Arc of a ball acceleration days four and five

A racquetball in flight generating an arcing path


The boards span roughly 480 centimeters, divided by six is 80 centimeters per panel. 


The board was divided into six 80 centimeter panels.



Students were invited to come up as pairs to trace the path of a raquetball. Six groups, six racquetballs, six arcs. K'con, Ivan, Billy, Polly Melina, and Milain at the board above.

Billy tests an arc


Afterwards the students were encouraged to form larger groups to try to find a mathematical equation that would describe the arc. 


Desmos was recommended for this.

K'con

The result was an engaged exploration of mathematics and quantitative reasoning. 


Some of the arcs on the board. Labelling with names would prove useful later. 


That the horizontal and vertical radii are not equal means that a circle cannot describe these arcs. 

K'con and Ivan continue to work on finding an equation

Polly Melina and Billy

On Monday I invited the groups to present, group by group. I led off with an introduction about the nature of scientific gatherings to share data and theories. 

Jarret, Athina Viola, Jonathan

A key take-away from this is that I obtained two days of students engaging actively with mathematical theory. This is how mathematics and quantitative reasoning should be done, not "problems one to thirty, even numbers only." Mathematics is being taught all wrong. Little wonder there is no retention and no true comprehension. Two days on one equation, one problem, based in a concrete system. That is how mathematics might be learned. Not thirty problems per day. Drill and kill should never be understood as learning anything. 

K'con and Ivan

Morales put up the results for the second arc

Milain at the board

Groups opted to post equations but were not comfortable explaining their results. 

BLson and Jonathan


Afterward I pulled together some of the common elements. 

I also tried to run a derivation from the roots and y-intercept, but the result was surely more confusing than enlightening. 

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