1. Driving SCIENCE STEM Activity Race Flag Design Ratios and Proportional Reasoning

2. Why do motorsport events use flags? What do you think the displayed flags mean? What other organizations use flags? Engage

3. Steps 1 2 3 4 5 6 Investigate Represent a 6 cm by 6 cm checkered flag on grid paper. Number the steps. Think, Pair, Share What patterns can be seen in the flag design?

4. Represent the flag data in a table on the grid paper. Think, Pair, Share What patterns can be seen in the table? Step123456789 Perimeter (cm) 48 12 16 20 24 28 32 36

5. Make a prediction. Will the line be straight? Will the line go through the origin? 1 2 3 4 5 6 7 8 9 36 32 28 24 20 16 12 8 4 0 Draw the grid on your centimeter paper and represent the table data on the coordinate grid.

6. Tests to determine whether two quantities are in a proportional relationship: 1.Test for equivalent ratios in a table. 2.Test whether the graph is a straight line through the origin. Are perimeters of the squares in the checkered flag in a proportional relationship? Are areas of the squares in the checkered flag in a proportional relationship? 1.Represent the area data in a table. 2.Represent the area data in a graph. (Use intervals of 10 on the y- axis. 3.In writing, use mathematical reasoning to explain whether the data are in a proportional relationship.

7. What did you write about whether the area data have a proportional relationship? What mathematical reasoning did you hear from others? Reflect

8. Working in a group, test the following data for proportional reasoning using a table and a graph: (1, 3) (2, 6) (3, 9). Working independently, test the following data for proportional reasoning using a table and a graph: (1, 3) (2, 6) (3, 9). Explain in writing whether the quantities have a proportional relationship. Working independently, Test the following data for proportional reasoning using a table and a graph (y-axis = intervals of 2): (1, 1) (2, 3) (3, 5). Explain in writing whether the quantities have a proportional relationship. Working in a group, design a flag with a proportional relationship. Show the relationship in a table and graph. Working in pairs, design a flag with a proportional relationship. Show the relationship in a table and graph. Working in pairs, design a flag with two proportional relationships. Show the relationships in tables and graphs. Apply

9. For more information about racing flags visit: Flags Used in Auto Racing NASCAR Flags Thanks to our partners who sponsored the development of this activity: DuPont CU-ICAR EcoPower Safety-Kleen Daytona International Speedway United States Conference of Mayors Copyright © 2013 Clemson University, Clemson, South Carolina (SC).