
06035698
j
2012c.00420
Ellis, Amy B.
Informing practice: The proof is in the practice.
Math. Teach. Middle Sch. 16, No. 9, 522527 (2011).
2011
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
E53
proving
justifying
generalizing
foundations of mathematics
growing rectangles
perimeter
area
polygons
angles
From the introduction: Imagine an eighthgrade classroom where students are exploring relationships between the heights and areas of rectangles. They are investigating a special set of rectangles that grow in a particular way by iterating the height and length values so that the rectangles remain similar. The students create tables, comparing the rectangles\rq\ heights and areas, and notice something interesting: The second differences for the area are always constant, no matter what type of rectangle the students use. One student, Sara, makes the conjecture that this will be the case for any rectangle. This situation is ideal for giving students the opportunity to develop proofs.