Gold Seal Lesson:
Pyramid Under Construction

Copernicus Education Gateway

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

• Mathematics as Problem Solving: Develop and apply strategies to solve a wide variety of problems.

• Geometry: Represent and solve problems using geometric models. Understand and apply geometric properties and relationships.

• Measurement: Apply measurement knowledge and skills in the solution of problems.

• Mathematics and Technology: Understand the principles of design.

• Computation: Apply computation in problem solving situations.

Performance Task:

Working with one other student in your class, your task is to design and construct a model of a pyramid that would fill your classroom. Your pyramid is to have a square base and the height should extend from the center of the base to the vertex, a point on the ceiling. Leave sufficient room so that people would be able to walk its perimeter. Use a compass, protractor, and/or straight edge to construct the model.

Compute the cost of the pyramid assuming the cost of the plywood is $8.00 per sheet and the dimensions of a sheet are 4 feet by 8 feet.
Prior to constructing your model pyramid, each of you should make a scale drawing of it on paper showing all of its dimensions. Each of you is also required to make a written explanation of the project in your math journal. Include the following items: 

• the dimensions of your classroom and an explanation of how you obtained them

• the scale used to construct your model the dimensions of your model, including an explanation and/or calculations used to obtain them, an explanation as to how you located the center of the base of your model

• the cost of the pyramid, with calculations, formulas used, and/or explanations verifying how
  you determined this cost.

Your grade will be based on the following:

1. the accuracy and neatness of your scale drawing and constructed pyramid model
2. the completeness, accuracy, and neatness of your journal entry
3. how well you work with your partner.

Note to the teacher: You may wish to have students perform this task in conjunction with a unit in Social Studies dealing with the history of pyramids in Egypt.

Knowledge / Skills:

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.  (m1)

Use writing as a tool for learning in formats such as learning logs, laboratory reports, note-taking, and journals.  (ela40)

Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.  (m29)

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min).  Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.   (m33)

Plan and apply real or hypothetical models and constructions to facilitate investigation and learning and the solution to practical problems.  (s115)

Rubric:

4 Points  =  The student accurately finds the measurement of the classroom, giving a clear explanation of how he/she obtained these measures. He/she demonstrates a full understanding of ratio and scale concepts and the ability to use measurement tools to make a scale drawing and model. All work is accurate, neatly presented, and thoroughly developed. All requirements of the journal entry are fulfilled. The student accurately computes, with justification, the cost of constructing the model. Total product is very thorough, clear, and well written. The project is a team effort, with the student demonstrating the ability to work cooperatively with his/her partner.

3 Points  =  The student accurately finds the measurement of the classroom, but the individual explanations of how these measures were developed are unclear. He/she demonstrates a fairly good understanding of ratio and scale concepts, but needs some help in applying these concepts to the drawing of the scale diagram and the construction of the model. Work is generally accurate, with only a minor error or two present. Work is fairly neat, but not well explained. All requirements of the journal entry are fulfilled, but some entries are not as clearly developed as they should be. Cost figures are present, but not well explained. Total product is relatively clear and thorough, but not necessarily smoothly written. The student works cooperatively on the project, but sometimes seems to work as an individual rather than as a team member.

2 Points  =  The student does not make accurate measurements of the classroom and gives no meaningful explanation of how these measures were obtained. He/she demonstrates only a partial understanding of ratio and scale concepts and needs substantial assistance in applying these concepts to the drawing of the scale diagram and the construction of the model. Even with assistance, the scale and model are not accurately made. Many errors occur in the student's work. Not all journal requirements are met, and little explanation or justification of the components of the project is shown. Cost figures contain errors and are inadequately explained. Total product is unclear, not thorough, and poorly written. The student is not uncooperative with his/her partner, but rarely, if ever, works as a member of the team.

1 Point  =  The student has many errors in all calculations involved in the project. He/she demonstrates little, if any, understanding of ratio and scale. He/she is unable to complete a reasonable model. There are few, if any, written explanations or calculations shown. It is very difficult or impossible to follow the student's thinking or justification in the decisions made in the construction of the model and in the cost analysis. The journal entry is missing most components. Any written material is meaningless and very poorly written. Total product is of very poor quality. The student does not cooperate with his/her partner on the task.

Keywords:

GEOMETRY
AREA
PYRAMID
PERIMETER
MODELS & CONSTRUCTION
CONVERSION
TEAM WORK
JOURNAL STATISTICS
MEASUREMENT
COMPUTATION 
TRIGONOMETRY
RATIOS

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [X] - 6 [X] - 7 [X] - 8 [X] - 9 [] - 10 [] - 11 [] - 12 []

ICLE Application:

D

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