Math in Our World: Gardens & Dirt

Kiyoshi’s family built some raised garden beds to grow vegetables this year.

Kiyoshi's family has 4 raised beds. Bed A has dimensions of 7 and 1-half by 7 and 1-half.
  • The soil in bed A is 1 foot deep.
  • Bed B holds twice the volume of soil as bed A.
  • Bed C is a square with side lengths between 4 and 5 feet. The soil is deeper than bed A.
  • Bed D holds twice the volume of soil as bed C.

KIyoshi's family had to order soil, so they looked at the different prices.

Soil prices: $3.97 per cubic foot or $71 per cubic yard. Great Savings! 5 cubic yards for only $214.
  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!
  • Sketch a picture of bed A and label the dimensions. What is the cubic volume of the soil in bed A?
  • The volume of a rectangular prism = length × width × height, expressed in cubic units.
  • What do you notice about the relationships among the sizes of the garden beds?
  • How many cubic feet are in a cubic yard?
A small cube with dimensions of 1 foot by 1 foot by 1 foot. A large cube with dimensions of 1 yard by 1 yard by 1 yard. 1 yard is equal to 3 feet.
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer!

The exact dimensions of Beds B, C, and D are not given. Pick one or more of the beds and come up with at least two different sets of dimensions that the beds could be, based on the clues in the instructions.