Calculator part: 18 of 25
Use the information provided in the animation to answer the questions about the geometric construction.
To pause the animation, select the animation window.
The students are supposed to watch a video of a construction and then say things about the proof enacted through the constructions. This is a very specific skill that needs to be practiced. Daniel Schneider kindly sent me a link to a website with a large number of construction animations (along with proofs) in case you need more to use in class.
However, there’s a serious interface problem. Here’s what the video looks like when paused, as well as a question to go with it:
Point “C” is completely covered. Whoops.
Non-calculator part: 6 of 7
This is one of those simple-looking questions which has enough of a trick to it I’m not sure how many students will get it right.
Part A requires students to work a double-completing-the-square manipulation, hopefully not getting sidetracked by the presence of b on the right hand side:
Part B requires noticing that a radius of 7 means the right hand side will be 49, so and thus .
In principle this problem is solvable, but the lack of partial credit on a problem with a “trick” that I worry a student who can normally complete the square would still get no points due to the indirection.
Calculator part: 13 of 25
This problem’s rough for three reasons:
a.) Even with the phrase “the pipe is open at both ends” placed in there, this is something of a background knowledge problem; the students need to know the “outer surface” excludes the circles on the top and bottom.
b.) There are volume formulas on the formula sheet but not surface area formulas. Thus the students need to have memorized or be able to extrapolate it, and know enough to exclude the circles.
c.) If is set to be 3.14, there answer comes out to be 1356.48. If is set to be 3.14159 or something with more digits (not unusual since graphing calculators have a “pi” button) the answer comes out to be roughly 1357.168. Rounding to the nearest integer thus can give either 1356 or 1357 as an answer.
Non-calculator part: 7 of 7
Out of all the problems on the PARCC final exam for geometry, 28% are related to transformations.
I can understand a transformational emphasis in general: it leads to a function transformation understanding of graphs (which is far more powerful and useful than looking at each kind of graph individually). However, why do so many of the dilation and rotation problem — 4 out of the 9 — involve centers not at the origin? This is not rhetorical; I really want to know where the utility is.
Non-calculator part: 20 of 25
This is one of the easier problems on the test, but assumes background the students don’t necessarily have. I can assume what a “collar” means here (even though I’ve never heard the word used in this context) but my ELL students are more likely interpret it as gibberish.
Calculator part: 10 of 25
This is very similar to the other problem in relying somewhat on background knowledge. Technically speaking one can ignore all the external stuff about merchant vessels and probes and focus on the math, but the brain of the ELL student doesn’t have an easy time removing the context.
Also note the weirdness of the rounding; in problem 20 the rounding needed to be done to the nearest tenth, while in this problem the rounding needs to be done to the nearest integer off the list.
Calculator part: 3 of 25
I’m noting this one because nothing in my current textbook (Carnegie Learning, written for Common Core) has anything resembling this kind of problem. Anyone have a source with problems that are similar?
Calculator part: 23 of 25
I don’t think I’ve ever give this much emphasis to the vocabulary of proof. Getting my students to keep the reflexive, symmetric, and transitive properties of congruence straight is going to be a nightmare and a half.
Ok, one last problem, from HS Sample Math Items, 7 of 10 (so not the final exam, but the open response part):
Here the angle bisector video returns (complete with unhelpful play button covering the diagram when paused) but the student is supposed to free-write a proof.
Here is how you type the first line as given:
1.) Pick “geometry” on the side and pick the short line in the upper right; that’s a “line segment” and will give you a blank box under a line segment so you can type letters.
2.) Type the letters you want under the line segment. If you accidentally type more than two letters any extra keypresses will be ignored.
3.) Go to “relations” above “geometry” and find the congruence symbol. Pick that. This will give the congruence symbol and a blank box.
4.) Pick the “line segment” and it will take the blank box that just appeared and put a line segment over it.
5.) Type the letters you need for the other line segment.
Now you have one step of the proof, now you just need to give a reason and then do four more steps.
(What would constitute a valid reason here, by the way? The mathopenref site I linked to early in this post just states “They were both drawn with the same compass width” — would this be considered valid by graders?)