Responses to multiple POV Logic Puzzles
There are a group of 5 good logic puzzles Hats – Green-eyed guru – Perfectly logical pirates – Prisoners with Hats – Leprechauns. (I think they are good), and their responses need a place. Here it is.
Logic Puzzles from multiple points of view 4/5
Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.
None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.
Prisoners with Hats
Three perfectly logical prisoners are seated facing each other, with hats on their heads. Each hat has a counting number {1, 2, 3, 4, …} on it, and each prisoner can see the hat of the other two prisoners, but not his own.
The warden says,
- I will set free the man who can tell me his own number, but execute any man guessing incorrectly.
They look back at him in stunned silence.
- “OK, a hint. One of your numbers is the sum of the two. Alan?”
- I don’t know my number.
- Bert?
- I don’t know my number.
- Graham?
- I don’t know my number.
- Alan?
- I still don’t know my number.
- Bert?
- My number is 26.″
And he went free. What were Alan and Graham’s numbers? Explain your reasoning. Why did it take five questions to get an answer?
Place questions/clarifications below. To submit proposed solutions, click here.
Scores rise at “Do Not Apply” school – your reaction?
Back in March, I added PS/MS4 (Crotona Park West) to the Do Not Apply list. The principal was autocratic, mean-spirited, bossy, quick to dock pay, to give U-ratings…
And the response was immediate. The comments section quickly filled with scores of visceral reactions to the school administration and its system of favorites and arbitrariness. In fact, much of the reaction was so emotional that I issued a general warning and request to stay on-topic, then closed comments (I just reopened them.)
But math scores rose. There is this puff piece from the Daily News from last month. The numbers improved.
What do we make of that? What is the relationship between toxic schools and student achievement?
It would be easy if there were clear and direct correlation, ie, happy staff = high scores. It would also be easy, in a very different way, if staff satisfaction had nothing to do with scores.
But the answers must be much more complicated. Bronx Science is a miserable place to work. And its scores remain high. Is it fair to say that scores are completed unrelated to how well a school is run?
But I know a story of two adjoining schools, the older one poorly running, declining scores, unhappy staff, and the newer one with higher and rising scores, well-run, with a satisfied staff. The principal can be tough, but is considered fair. And they draw the same kinds of kids from the same neighborhood. It would be foolish to try to claim that the scores were unrelated to the other problems in the first school or the quality of leadership in the second.
What do you think?
Logic Puzzles from multiple points of view 3/5
Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.
None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.
Perfectly Logical Pirates
Logical Pirates enjoy (in this order):
1. staying alive,
2. getting lots of loot, and
3. killing other pirates.
Five Logical Pirates come upon a treasure chest of 100 indivisible gold coins.
They agree to draw lots and establish an order (A, B, C, D, and E) and that then each pirate in turn, starting with A, must suggest how to split the loot and all (living) pirates, including the proposer, will vote on it. If a suggestion gets a majority vote, they split the gold according to that suggestion and go home. If a suggestion fails to receive a majority vote (a tie loses), the proposer is killed, and the next pirate makes his suggestion.
Pirate A steps up
- I suggest that the gold be divided in the following way: ___________ ______________ __________ __________ _____
What does he suggest? Explain why it is his best suggestion.
Place questions/clarifications below. To submit proposed solutions, click here.
Why walk with no camera???
Took a Bronx walk this morning, almost 6 miles, zigzag around 149/138, then a shot up the valley east of the Concourse, ending at Tremont and Webster.
Then a straight shot, almost 4 miles, this afternoon, from Westchester Square, straight up Williamsbridge, across Allerton, skirting the Botanical Gardens, again crossing Webster.
I wouldn’t have taken many photos, but…
- The red-tailed hawk perched precariously on an upper window ledge, at Hostos Community College.
- The monument to Major Deegan (real guy. think he doled out lots of patronage)
- The east west side of Franz Sigel Park – damp and dank and shady and musty… (west, west, not east, which I’ve walked by dozens of times. This was my first time on the Walton side)
- Some of the narrow streets around the Hub. I forgot they were so small.
