Math Focus 9

Designing Park Structures

INTRODUCTION

Park structures such as skateboard ramps and tree houses need to be structurally sound and built to withstand years of use. Their supports and surfaces need to be carefully designed to ensure users’ safety. The environment such as the health of trees also needs to be considered. Park designers exercise their creativity when planning parks.

Imagine that you have been hired to design park structures. You can choose between two types of structures for this task:

• Design two skateboard structures for a park so that the surface area of one is twice the surface area of the other.
OR
• Design a tree house and determine the amount of paint needed to paint it.

Use only rectangular prisms, triangular prisms, and cylinders for the structure you choose to create.

THE PROCESS

Answer questions 1 to 6 for a skateboard park or questions 7 to 12 for a tree house. Then, for either choice, answer questions 13 and 14.

Skateboard Park

1. Visit Skateboard Parks and Designing and Constructing Skateboard Parks.
2. Sketch a composite structure for skateboarding. Use only rectangular prisms, triangular prisms, and cylinders—or parts of cylinders. The area of a curved surface can be determined by using part of a cylinder as a model.
3. Estimate and label dimensions needed for calculating the surface area, not including the underside of the structure. Describe how to calculate the surface area, and then follow your description. Adjust your description, if necessary.
4. Sketch a different composite structure for skateboarding so that it has a surface area that is about twice the surface area of your first structure. Label the dimensions.
5. Explain how you know that the surface area of one structure is twice the surface area of the other structure.
6. Exchange sketches with a classmate. Talk about whether the surface area of one structure is twice the surface area of the other structure.

Tree House

1. Visit Tree House Guide and Tree House Designs.
2. Sketch a tree house for a children’s park, estimating and labelling the dimensions. Use only rectangular prisms, triangular prisms, and cylinders in your construction and be sure to include one of each. Include areas that overlap in your design. The tree house can be self-supporting, or a tree can provide support for it.
3. The entire outside needs to be painted using at least two colours. Describe how you would like to paint the house, then decide on a strategy for determining the area to be painted with each colour. Add more dimensions to your sketch, if necessary. Follow your description to calculate the area to be painted.
4. Describe a different strategy to determine the area to be painted. Exchange with a classmate who will follow this strategy.
5. Compare solutions. Discuss how the solutions are the same and how they are different.
6. Which strategy do you prefer for determining the area of your tree house to be painted? Why?

Both

1. Choose three estimated dimensions that you recorded on your sketch. Explain why they are reasonable.
2. Explain what you have learned from this task. Explain whether you think your learning is important.

RESOURCES

Websites:

Skateboard Parks

Designing and Constructing Skateboard Parks

OR

Tree House Guide

Materials:

• a pencil
• a ruler
• paper
• rectangular prisms (optional)
• triangular prisms (optional)
• cylinders (optional)

ASSESSMENT

 Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Problem Solving: Make a Plan Develops a thorough plan for solving the problem. Chooses an efficient and effective strategy. Develops a workable plan for solving the problem. Chooses an appropriate and workable strategy. Develops a basic plan for solving the problem. Chooses a simplistic and routine strategy. Develops a minimal and/or flawed plan for solving the problem. Chooses an inappropriate or unworkable strategy. Problem Solving: Carry out the Plan Shows flexibility and insight when solving the problem, adapting if necessary. Shows thoughtfulness when solving the problem. Shows understanding when solving the problem. Attempts to solve the problem. Problem Solving: Look Back Verifies solutions by comparing and discussing thinking about solutions and correctly determines appropriateness of the response. Verifies solutions by comparing and discussing thinking about solutions and reasonably determines appropriateness of the response. Attempts to verify solutions by comparing and discussing thinking about solutions and determine appropriateness of the response. Has difficulty verifying solutions by comparing and discussing thinking about solutions.