# Integrated Geometry – June 2009 – issues with some questions

I liked the exam, almost by accident. It feels more like a content exam, since the indicators are bunched in geometry, but it is still standards based, so there was over- and under-testing. And it is still the New York State Education Department, so there were bad questions.

For reference: here’s the test.

#3. Triangle looks rotated 180. We can accomplish this by rotating, of course, or dilating by -1. But both are choices. Look, we know they wanted rotation, but how could you mark dilation wrong?

#4. The lateral faces of a regular pyramid are composed of: First, what’s a regular pyramid. Seriously. Second, if it is what I think they mean, shouldn’t equilateral triangle have been a choice?

#8. They show a triangle that’s been transformed. Looks to me like a dilation by a factor of -1/2, but they want the kids to match it to a composed transformation. Not terrible, but disappointing.

#9. I never quite got this. What’s the difference between the sum of the interior angles and the sum of the exterior angles of an equilateral triangle? Is it conventional to ignore the fact that there are 2 exterior angles at each vertex?

#19. They want the midpoint of the diagonal of a square on the coordinate plane. Folks, I deduct points from kids who fail to indicate units. Why should we hold you to lower standards?

#21. “Nearest cubic inch” language. Why? Why not: “the volume of the cone is closest to?”

#28. Jeez. “In three dimensional space, two planes are parallel and a third plane intersects both of the parallel planes. The intersection of the planes is a:” Come on. We know what you meant, but it’s not what you asked. The answer you wanted was two parallel lines, but as asked, the three planes do not have a common intersection, and a good student would answer “the empty set”

#32. You want a sketch? Right after you had the kids doing constructions? You knew you would get constructions, right? At least for finding all points equidistant from A and B. But since you said AB was 3″, and asked for all points 2″ from A, what did you expect the kids to do? Fake the length? I think that’s what you wanted. But that’s really not right. Whether you meant to or not, you kind of implied that students should calculate that length, and do a much harder construction.

#33. A disjunction? In geometry? Why not stick to conditionals. Really. Or try this one: “n is an even integer or n + 1 is an even integer” You want to see if kids get “or”? My question does it. Yours doesn’t.

It really is a better test. But the complaints are real, too.

For more discussion, see the Association of Mathematics Teachers of New York State (AMTNYS) listserve.

I agree with most of your comments.

For #3, dilation is also an appropriate response. This is not the first time the state has made this error. Let’s also mention that they never even indicate whether or not the triangles are congruent, so really none are true.

For #32, a few of my students beautifully trisected the segment and then used those marks to build the appropriate sketch. However, providing an arbitrary measurement in the copy but then no way to adhere to an accurate “sketch” without such things as measure indicators or even coordinates made for some creative grading.

I recall a source defining dilations without negative dilation allowed. If NY allows that though it’s definitely a mistake.

A regular pyramid is a pyramid with a regular polygon as its base. Is there some other interpretation?

#19 is abstract. I don’t see why it needs units (just as how one can speak of the x-axis and y-axis with or without particular meanings).

#32 is in truth quite odd.

My biggest complaint about the test was that it was repetitive, but for the most part I thought it was fair.

#4: This was specifically address in the NYS curriculum so I don’t know how anyone can complain about that one: “lateral faces are congruent isosceles triangles” (regular just meaning the base is a regular polygon not that the edges are all congruent).

#19: I completely agree- there should definitely be a scale.

#33: I’ve heard many complaints about this question within my dept, but I don’t quite understand why people are so bothered by this question?

Sooo many did a construction for the locus sketch question but those who did got it right! My issue with that problem is WHY DID THEY HAVE TO CONNECT THE POINTS! Almost every student who answered incorrectly had two lines and a circle, one above and one below just like what they studied when they looked up notes on locus theorems!

Yes it is understood that when discussing exterior angle sum there is only one exterior angle at each vertex

It was an excellent test however I think those green review books were terrible and I will not use them again. I understand the issues with the test but I think it was much more fair than the Algebra exam

the curve should be interesting..i hope it is higher that Algebra, that conversion is crazy