- The funny mix of old buildings and newer houses and remaining empty lots and community gardens along Sherman Avenue.
- The mall in Mt Eden Parkway.
- Some good shots capturing both the Cross Bronx and regular people stuff, like playgrounds, buildings, stores. How can such a busy, choked, pollution-generating gash of concrete have been built right where people live and sleep? NIMBY? Not in anyone’s backyard!
- Pelham Parkway. Driving it, it’s easy to forget what an oasis it is.
- Mulberries and Lindens. Images of favorite tastes and smells.
- The Bronx River, flowing swiftly.
- Chipmunk. He would have disappeared before I could snap his picture, but I would have tried.
if I’d brought a camera.
…en otros frentes…
…for some friends…
Half millionth visitor
At 4:50 PM a visitor from Eden, NY signed on to read about the Geometry Regents. He read that one page and left.
That was visitor 500,000 to this blog, since Sitemeter was installed. There have been 775,000 page views.
June was a very busy month, with lots of regents-related traffic. Almost 50,000 visitors opened over 80,000 pages.
Thanks folks. Hope you found something interesting or useful.
Logic Puzzles from multiple points of view 2/5
Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.
None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.
Green-eyed Guru
On a wonderful, magical island live 201 enchanted islanders. One hundred have blue eyes, one hundred have brown eyes, and one, the Guru, has green eyes.
None of the islanders knows their own eye color. There are no mirrors. Water does not reflect. Good thing, too, since upon learning his or her eye color, an islander would have to, at the next midnight, swim off the island (through shark-infested waters, if you don’t mind scaring your students)
And none of the islanders can speak, except the Guru. But the Guru sleeps and sleeps and sleeps, wakes up once every hundred years, says something, and goes back to sleep.
The day for the Guru’s waking comes, and all the islanders gather around her, expectantly. She opens her green eyes, stretches, and says
- I see someone with blue eyes
and goes back to sleep.
Who leaves the island, and when. Explain your reasoning.
Place questions/clarifications below. To submit proposed solutions, click here.
Logic Puzzles from multiple points of view 1/5
Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.
None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.
Hats I
Pal, Ral, and Sal are blindfolded. Each has a hat placed upon his head. There are, and all know this, 3 red hats and 2 white hats.
We need to make this interesting. The 3 X-als are prisoners. If they can correctly state the color of their own hat, they go free. If they incorrectly state the color of their own hat, they are executed.
They are not risk takers. No one will guess.
Pal’s blindfold is removed. He can see Ral’s and Sal’s hats, but not his own.
- What color is your hat Pal?
- I don’t know.
Ral’s blindfold is removed. He can see the other two hats, but not his own.
- What color is your hat Pal?
- I don’t know.
The jailer approaches Sal. But before he can loosen the blindfold, Sal stops him.
- The color of my hat is ____
Finish Sal’s sentence. (ha ha). Explain his reasoning.
Place questions/clarifications below. To submit proposed solutions, click here.
Portrait of a class in its last days
My small school just graduated its fourth class. That makes seven years for me, seven classes both here and gone; 300 odd graduates, 280 current students, another incoming class of 100. I’ve known them all; I’ve taught the vast majority.
Class #4. Class of 2009. What was the matter with them? All of us were concerned from the end of their freshman year. And over time, they got worse.
They misbehaved in small, but very noticeable ways. They talked back and argued. “A students” earned A minuses and B students earned Cs. Too many of them failed courses “here and there.” Their collective homework ‘habit’ was suspect. They were chronically late. There was a developing “pack” mentality. We worried.
