Math in Our World: Backyard Design

Liz designed the ultimate summer backyard in her art class. She has a sketch and some notes below, but she is not done working yet.

Liz's design is a rectangle, 25 feet by 13 feet. The different spaces are all rectangles. Starting in the top left and going clockwise, here are the spaces. The deep end of the pool is 84 square feet, with one side 7 feet long. It is 6 feet deep. The trampoline is 28 square feet, with one side 7 feet long. The deck is 117 square feet, with one side 13 feet long. The grassy area's dimensions are unknown. The shallow end of the pool is 36 square feet. It is 4 feet deep.
8-foot boards: $5. 30 gallons of water per square foot in the shallow end. 45 gallons of water per square foot in the deep end.
  1. Use pictures, models, or numbers to show what is happening.
  2. What do you notice? What do you wonder?
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!
  • What kind of measurements do you see in the drawing and on the notes?
  • What is the area of the backyard?
  • How could you use the dimensions given to find other dimensions or areas that are not labeled?
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer!

Try making your own design. It could be a backyard, an amusement park, a playground, or somewhere else you might enjoy spending time over the summer.