# PARKING GARAGE SCALE

*A creative approach to teaching addition and subtraction*

The final project in my *Engineering Graphics and Design *course in Columbia’s Mechanical Engineering department was given by the following prompt: design a toy that teaches children how to add and subtract. I eagerly ran with this open-ended prompt, letting my imagination roam free to find a child-friendly solution to this unique design challenge. The resulting design was the Parking Garage Scale, which earned an A+ grade:

Using my approach of physics-informed design, I designed the toy around a spring scale, which employs the force of gravity and the opposing force of a hanging spring. The downward force of gravity is equal to the mass of the object multiplied by the acceleration due to Earth’s gravity (F = mg), and the opposing force on an object attached to a hanging spring is equal to the spring constant k multiplied by the change in length of the spring (F = -kx). In equilibrium, these forces add to zero (mg – kx = 0). Rearranging terms gives (mg = kx) and dividing both sides by k gives (x = mg/k). This equation shows that the distance the spring stretches (x) is linearly dependent upon the mass, meaning that if the mass increases in regular increments, the stretching distance will also increase regularly. The Parking Garage Scale uses discrete masses in the form of toy cars corresponding to the digits 1 through 9 to stretch a spring scale in regular increments, measured by an enclosure beam displaying the digits 1 through 10. The Number 1 car begins at a mass of 45 grams, then the subsequent cars increase by 45 grams for each corresponding number.

The addition functionality is illustrated above. When a child places multiple cars on the scale, the spring will stretch according to their added mass. This means that the number 1 car and the number 2 car placed on the scale simultaneously will stretch the spring the same distance as the number 3 car on its own, simulating 1 + 2 = 3. Subtraction works just the opposite way, as removing the number 1 car in this situation would raise the scale from 3 to 2. This mechanism is quite simple, but incredibly effective, as it allows children to associate addition and subtraction in a very intuitive way (adding is putting numbers or objects together, subtracting is removing numbers or objects from a group) as well as teaching them to associate smaller objects with lesser numbers and larger objects with greater numbers.

The most challenging aspect of this design was simultaneously achieving an appealing aesthetic and implementing the function of the scale. To achieve this end, I designed the frame of the scale in a circular shape, allowing the beams to hug the scale platform such that it can only move up and down. In addition to serving their functional purpose, the circular base and beams created a great deal of open space within the frame, so that the platform is easily accessible and cars can be clearly seen when on the scale. The bright colors, curved lines, and rounded edges I used are a tried and true aesthetic for children’s toys, as they create an inviting, friendly impression, inspiring children to engage their attention in an unreserved manner.