Going into senior year, this year, we looked down the list. Graduation numbers? We held our collective breaths, while calculating the worst. Ugly was possible. Ugly seemed likely. And by April? “Not ugly” started to look possible, but the more likely outcome was told by the numbers of 55s and 65s in required courses… deep breath…
But a few things happened, some counterweight. The behavior became a little less perplexing, less annoying. Last year’s “pack” was this year’s mutual caring and responsibility. And for a bunch of under-achievers (many, not all, fell into this general category), they were shooting the lights out with college acceptances. Last year’s behavior had become this year’s “personality.” And boy, they had personality. They were fun. Their trips were fun. They held together nicely. And it still beats the hell out of me how they did it, but they ended with our highest graduation rate ever.
I think I always liked them better than most of my colleagues did, but this year I adored them. And they pulled it together. And prom was wonderful. And what a nice graduation. It was not 2008 when I was occupied elsewhere. It was not 2007, when I spoke about giving back, including a line against the war; when I choked back tears through the whole ceremony. Different connection. I was happy. For them. For me for knowing them.
And Thursday they got their diplomas and transcripts, watched each others’ documentaries, and they were through. Done. Nothing left. But they didn’t care. Almost all of them came back on Friday for our year-end barbecue (unlike last year). They stayed past the barbecue. They stayed longer than the underclassmen. They chatted with teachers, and each other, and each said goodbye to the same peer or adult 2, 3, 4 times.
I walked outside the school. The linden blooms’ sickly-sweet perfume hung heavy. It reminded me of the last day, two years earlier, when I felt empty. But no emptiness this year. Joy. And concern about the blandness of school without my biggest little friends.
Reaching Fellows (reprint)
This was originally published in June of 2008. Some things have changed:
the number of NYC Teaching Fellows is far smaller; teachers are being excessed from schools; there is a hiring freeze.
But there are still new Fellows, they will become new teachers, and now is the perfect time to start talking to them.
One more detail: The “Do Not Apply” list may be much more of a “Be Cautious If You End Up There” list given the likely tightness of jobs.
— — —
Given that the Fellows, as a group, are indifferent or even hostile to the union, how could we possibly talk to them? Organize them?
Before the union meets the Fellows, they have already been carefully inoculated against us. That first summer is key.
And what happens in the first summer? They get bossed around by the Fellows and the DoE and their university. They face arbitrary decisions, rules that don’t make sense. They get assignments they don’t want. They work/study brutally long hours, with massive amounts of homework.
And they do it together, in groups of 25 or so.
Wouldn’t it be nice for us (current teachers and our union) to find ways to reach these small groups of fellows? to have conversations? to clear up misconceptions before they occur?
They are being badly treated. This is the moment when they may be first open to hearing from the union. This is the moment when the Do Not Apply list, if it existed, would be most useful.
And they are sitting together in groups. Can’t be that hard to find them, right?
Reaching fellows with a pro-union message, giving them advice, survival skills, saving them from signing up at career-ending schools, this can and should be done.
Bronx Science U’s teacher 2 days shy of retirement
The letter speaks for itself:
Bronx Science new alum exposes harassment of teachers
Mark hit this out of the park. Look through his well-put-together report: http://www.mzakariya.com/Bronx_Science_Teacher_Report.pdf
The End?
June 26, 2009. The last day for teachers. This has been one long damned year.
The agreement to trade pension concessions for a post-Labor Day return passed. (I voted no, twice). We go back Tuesday, September 8. And then a follow up pushed the kids’ start back to Wednesday, September 9.
Can you imagine we had to negotiate to get the DoE not to start kids and teachers on the same day? In the spirit of the moment, a friend proposed that we work the Jewish holidays as well, and in exchange start Thursday, one day after the kids…
The summer, for me, is not yet in focus. Possibilities exist…
- A math conference in the Finger Lakes in August. (5 days, definitely going). Tom Chapin’ll be there… ? ..?
- The AFT called me (called ME) to ask about summer volunteer teacher organizing in the South. (two or three weeks, if I do it)
- Presentation on methods in the mathematics classroom (not as much of a yawn as it sounds, problem solving, mostly) in a warm, Caribbean nation, along with a full week stay?
- Programming. The last Summer.
