The Penny Farthing Puzzle gives students practice calculating angles and edge lengths of right triangles. Your struggling students will be engaged learning the curriculum while your top students can get wrapped up in problem solving.
This puzzle is good to engage students for 45 minutes.
I'll offer $500 for the first classroom that solves The Penny Farthing Puzzle.
Standards for Mathematical Practice:
All MathPickle puzzles including Klingon Attack are guaranteed to engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:
MP1 Toughen up!
This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.
MP3 Work together!
This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.
MP6 Be precise!
This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.
MP7 Be observant!
One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.
The Penny Farthing Puzzle targets Common Core State Standards for students learning trigonometry:
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*