach about scale factor, similar triangles, how to use proportions to find missing sides.
Evidence of Learning:
Students will have to write out all their proportions/scale factors they used to find the lengths of the missing sides of their models as well as what all the angles are. They must also give the scale factor between their model and the actual pyramid (which shows the relationship between similar shapes).
Task 2: Scale Model Blueprint
Using your Archeologist Log Sheets, you will now find all the measurements of your scale model. Your scale model of each pyramid will be similar to the original. Using scale factor, proportions, and what you know about similar shapes, find all the missing sides and angles of your scale model. Show all your work. Also, write what the scale factor is between your model and the original pyramid.
Task 3: SQUAREIndicators: #2 Determine sufficient properties that define 2D or 3D objects
Essential Question:
What special properties define the 2D or 3D object?
Unwrapped Content Knowledge and Skills:
Determine (properties of 2D and 3D objects)
Application:Students will build models of the pyramids based on their blueprints.
Instruction, Information, Resources:
Construction paper
Scissors
Tape
Protractors
Compass
Rulers
Show how to make triangles using a compass
Evidence of Learning:The students will label their 3D shapes to show that they have create similar pyramids. Their model will show all the attributes of a 3D pyramid.
Task 3: Building ModelsUsing your scale model blueprints, you are now going to construct similar pyramids based on your measurements and calculations. Each side of the pyramid must be measured using a rule and compass. The angles also must be calculated using a protractor. Each side’s measurements must be clearly labeled. Your will then put the name of the pyramid on one of the sides, and tape it together. You must do this for each of your 3 blueprints.
Task 4: SQUAREIndicators:
#2 Determine sufficient properties that define 2D or 3D objects
Essential Question:
What special properties define the 2D or 3D object?
Unwrapped Content Knowledge and Skills:Determine (properties of 2D and 3D objects)
Application:Students will type a complete report about each pyramid using their Archeological Log to be displayed with each model.
Instruction, Information, Resources:Archeological Logs and Blueprints
Word Processor
Go over grammar rules of punctuation, spelling, and capitalization
Evidence of Learning:
Students must use correct grammar to discuss the features of 2D and 3D shapes.
Task 4: Informational SketchBased on the information you collected in your Archeological Logs, you will now type 3 simple reports about each pyramid that will be displayed with your model in the museum. You must include the following information: Geometric features and measurements, special features, what it was used for, whose it was, time period, how your model is an accurate representation. Each of your reports must use correct grammar, punctuation, spelling, and capitalization. You must write in complete sentences. Each report must be 1 page size 12 or 14 font Times New Roman.