- Working (informally) with fellows and new teachers.
- Working a couple weeks with not so new teachers?
- A real trip (when I finally decide I can’t fit it in, I may describe where I would have gone. Would have been fun!)
- And finally, a slim chance that I will trade blogging for a completely new sort of activity… (I’ll explain only if it happens)
So this is really a beginning, right? (Just like “commencement” is the end and the, honestly, it doesn’t make that much sense)
For NYC teachers, it is the end.
It’s the end of a long year. Full of stress, exhaustion. Teachers with awful principals felt it. Good teachers in good schools felt it. This year was long for all of us.
Relax. Recharge. Make your own plans. Or don’t. But this time is yours. You’ve earned it.
While we are horse-trading days…
…a friend proposed that we work the Jewish holidays as well, and in exchange start Thursday, one day after the kids…
Halfway there – Eximius to phase out middle school
Earlier this month the principal of Eximius wrote to middle school parents.
She announced the phase out of grades 6 - 8. About time!
There was discussion on this blog: Not closing? -- Rumor lives on.
Eximius remains one of the worst - even with just 9-12 - Do Not Apply schools in NYC Here is the text of that letter:
June 2009
Dear Parents and Guardians:
As you know the Morrisania Educational Complex where we are housed has limited space. Currently BCMS has 15 classrooms and we have 17 classrooms. In order for us to have a full middle school/ high school program we need a minimum of 21 classrooms. When our school and BCSM moved into this complex four years ago we anticipated that extensions to the building would be built as both schools started to get closer to full capacity. However, as our population expanded no corresponding increase in the space materialized. Now that we are near capacity the space problem has become acute.
I met with a team of my teachers and administrators and we have decided to slowly phase out our middle school and become a full grade 9-12 high school in three years. Hence, we will not be taking in a 6th grade cohort in the coming school year. But, we will keep our 7th and 8th graders until they move into Eximius’ high school. In addition to solving the space problem this will also enable us to focus all of our energies and resources to one school instead of two. The space that is freed by the slow phase out of the middle school will allow us to have a plethora of resources. These resources include 1) our own Science lab which will be completed August 2009, 2) a library in the building which will be completed January 2009, 3) a college office which will be completed August 2009 and 4) a SAVE room which will be completed August 2009.
Please rest assured that the gradual middle school phase out will enable us to bring our vision to full fruitition. I am excited about the additional resources this change will afford our students! If you have any questions or concerns please do not hesitate to contact me or the parent coordinator, Ms. Gil.
Sincerely,
Principal Smith
Geometry scores
The New York State Education Department released the cut scores for the Geometry Regents (anyone else notice that the test was not called Integrated Geometry?)
Total points: 86
Passing points: 41 (that’s about 48%)
Mastery (that’s what we call an 85 or up): 71 (that’s 83%)
41, 71 for passing and mastery.
Kiddies: if you know your raw score, hit the link in the first line to look up the conversion. If not, your schools will have your scores today, or tomorrow morning at the latest.
Vote no on pension de-equalization; stand up for new hires
Dear colleagues,
I am writing to let you know that the UFT today concluded negotiations on an agreement that restores the traditional post-Labor Day school start for our members, leaves intact the pension and health benefits of all current UFT members in active service or retired, and preserves our hard-won age 55 retirement benefit in the face of enormous political pressure to roll that back. We have agreed to support legislation to modify pension measures for newly-hired UFT members, which will provide the city with much-needed cost savings during this severe economic downturn…
So begins a letter from Randi Weingarten to tens of thousands of UFT members.
The proposal is outlined in a letter. I’ll find it and link it, or retype it later. But here’s the points:
- we don’t have to show up the two days before Labor Day anymore
- The fixed TDA bumps down to 7%
- New hires will contribute 4.85% to pension for 27 years, instead of 10 years. Vesting occurs after 10 instead of 5 years.
- New hires will need 15 years, instead of 10 years, to be eligible for health coverage after retirement
- The teachers owe the DoE 1.08%, of which points 2 and 4 cover 0.5%, with the remaining 0.58% to come out of the next contract.
