From: email@example.com [mailto:firstname.lastname@example.org] On Behalf Of TKENYON@crcs.wnyric.org Sent: Monday, May 19, 2014 8:12 AM To: email@example.com Subject: Re: trapezoid clarification
When doing trapezoidal approximations to find the area under the curve, if two consecutive values of f(x) are equal, the trapezoid isn't a trapezoid under the old definition. With an exclusive definition, this leads to an inconsistency.
-Tom Kenyon CRCS Mathematics/Physics firstname.lastname@example.org<mailto:email@example.com> With all due respect Meg, I do not believe there is anywhere in the US where this "Although this might be a surprise to NYS teachers who have used the exclusive definition, this is a common definition for trapezoid." is true.
It might be a better convention, but in this country, it has never before been ours.
I am quite disappointed that AMTNYS transmitted this information, and did not lead a campaign to challenge it.
Jonathan Halabi the Bronx
On Sat, May 17, 2014 at 8:31 AM, Meg Clemens < firstname.lastname@example.org<mailto:email@example.com>> wrote: At training in Albany this past week, NYSED released a standards clarification document for Geometry that states (among other items) that a trapezoid is now defined with the 'inclusion' definition: a trapezoid has at least one pair of parallel sides. Although this might be a surprise to NYS teachers who have used the exclusive definition, this is a common definition for trapezoid.
1. Is this standards clarification memo posted on engageny anywhere yet? I couldn't find it.
2. How do we treat conflicting definitions next year when we are preparing students for both regents?
3. With the new definition, what is an isosceles trapezoid? I think we need clarification on this.
a. If I use trapezoid w/ one pair of opposite sides congruent, then a parallelogram is an isosceles trapezoid but its base angles are not congruent.
b. If I use trapezoid w/ one pair of opposite sides congruent and base angles are congruent, then rectangles and squares are isosceles trapezoids, which might be OK.
c. There is an alternative definition that uses one axis of symmetry and one w/ no symmetry to yield the usual depiction of an isosceles trapezoid.