### The Advantage of "Robot Math"

Robotics teams that effectively use math concepts, like proportional reasoning and scale, usually have the upper hand in competitions. When these teams form alliances with others during the competition, they can quickly make changes, like mapping out a new path or determining the correct motor rotation values for their autonomous programs. Knowing the math behind the changes can save valuable time. Teams then use that time to make other physical or program changes to their robots that can increase their chances of winning. Using "robot math" like proportional reasoning and scale can definitely maximize a team's performance.

In the image above, the team is using the actual measurements of the field that VEX provided to calculate the distances between different locations on the field. They then calculate the shortest distance from a particular location to the planned destination. These are particularly important calculations for moving the robot accurately during the autonomous program.

Motivate Discussion - Applying Math to Scale

**Q:** Why would you use "robot math" instead of guessing and checking?

**A:** Guessing and checking takes too much time. Plus, if you use math to determine how to adjust your robot or its program, you can apply changes to your numbers/values systematically instead of guessing and checking each new value.

**Q: **You are drawing out the VEX V5 competition field on paper. The actual dimensions are just under 12 x 12 feet as the perimeter of the interior of the field is 11.7 by 11.7 feet. You want to scale it down so that 1 foot is represented by 10 millimeters (mm). The drawing size/actual size ratio is 10 mm/ 1 foot. What is the scaled down drawing dimensions?

**A: **The scaled dimensions are 117 mm by 117 mm.

**Q: **The perimeter of the exterior of the competition field is 11.9 by 11.9 feet. What are the scaled down dimensions of the exterior of the field so that you can add them to the drawing that you already have for the interior?

**A:** The dimensions are 119 mm by 119 mm using the same process as above.

Extend Your Learning - Scaling a Competition Field

Create a scaled drawing of this year's VEX Robotics Competition Field. The following is an example picture of the 2019-2020 Tower Takeover Field but images of the current year's field are available at this link.

Beginning students might use an image of the competition field, like this one, and figure out the scale based on the actual measurements provided by VEX and the measurements within the image.

Experienced students could create their own scaled drawings of this year's field based on the dimensions provided by VEX.

Advanced students could create their scaled drawing of the field and then iterate (plan, test, and refine) an autonomous program.