PreCalculus 11 Sequences and Series
Specific Curriculum Outcomes
RF09 Students will be expected to analyze arithmetic sequences and series to solve problems.
RF10 Students will be expected to analyze geometric sequences and series to solve problems.
RF09 Students will be expected to analyze arithmetic sequences and series to solve problems.
RF10 Students will be expected to analyze geometric sequences and series to solve problems.
Activities




 Plotting an Arithmetic Sequence using Desmos  A Desmos graph showing how to use a list, sliders and the formula for an arithmetic sequence to plot points.
 Super Ball from Dan Anderson  Use a bouncing super ball to model an infinite geometric sequence. Each time the ball bounces, it has 92% of its previous height.


 The Paper Master Activity from Sam Shah  An excellent intruduction to infinite geometric series using a single sheet of paper and groups of three students.
 Geometric Series Formula YouTube video from James Tanton  What is the geometric series formula? When is it valid? How do we derive the formula? All explained by James Tanton, the Mathematician in Residence at the Mathematical Association of America in Washington D.C.
 The Cake by Matheatre  A 8 minute video about a road trip and eating cake... but just half. A fun application of infinite geometric series. By the same folks who brought you Calculus: The Musical (if you teach Calculus and you haven't heard this, you are seriously missing out.)
 Astounding: 1 + 2 + 3 + 4 + 5 + ... = 1/12 from Numberphile  A Numberphile video that explains some counterintuitive sums and the incredible results when working with infinity. Mind blowing! This could be included in a discussion of convergent and divergent sequences. It might generate some student interest in infinity and string theory.
 The Infinite Hotel Paradox video  The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it's completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert's paradox.