Math Focus 9
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# Circle Inventions and Designs

## INTRODUCTION

Many objects consist of circles or parts of circles. Some circular objects are created to serve a purpose. For some, the purpose is unknown. Other circular objects occur in nature. Purposes, as well as reasons for occurring in nature, are often related to properties of circles. What can you think of that would not work, or would not work well, if it were not circular?

Your task is to research circular objects and designs, and connect properties of circles to the purposes of these objects, or reasons for occurring. You will invent or design something for which circle properties contribute to its use, and then explain connections between the use and the circle properties.

## THE PROCESS

1. Search the Internet for circular objects and designs. Choose at least three examples to sketch and explain how circle properties are connected with them. Then use your understanding of circle properties to state a fact about each of the three examples, and to explain how you figured out the facts. Some websites about circles:

Bike Gears

History of Medicine Wheels

Invention of Microscopes

Telus World of Science

History of Wheels

Rings of Saturn

Pulley

Balls and Sports

1. Describe and sketch an invention or design that includes a circle, and uses circle properties. Explain the purpose of your invention or design.
2. Label some measurements on your sketch that would be appropriate for your invention or design. Explain how you could use circle properties to determine other measurements.
3. Explain how the use of your invention or design is connected with circle properties.
4. Write a problem about your invention or design that involves circle properties. Explain how to solve your problem.
5. Trade problems with a few classmates. Compare your explanation about solving your problem with their solutions. Do you agree with the solutions?

## RESOURCES

Websites:

Bike Gears

History of Medicine Wheels

Invention of Microscopes

Telus World of Science

History of Wheels

Rings of Saturn

Pulley

Materials:

• geometry software
or
• a pencil
• paper
• a compass
• a protractor
• a ruler

## ASSESSMENT

 Mathematical Processes Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Communication Uses effective and specific mathematical language to enhance communication about the role of circle properties for the purpose of objects Uses appropriate and correct mathematical language to support communication about the role of circle properties for the purpose of objects Uses mathematical language to partially support communication about the role of circle properties for the purpose of objects Uses mathematical and non-mathematical language incorrectly and /or inconsistently, which interferes with communication about the role of circle properties for the purpose of objects Connections Demonstrates a sophisticated ability to transfer knowledge of circle properties to the uses of circular objects and designs Demonstrates a consistent ability to transfer knowledge of circle properties to the uses of circular objects and designs Demonstrates some ability to transfer knowledge of circle properties to the uses of circular objects and designs Demonstrates a limited ability to transfer knowledge of circle properties to the uses of circular objects and designs Visualization Uses exceptionally  insightful visual reasoning that leads to a creative, useful, and efficient invention or design Uses insightful visual reasoning that leads to a creative, useful invention or design Uses some visual reasoning that leads to an invention or design that has some purpose Uses unclear visual reasoning that does not lead to creative, useful invention or design