The Ratio Design Challenge is an online, interactive tool designed to engage middle school students in developing an understanding of ratio and proportional reasoning while highlighting the value of math in real-world situations and careers.

The interactive tool enables the student user to construct scale designs of an architectural venue by applying ratio/proportion calculations. Each word problem includes a guiding hint if a student answers incorrectly, and after several tries, an explanation of the correct answer will display. Critical-thinking reflection questions at the end of the user experience will challenge students to draw overarching conclusions about the math concepts and to reflect on the real-world implications.

The interactive tool has three stand-alone modules, each with a different venue theme:

• Baseball Stadium (topic: ratio basics)
• Amusement Park (topic: ratio basics)
• Aquarium Research Center (topic: unit rate)

Each theme of the tool can be used for whole-class instruction, independent practice, and/or homework. A Using the Tool page is included to help students extend their thinking about ratio concepts.

The interactive tool supports both the Common Core State Standards for Mathematics (including Practice Standards) as well as the National Council for Teachers of Mathematics (NCTM) Principles and Standards, both at the middle school level.

## Ideas for Classroom Use

• Accompanying Interactive Lesson: The tool is integrated into an interactive lesson on ratios and unit rate. A series of printable activity sheets can also be used in place of, or to complement, this online tool.
• Whole-Class Instruction: The tool can be used on a whiteboard as part of a whole-class introductory lesson on ratios and unit rate.
• In-Class Project or Homework: Individual students or small groups can be assigned a theme module(s) to work on independently.
• Think About It: Using the reflection questions that appear at the end of each venue theme, or assigning your own, will enable students to deepen their understanding of the applicable ratio and proportion concepts. The intent is to get students to go beyond thinking about the correct mathematical answers and consider what the answers mean in terms of real-world implications. The questions can be used to prompt discussion or writing. Although responses to the questions will vary, some possible answers are included in the Answer Key.
• Additional Prompts for Extending Student Thinking: Encourage students to list other ratios in the completed designs that weren’t specifically mentioned in the math questions. Have students brainstorm other venues where knowledge of ratio concepts would be necessary for a successful design. Invite students to come up with their own thought-provoking questions, including exploring what the real-world consequences might be of changing the existing ratios in the tool’s three venues, or another venue.
• Project Idea: Once your students are familiar with ratio concepts and have had a chance to explore the Ratio Design Challenge, consider assigning a project that gives students a chance to exercise their imagination and extend their skills and knowledge of ratios by designing a venue of their choice. After determining the type of venue (e.g., a state-of-the-art recording studio), students create a scale drawing of the venue. Students determine the scale of the drawing, i.e., the ratio between the size of an object in the drawing and its size in the real world. Students should select at least five items in their drawing and, taking into account their measurements and the drawing’s scale, calculate the size of the items in the real world.

## Related Lessons and Activity Sheets

• Conversions Rock: Build and reinforce students’ skills in converting between percentages, fractions, and decimals—a skill used in the Ratio Design Challenge.
• Designing With Geometry: Develop students’ skills in using geometrical concepts and graphing in real-world design scenarios.
• Plan, Save, Succeed!: Address important personal finance concepts—such as budgeting, income, saving, and credit—using fractions, percentages, and decimals.

## More Interactive Tools

• Data Sampling—Representing Many by Sampling Some: This highly interactive and adjustable tool—in which students survey a fictional town about policy issues of interest to teens—gives students the opportunity to experiment with why it is important to select representative samples when drawing conclusions about a population.
• Data Displayer: Use this data-analysis classroom tool with your students to calculate and graph data. Functions include: mean, median, and mode; box-and-whisker plot; scatterplot; and standard deviation. Preset data is provided (in the themes of movies, sports, and agriculture), and custom data can be entered as well.
• Probability Lab and Probabilities Tour: In the Probability Lab, students explore the difference between theoretical probability and experimental probability by running their own probability experiments. In the Probabilities Tour, students will consider both theoretical probability and potential financial rewards to help plan a concert tour for a band.

## Free Math Lessons, Activity Sheets, and Interactives

Explore the rest of the Expect the Unexpected With Math® series at scholastic.com/unexpectedmath.