Unit 3 Project: Applying Geometric Principles

 

This project consists of Parts A and B. In total, Parts A and B are intended to take six hours to complete.

 

Have you heard of the term snookered? It is often used to describe the predicament of being blocked from completing a task. This term comes from the popular billiards game in which a player tries to place the cue ball in a position that makes it very difficult, if not impossible, for his or her opponent to successfully make the next shot. Another billiards term is playing shape, a situation in which a skilled player thinks ahead to the next shot and works to have the cue ball end in the correct place to set up that next shot.

 

Geometry is an important aspect in games, art, and the design of structures. In this unit you will look at many geometric principles as you complete your work in these modules:

• Module 5: Angles

• Module 6: Triangles and Other Polygons

• Module 7: Trigonometry

In these modules, each lesson has many examples. Many of these examples present geometry in games, art, and design. The examples will help you think about geometry in new ways.

 

Are you a fan of baseball or curling? Or are you more interested in scrapbooking or animation? Maybe you have always had an interest in building or bridge design. This is your chance to explore a game, sport, art, or hobby that you enjoy and to discover how your chosen pastime relates to geometry.

 

A list of possible topics follows. However, feel free to choose something not on the list—either way, you must have your idea approved by your teacher. You will be prompted to work on this project throughout the Unit 3 lessons. Therefore, it is best to decide on your topic before you complete Module 5.

 

Project Topic Suggestions

 

Games/Sports/Hobbies	Arts/Design
baseball	animation
hockey	bridge design
curling	sewing
soccer	quilting
chess	scrapbooking
skiing	painting
snowboarding	beadwork
board games	carving
skateboarding	making jewellery
model aircraft	drawing
gaming (video games)	your own idea
model railroading
mechanics
your own idea

 

Part A: Exploring Geometric Principles Related to Your Topic

 

Part A of this project will take place throughout the lessons of this unit. You will be prompted to investigate how geometry is related to your chosen topic as new geometry principles are introduced. You will summarize your findings from Parts A and B in a final presentation. As you work through the lessons, make sure you keep a record of all of the connections between your topic and the geometric principles you learn about in each lesson.

 

Part B: Recognizing a Problem or Situation in Which Understanding Geometric Principles Can Help Give You an Edge

 

Part B will take place at the end of Unit 3. Once you have identified all the geometry principles involved in your topic (completed in Part A), you will think of a problem or challenge that your knowledge of geometry can help solve. You will explore how applying your knowledge of geometry principles can help you solve a problem related to your topic. Include the mathematics. For example, if you choose the Pythagorean Theorem as a principle related to a problem you report, show the steps in your solution of this problem.

 

Presentation of Parts A and B

 

Both Parts A and B will be summarized in a final presentation.

 

Here are some of the geometry principles from the modules in this unit:

 

Module 5: Angles	Module 6: Triangles and Other Polygons	Module 7: Trigonometry
classifying angles by size complementary and supplementary angles angles formed by parallel lines cut by a transversal perpendicular lines	similar polygons similar triangles similar right triangles the Phythagorean Theorem	tangent ratio sine ratio cosine ratio mathematical games

 

Your final Unit 3 Project presentation will be assessed on how you complete the following:

1. Explain geometric principles.

 

• Did you show how each of the geometric principles is involved in your topic? At least one principle from each module must be included. (This is the information you created, collected, and saved from each lesson of this unit as required for Part A.)

 

• Did you explain how one specific problem related to your topic could be solved by applying one of the geometric principles? (This is the information from Part B.)
  

2. Present your understanding.

 

• Did you select an effective way to get your message across, such as audio, video, graphics, or a step-wise animation?
  
  

 

• Did you prepare a high-quality presentation using examples and, where possible, data, calculations, and sketches or images to support your reasoning?

Remember, this project should be completed in six hours.

• A simple approach may be better than choosing something too involved and time-consuming.

• To assist you in developing your project, you might wish to use a flow chart.

There are 18 marks possible. Your project will be evaluated based on this scheme.

 

Score	Explanation of All Geometric Principles Involved in Topic (Part A)	Problem or Challenge Context (Part B)	Selection and Reference to Geometric Principle in Solving the Problem (Part B)	Visualization (presentation)	Mathematical Representation (presentation)	Communication (presentation)
3 Acceptable Standard	Geometric principles from all three modules are relevant to the topic and their connections to the topic are thoroughly explained.	A relevant problem situation is presented and developed.	The geometric principle selection is appropriate to the problem context, and its use in solving the problem is thoroughly explained.	Complete diagrams and/or images are appropriately used for both parts of the project.	All required mathematical representations are complete and correct.	The response explicitly states correct and insightful examples of personal experience, societal, or technological relevance of the project design.
2 Contains Minor Omissions or Errors	An explanation of geometric principles and their relationships to the topic are complete, but include minor errors or omissions.	The problem-solving context is developing in the direction of the project focus, but includes minor omissions.	The selection of geometric principle has occurred, and a solution to the problem has been explained, but contains some errors.	The student used a diagram or image with minor omissions.	All required mathematical representations are completed but with minor errors.	Progress has been made to communicate, but some clarification would be appropriate.
1 Below Acceptable Standard	There is a partial attempt to relate geometric principles to the topic.	There is a partial development of problem context, but with limited engagement in the project focus.	A selection of geometric principles has occurred, but no attempt to solve the problem has been made.	The student’s diagram or image use is insufficient or unrelated to the context.	An initial attempt at using required mathematical representations has been made but with major errors or omissions.	There is some communication about engagement in the project.
0 The design does not meet minimal standards for the course.	Geometric principals are not explained, nor is there a relationship to the topic.	The problem-solving context has not been developed.	There is no selection of a geometric principle or any attempt to solve the problem.	A diagrams and/or images are absent.	Mathematical representations have not been used.	There is little or no communication about engagement in the project.
Total Score /18	/3	/3	/3	/3	/3	/3

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