Randi wrote “will provide the city with much-needed cost savings during this severe economic downturn“
But new hires would have contributed for the next ten years anyhow. There’s no “savings” (ie loss for teachers) until 2019.
So why has the DoE become so generous?
They haven’t. They are willing to swallow the two days to achieve their long-term goal: pension reduction and pension de-equalization.
The union is delivering current members something we want – those two days. We hate, despise those days. We hate reporting in August. We lose the Labor Day weekend. In my chapter, most people were willing to take a hit on the wage settlement in the next contract in return for getting those two days back. And I assume that there is similar sentiment in schools around the City.
And we will not bear the cost… Not directly. But we are paying out of our future colleagues’ pensions. A union agreement would stand for solidarity, for sharing what pain there is, for sharing the gains amongst us. This is not a union agreement – it is a political agreement, it is a business agreement. Someone has cynically calculated just how much it will cost to get us to deal away part of our “unborn” colleagues pensions. They are counting on us having no sense of solidarity, no union spirit. We should say no.
Tomorrow, at the Delegate Assembly, we will vote on this proposal. Vote no.
Some of you, as unionists, as defenders of workers rights and gains, know that NO is the right vote, but may feel constrained.
If you are constrained against voting no, step out of the room. Or don’t come.
And if you must be there and vote the wrong way, decline to speak in favor.
And for the rest of us: come; speak; vote no.
My favorite bad exam target: Math B (and a puzzle)
I don’t like high stakes tests (I think necessary testing can be done in a way to reduce the stakes, and lots of testing is not necessary). And I don’t like bad math. And, if you read this blog you know, I hate Math B. How much? Take a look at some of these old posts:
Math B later today – not quite the end
One of the worst standardized mathematics examinations I have encountered, Math B, is entering its final lap.
The final administration will be June 2010, preceded only by January 2010, August 2009, and today.
This afternoon students across New York State will sit down to work on a mishmash of Algebra 2, Trigonometry, Statistics, Geometry, Probability, and who knows what else questions, united by bizarre penalties for rounding appropriately, and strange, often impossible/unreasonable ‘context.’ With luck the actual mathematical errors will be few, and will not be terribly distracting.
For those of you kiddies taking this thing:
You’ll need about half the points to pass. That number floats up and down every year. Don’t get thrown off if something is too hard for you; it may be. Just move on to the next question. Missing one is not horrible.
On Part I, if you leave some blanks because you really don’t know, that’s ok. But guess before you turn the paper in. There is no penalty for guessing on multiple choice.
On Parts II, III, and IV, write something, almost anything, for every problem. No blanks. Give the graders a chance to award partial credit.
Pencils and Pens. Calculator. (w/fresh batteries, PLEASE!)
Plan to stay most of the three hours. No rushing out. If you feel stressed or fatigued, take a break (Could be a stroll to the bathroom. Or try to remember the lyrics to your favorite song. Or count ceiling tiles.) Something to take you off focus for a limited period of time (no naps!) You may find you come back with restored mental energy.
Starting tonight or tomorrow I’ll post discussions of some of the interesting/awful/strange/bizarre questions. Check back.
And good luck. We got rid of this monstrosity, but not quickly enough to spare you. Sorry.
Eximius Middle School to phase out starting this fall
There is a letter from Eximius to parents stating that the Middle School will be phased out, beginning this September with no new 6th grade, due to limited space and the school’s need to focus on the 9-12 grades.
Eximius is among the worst of the worst, one of the top three schools on the Do Not Apply list. It is a horrendous place to work, and former employees come away shellshocked by the experience. Students are treated poorly. It does a lousy job in every respect.
It is good that they are losing three grades, but the high school will remain open, and that is not good. The whole thing should be shut, and the principal should be removed.
I’ll either reproduce or retype the letter, and post it here in the next day or so.
