The Ratio Design Challenge is an interactive tool that illustrates how ratios and proportional reasoning help solve real-world problems in architecture and construction. Use the Ratio Design Challenge to construct scale designs of three architectural themes. Watch the scene coming alive as you apply ratio concepts to build a baseball stadium and amusement park, and unit rate concepts to build an aquarium research center.


  • Ratio: A ratio shows a comparison between two or more related quantities. Another way to explain it is to say that a ratio shows the relationship between one part and another part. (In contrast, a fraction shows the relationship between a part and the whole.) A ratio can be expressed using three different notations: 6 to 2, 6:2, and 6/2. When saying 6:2 or 6/2 out loud, it should be read as "6 to 2." Care must be used in using the third notation to avoid confusion with fractions.
  • Unit Rate: A unit rate is a ratio comparing two measures in which one of the measures has a value of 1 (the word "unit" in "unit rate" refers to one unit).
  • Proportion: A proportion is an equation stating that two ratios (or two fractions) are equivalent. For example, 2:4 = 4:8.
  • Scale: A scale is a ratio of the size of a representation to the actual size of an object being represented. For example, in an architectural drawing with a scale of 1:100, a door 1" tall in the drawing would be 100 inches tall (9' 4") in the completed structure.
  • Simplify (Simplest Terms): A ratio (or fraction) is simplified when the numbers representing the two parts have no common factors other than 1. For example, 4:8 can be simplified to 1:2 because 4 is a common factor of 4 and 8, but 1:2 cannot be further simplified since the only common factor is 1.
  • Revenue: Revenue is the amount of money received by a company from its customers for the sale of goods or services.


  • Talk It Out: Check out the critical-thinking questions that appear at the end of each theme. Be sure to include both your mathematical calculations and their real-world implications in your responses. Share your thoughts with peers and get their input.
  • Take the Lead: Come up with your own thought-provoking questions, including exploring what the real-world consequences might be of changing the existing ratios in the venues. Discuss with your classmates.
  • Find Hidden Ratios: Examine the completed design in each theme. What other ratios can you find that weren’t specifically mentioned in the questions you answered?
  • Extend Your Thinking: What other venues can you think of where knowledge of ratio concepts would be necessary for a successful design?


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