Wednesday, June 19, 2013

Let's Talk Geometry Regents

EDIT: Welcome to my website. If you like the information in this blog entry or find it useful, please, feel free to leave a comment. Thank you for visiting. The extended-time tests are finished, so I assume that it's safe to talk about the New York State Geometry Regents exam given this morning.

By my count, in the multiple-choice, 15 problems were definitions, theorems, postulates, formulas, etc, with no calculations involved. That is, you either knew it, or you didn't, but there wasn't anything to work out. The other 13 required some kind of calculation or working through of steps. (Your opinion of what counts as working through steps may vary.)

For the test as a whole, I notice four questions regarding the equation of a circle. If you didn't know

(x - h)2 + (y - k)2 = r2
then there were a bunch of points lost. Yes, that means if you forget that subtracting a negative number means adding a positive number, then you had problems. (Don't worry, I won't make you write the contrapostitive of that statement.)

Additionally, there was a question involving the vertex form of a parabola, just to be different.

There were two transformation problems: one multiple-choice, one open-ended. The open-ended was also a composition. You did do it right to left, right? You did the Translation of the Dilation, and not a Translation followed by a Dilation. You'll probably get a point for doing the wrong thing, if it's done correctly.

Two locus questions.

Two constuctions: one multiple-choice, which hopefully provided some assistance to the open-ended question. For an added twist, you needed to make the equilateral triangle with sides congruent to the diagonal of a given triangle. That just tells you how wide to make the compass. I really wonder how many scorers are going to measure those triangles.

Two questions involving right triangles and one more that used the distance formula.

And there was one question using quadratic equations. (Two, if you didn't know the vertex form of a parabola and had to work it out.)

Personally, I had two problems when I took the test. (Yes, I take the tests along with the students. Sometimes I can't assess the difficulty of a question until I actually do it. It may or may not look at difficult as it is.)

My biggest problem was question 24, the similarity problem:

24. In trangles ABC and DEF, AB = 4, AC = 5, DE = 8, DF = 10 and [angle A is congruent to angle D].
Which method could be used to prove [triangle]ABC ~ [triangle]DEF?

The choices are AA, SAS, SSS, and ASA.
This is a STUPID question.
The only postulate or theorem which gets used to prove similarity is AA, because two triangles are similar if their angles are congruent. But we only know about one pair of angles, and we don't even know their size. There's no way to find information on any other.

Now, you are given information about the pairs of sides which include the congruent pair of angles. That much is true. But those sides are NOT congruent. SAS is used for congruence. If two triangles are congruent, then, of course, they are similar. But these aren't congruent. The sides are proportional, as corresponding sides of similar sides should be, but that in itself isn't proof. (For one thing, we don't know about the third pair of sides.)

So I have a problem with this question. They were looking for Number 2. The only answer which makes sense is Number 1, and that one isn't useful, either.

You may argue and disagree all you like, but SAS for similarity is NOT in the curriculum.

My second problem was question 36. They laid a trap and I fell into it. Three times. I wouldn't have gotten the right answer, despite the fact that I knew I had the wrong answer.
How did I know? Test-taking Strategies and Number Sense. Basically, the part that said "Determine the length of OA" gave me trouble because I got an irrational answer. However, the answer COULD NOT be irrational because they neither stated "round to the nearest ####" or "give the answer in simplest radical form".

What was the confusion? The setup was complicated enough, and I just through all the hoops fine, except for the last one. It gave CF = y + 10 and CD = 4y - 20. I read the latter part as FD. So on top of all the radii you had to pencil in, and using the Pythagorean Theorem, and knowing that when a radius is perpendicular to a chord it bisects the chord (into two congruent pieces), you had to know enough to double y + 10 into 2y + 20 before setting it equal to 4y - 20.

So I had y = 10, instead of y = 20, which was correct, but not the answer. You then had to substitute to get the length of DF. You know, the segment that I thought was 4y - 20, but was really half as big. So DF = 30.

Now the last answer was obvious to me (once corrected) because 16 and 30 are part of a Pythagorean Triple. That being said, just because the answer is obvious doesn't mean that you don't show the work!!! OA is 34. (I don't have to show it. Exercise left to the reader and all that.)

So how did you do?

Any questions?

Anonymous said...

My teacher did AA~ but also SAS~ and SSS~. We used the last two to prove the first. I thought the test was fairly OK, but had to read questions carefully. My friends in 2 other schools also did 3 methods for similarity. One of my friends thought last proof was hard bc she forgot halves of equals are equal.

(x, why?) said...

I knew students who knew, but just weren't sure how to phrase it or what the correct reason would be, which shouldn't be too big of a problem for them.

If they didn't realize this and stopped, then I hoped they at least got some other steps in to get at least half of the points.

As for SAS, I've yet to speak to a teacher who has used it for anything other than congruency. I could see that this was the answer that they going for, but that doesn't mean that I have to like it.

One Brow said...

I teach developmental Geometry at a local (to me) community college. SAS~ is in our curriculum.

Anonymous said...

It is in the curriculum but not stressed. I usually only teach the AA while doing proofs. I actually showed my students SAS and SSS to prove similarity on the last day of school, just in case. Many of them still forgot it though and chose AA,

RickJ said...

As a fellow Geometry teacher, I had a problem with #33. The question asks for a SINGLE locus. Yes, a SINGLE locus. Read the question... "...graph the locus of points 4 units from the x-axis AND equidistant from the points..." Normally the question is worded .."graph the locus of points...and graph the locus of points..." If a kid did the locus satisfying BOTH conditions at the same time, namely only the 2 coordinates, they lost points. Yes, we did have students do this.

(x, why?) said...

Wow. I didn't see the sample answers for question 33. When I wrote it I had two horizontal lines and two "X"s. I didn't bother drawing the vertical line.

Since I didn't grade that question, I don't know what the standard is. The rubric is confusing. 2 points for both loci and the correct co-ordinates, 1 point for neither loci being graphed. There isn't anything stated about one locus graphed.

RickJ said...

True, yet the question is written as ONE locus with 2 conditions. It is completely unfair to require the 2 separate conditions to be graphed separately. As written a completely correct response would be just the 2 points.

(x, why?) said...

Two X's without any supporting work showing how you arrived at them is never worth full credit, regardless of the wording of the problem.

My response to that is that graphing the locus as two points would be the work shown, and then putting the X's where the points are would be the answer. So, as long as a student shows 2 nice clear points as well as X's, they should get full credit. What might a student get if they did what I suggest and explained their rationale verbally in the margin?

(x, why?) said...

The two points is not the "work shown" and never has been. You could make a case for explaining in the margins if you wrote something that wasn't a re-iteration of the question (like the equations of the line and where the lines intersected), but, frankly, drawing something would be more efficient.

(x, why?) said...

By the way, can we all agree that pretty much all the locus of points questions -- ever -- are pretty silly?

Anonymous said...

As a fellow teacher, I have to disagree with your take on question 24. SAS is in the curriculum. Copied directly from the Geometry Core Curriculum:
G.G.44 Establish similarity of triangles, using the following theorems:
AA, SAS, and SSS