Bronx Science math teachers finally get their day
THE BEGINNING OF THE END
Publicola
(blog reader)
For the past week, I have been listening to experts state that the actions of the Iranian regime to popular sentiment has undermined the legitimacy of the regime, that it may be the beginning of the end.
Tomorrow, the Math teachers at Bronx Science will begin to testify against their regime to a binding arbitrator. The actions of Rosemarie (I Am A Dinner Jacket) Jahoda over the past two years – handing out “U” ratings, denigrating teachers in front of their colleagues and students, retaliating against teachers who question her dictatorial regime, forcing teachers to leave – and the unquestioning, union-busting support she has received from (Grand Ayatollah) Valerie Reidy have undermined the legitimacy of this regime within the school. The key now, as the protesters in Iran have shown us, is to bring this to the attention of the outside world. Teachers should be prepared to testify, truthfully but forcefully, against this regime. Document all their actions and testify about them!
If the arbitrator asks what would satisfy the teachers, tell them nothing less than regime change. Remove these two, and their sycophants, from their administrative positions and reward them with the retirement they so richly deserve!
— — — — — — —
Notes by jd2718
Since Valerie Reidy took charge in a botched principal selection process, and since she was poorly greeted by her new staff, she has gone after them, department by department. English, Chemistry, one by one. There is hatred and malice.
2007 -08 was the math department’s turn. She hired Rosemarie Jahoda as AP Supervision to bully and berate, and bully and berate she did. Last May 20 of 22 department members signed a Special Complaint. It should have been heard and completely resolved early in the Fall, at the latest.
The New York City Department of Education did not allow the Special Complaint to move forward. They violated the contract. They are at war with us. It wasn’t just Science, they sat on every Special Complaint. We should know they are at war with us. We should act as if they are at war with us. Our union leaders do not.
Admitting they are at war with us means admitting that every agreement we sign is suspect. It means admitting that our contract is getting beaten up, our teachers abused. And it means saying we are ready to fight back, as best as we can. But our leaders do not admit that agreements are suspect (Randi was shocked, absolutely shocked that the Rubber Room agreement was being violated); they think admitting that we’re getting beaten up makes them look weak. And I do not know to what extent they are ready to fight back.
Is the delay the UFT’s fault? Absolutely not. It is the DoE that went after our rights, our members, even some of our jobs. And even if the UFT had stood up, hard, there is no guarantee that we would have done better.
But it would have been better, it would have felt better, it would have helped ensure more union participation if our members had seen our leaders in the trenches (up against admin trenches, I don’t mean the classroom), next to us. There is no way what continues to occur at Science, the outrageousness of union communication being prevented, vindicative letters in file, teachers held to follow rules that are nowhere written down, retaliatory U’s, distribution of anti-union literature, destruction of new teachers’ careers, there is no way that this should be going on without the UFT shining a light for all the world to see the DoE and one of their twisted minions at their vile worst.
More vigorous union action may not have gotten more done. But the lack of union attention is embarrassing. It is shameful.
In the meantime, many of the 20 signers have left. U’ed. Forced into premature retirement. Forced to transfer. The signatories can be found in a specialized high school in north Jersey, in fancy schmancy schools in Westchester, in the top-rated middle school in Manhattan. And in other schools, other places. The real danger today and Friday is that Jahoda and Reidy have buried the witnesses – have moved so many of them so far away, that they will not be able or willing to come back and face their tormenters. Let’s wish them for today and Friday the will, the stamina, the anger, and the opportunity to come, to speak, to accuse. Let’s wish them good luck as they stand up not as victims, but as heros.
--- --- --- --- --- --- ---
Previous coverage of the mess at Bronx Science, and the damage being done by its current administration:
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More Bronx Science
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Do Not Apply
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Bronx Science math teachers: inspiration
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Bronx Science Math Department woes in Daily News
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More about Bronx Science: Special Complaint
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Do Not Apply: The Bronx High School of Science
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Surprise addition to Do Not Apply list
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Do Not Apply – new, surprise entry
Math Regents Update – Sunday night
Math A – gone.
