Math Focus 9
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# Designing Courts

## INTRODUCTION

Various sizes and shapes of courts are used for different sports. Some courts are designed so that they can be used for a variety of sports.

You will design two courts, and write polynomials to describe their areas and perimeters. Then, you will change their dimensions, and use polynomials to describe the changed areas and perimeters.

## THE PROCESS

1. Visit Flex Court to find out about outdoor and indoor courts. Click on “Photo Galleries” to see photos for various types of courts. Follow links from types of courts such as “Multi-Game Courts,” or “Basketball Courts” to see photos for commercial and residential courts. If you want to see dimensions of courts, click on “Court Designer.” You can use a Length Converter if it helps to read the dimensions in the metric system.
2. Choose a type of court. Sketch the court, using variables instead of measurements for the dimensions. The size and shape do not need to match any courts on the web site.
3. Use the variables from your sketches for step 2, and write a polynomial to describe the area of the court. Refer to Measurement Formulas if you need a reminder for area and perimeter formulas. Explain how you know that your polynomial describes the area.
4. Use the variables from your sketches for step 2, and write a polynomial to describe the perimeter of the court. Explain how you know that your polynomial describes the perimeter.
5. Repeat steps 2 to 4 for a court with a different shape.
6. A customer who is buying the two courts might want to know the total area and total perimeter. Write a polynomial to describe the total area and a polynomial to describe the total perimeter of the two courts for you designed.
7. A customer who is deciding which of the two courts to buy might want to know the differences in area and perimeter. Write a polynomial to describe the difference in area and a polynomial to describe the difference in perimeter of the courts you designed.
8. Choose one of the courts you designed. Suppose each dimension is doubled. Explain how to write a polynomial to describe the area and a polynomial to describe the perimeter of the court, with each dimension doubled. Follow your explanation to write these polynomials.
9. Choose one of the courts you designed. Describe a way to change one dimension. Explain how to write a polynomial to describe the area and a polynomial to describe the perimeter of the court, with this changed dimension. Follow your explanation to write these polynomials.
10. For each of your explanations, ask someone to read it, express it in their own words, and then follow it to write a polynomial. Compare their polynomials with the ones you wrote.

Websites:

Flex Court

Materials:

a pencil
a ruler
paper

## 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 and conventions for polynomials and for explanations to enhance communication. Uses appropriate and correct mathematical language and conventions for polynomials and for explanations to support communication. Uses mathematical language and conventions for polynomials and for explanations to partially support communication. Uses mathematical and non-mathematical language and conventions incorrectly and /or inconsistently for polynomials and for explanations, which interferes with communication. Connections Makes insightful connections between sketches of courts and polynomials. Makes meaningful connections between sketches of courts and polynomials. Makes simple connections between sketches of courts and polynomials. Makes minimal or weak connections between sketches of courts and polynomials. Visualization Uses visual representations insightfully to demonstrate a thorough understanding of polynomials and operations with polynomials. Uses visual representations meaningfully to demonstrate a reasonable understanding of polynomials and operations with polynomials. Uses visual representations simply to demonstrate a basic understanding of polynomials and operations with polynomials. Uses visual representations poorly to demonstrate an incomplete understanding of polynomials and operations with polynomials.