In this unit, which is
designed for a Math 1 class, students will explore the Pythagorean
Theorem—its statement, converse, extensions, and applications. In
the first lesson, students use GSP to make a conjecture about the
relationship between a
2 + b
2 and c
2
in acute, obtuse, and right triangles. In the second lesson,
students work in groups to explore dynamic diagrams, then generate a
proof of the Pythagorean Theorem. In the third lesson, students
perform simulations with Fathom to further investigate the conjectures
they made about acute and obtuse triangles in the first lesson.
Finally, in the fourth lesson, students apply the Pythagorean Theorem
in three ways: in coordinate geometry to develop the distance formula,
in Excel to generate Pythagorean triples, and in GSP with shapes other
than squares on a right triangle's three sides.
Throughout the unit, technlogy is used to give students a deeper
understanding of the Pythagorean Theorem. GSP gives students the
opportunity to investigate the theorem in a dynamic environment, Fathom
quickly creates large sets of data for analysis, and Excel allows
students to easily generate Pythagorean triples. In designing the
unit's lessons, I initially had trouble incorporating technology other
than GSP, as I considered this to be a largely geometry-centered
unit. However, as I developed the unit further, noting important
applications and extensions of the theorem, it became clear that Fathom
and Excel would also be useful. By forcing myself to "think
outside the box" and look for non-geometric applications of the
Pythagorean Theorem, I not only incorporated more types of technology
into the unit, but also made the unit as a whole more mathematically
rich and better aligned with the Georgia Performance Standards.
Technology allowed me to create lessons that investigated the
Pythagorean Theorem from both a geometric and a non-geometric
standpoint, so students can see the connections among various branches
of mathematics while learning more about the theorem.
Time Required
Lesson
|
Number of
50-min. periods
|
Number of
90-min. blocks
|
1
|
1
|
½
|
2
|
2
|
1
(two halves)
|
3
|
1
to 2
|
½
to 1
|
4
|
1
to 3
|
½
to 1½ |
Total
|
5
to 8
|
2½
to 4
|
