Grade Level(s): 9, 10, 11, 12
Keywords: Trina's triangles, Trina, triangle, integer, squares, right triangle, polynomial identity, Pythagorean triples, Pythagorean theorem, converse, positive integers, distinct positive integers, squaring a binomial, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, Florida standards, resource, free, freely available, problems-based learning, student activities
This task is an exploration of the example suggested in MAFS.912.A-APR.3.4 Florida Standards, using the polynomial identity (x2+y2)2=(x2−y2)2+(2xy)2 to generate Pythagorean triples.
Students must investigate Trina's conjecture to discover that it does not work in all cases; in particular, the trick fails if the two chosen integers are the same, or if one of the integers is zero, since in these cases one of the sides of the triangle given will have length zero. This means that students must attend to precision when writing a corrected version of the conjecture, being careful to restrict to (for example) the case in which the two integers chosen are positive and distinct.
Source and Access Information
Name of Author/Source: Sarah Kahre
District/Organization of Contributor(s): Florida State University
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.