Integrated Trig/Algebra 2 – Not yet arrived
Integrated geometry. Administered Tuesday, June 16. Test with answers is posted at JMAP. Reaction. Cut score discussion. Distribution of topics. Problems. Conversion chart to be posted Thursday.
Integrated algebra. Administered Friday, June 19. Test not yet posted. Multiple choice answers. Free response answers. Conversion chart.
Math B. Will be administered Tuesday, June 23. Conversion chart will be immediately available. And there will be discussion here.
Links
For old regents exams – For all conversion charts – For math teacher discussions – For JMAP
Thanks
To those of you who have come by and asked questions, pointed out mistakes. My answers would have earned me about a 95 without your help!
And special thanks to two teachers who showed up unexpectedly, Kate and Mr. W., who’ve answered some of your questions as well.
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.
June 2009 Integrated Algebra 31 – 39
For the answers to the multiple choice, click here.
For the conversion chart, click here.
Notice: Feel free to try to answer other people’s questions.
Notice: before asking a question, read the previous comments to see if yours has already been answered
Notice: I have not seen the key. If you see I’ve made a mistake, leave a note.
Notice: New York State sets scoring rules in strange ways. I can guess how many points something will cost, but it is only a guess.
Part II
31. 60
Arrange 3 letters out of ANGLE. 
32. 4x(x + 3)(x – 3)
Partial factoring, eg. x(2x + 6)(2x – 6) will probably be worth 1 point.
33. 1/8; or .125
You probably need to show the sample space at 8 (either 10 – 2 or a list of books with 2 crossed off, including 1 English book)
Part III
34. 56
This was the trapezoid in a circle. This question involved far too much real work for 3 points. Use the circumference, 16π, to calculate the diameter, 16 (DA). Get the other base of the trapezoid (BC) to be 3/4s of the diameter, 12. Apply area formula for trapezoid (avg of bases * ht) = 4 * (16 + 12)/2 = 56. If you did SOMETHING right, at least one point. An answer with no work is usually 1 point. If you only had one mistake, it could be 1 or 2, depending on the nature of the error. (The State likes taking 1 point for calculation, 2 points for conceptual errors). Note, the diagram was waaaay not to scale. That trapezoid should take about a quarter of the circle, but in the diagram it takes almost half.
35. $5583.86
The interest problem. $5000. At 3.75%. Over 3 years. To the nearest cent. Slow, steady: Take 3.75% of $5000. Add it to $5000. Take 3.75% of the result. Add that. Repeat. Fast way: 
36. Correctly plotted points. An estimated line of best fit drawn. An equation for the line. Close to y = 5x + 25
You should have a 0 on both axes. The line should be straight, and pass near most points. Slope should be between 3 and 6, around 5 is good. Y-intercept should be in the mid-20s, though into the low 30s might work.
This is not a good question. You should know what a line of best fit is, but I don’t think we should be guessing at them, eyeballing them. Plus, even if you think the best line is a smidge steeper, the State is rewarding you for picking an easy-to-calculate slope. Bad State.
Part IV
37. 39 feet; 63 feet
You probably use tangent to find the distance from the pole to the stake, and then either sine or the pythagorean theorem to find the length of the wire. I’ll bet they take off 2 for messing up either one of these, plus they’ll take 1 if you don’t round, or don’t round correctly. Bravo, by the way, to those of you who saw Pythagoras and used him.
38. Completed table; Completed histogram. Freqs: 4; 5; 4; 8; 7; 2
I’m guessing you lose 2 for making a cumulative freq hist instead, but that’s a guess.
39. (5,-4) and (-1,8)
Correctly graphed line (y int 0,6, drops steeply to the right); Correctly graphed parabola (vertex at 3,-8, opens up, y int 0,1); 2 points of intersection marked, labeled. Many deductions will come from carefully drawn graphs, but no solution labeled.
JD2718 