# Mathemagics

Overview: There is a focused effort to plant a seed of interest in science and mathematics in incoming freshman students at Cal State LA.  Armed with the belief that students will become genuinely interested in science and mathematics if they are presented in an interesting way, a group of faculty members from various engineering disciplines at Cal State LA and Cal Poly SLO have started a Calculus and Physics workshop called Mathemagics for the incoming freshman engineering students.  The activities aim to spark an interest in science and mathematics in incoming freshmen students hoping that the connections they make between mathematical theory and physical reality as well as increased motivation will translate into success in STEM during their following academic endeavors.

### Acceleration of falling ball

In the first experiment, students were asked to determine the acceleration due to gravity by dropping a tennis ball in front of a measuring tape and plotting the position of the ball vs. time.  Students were asked to install a free app on their cell phones that allowed them to capture the free fall of the tennis ball as a video, which could be viewed in slow motion to record position of the ball vs. time.

### Velocity of falling ball

Two tracks were devised on top of one another, students were engaged in a discussion about vector components of velocity in general then were asked to predict the distance between the two balls when the upper ball is at the same height as the lower ball.  After discussing all possibilities within their groups of 4 students, they were asked to decide on the position of the upper ball with respect to the lower ball and justify their answer with reasoning.

### Ball trajectory off ramp

After coming up with a decision, they had to release the two steel balls simultaneously on their tracks and observe if their prediction was correct.  Finally, they had to come up with an explanation of distance, or lack thereof, between the balls.  This activity resulted in the liveliest interaction among the students.

### Gravity/Pendulum

A presentation on periods of oscillation of various systems in the universe was delivered to help students recognize naturally occurring frequencies built into systems all around us, from the period of the earth’s revolution around the sun all the way down to the period of oscillation of a water molecule.  They were also introduced to Foucault's Pendulum and how they may prove rotation of the earth.

### Mirror/Building heights

This activity started by discussing similar triangles with the students and how the ratios of edges of two similar triangles are constants.  Then the students were provided with 12-inch diameter round mirrors and a yardstick, and were asked to determine the height of CSULA library building.  Some possible approaches, using similar triangles, none of which were at any point presented to the students.  The students were asked to devise their own plan and measurements.  This resulted in a good level of inquiry on the students’ part.  After the students returned with their estimated heights, they discussed the relevance and applicability of similar triangles to this task.

### Archimedes

As a way of getting the students’ attention and getting them to form a better mental picture of buoyancy, the instructor for this workshop told the Archimedes’ story, the tale of the cheating goldsmith, and showed a depiction of Archimedes running naked on the streets shouting eureka.  Students were then led in a discussion on determining density of an object using Archimedes principle.Finally, they were given a piece of brass and three different set ups for estimating the density of the brass and the fraction of weight comprised of zinc in the alloy.