Monday, October 31, 2011

Two Puzzles for Seniors: 2004 #09 and 33

Round and Round we go!
Difficulty: Can they complete the square?
Difficulty: Medium.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 09, answer 33.

Sunday, October 30, 2011

Very Difficult Treasure Hunt

A while back, I was floating around the web and found the following treasure hunt. I saved the images, and put a description and source into a Word document which has disappeared. If anyone can help, I'd appreciate it.

Who is responsible for this nasty, wonderful, complex, multi-layered, multi-disciplinary, I-Can't-Wait-To-Edit-It-and-Give-It-To-My-Own-Students puzzle?


Yes, it will take you a while.








Two Puzzles for Seniors: 2004 #08 and 34

We're mixing it up today.
Difficulty: Algebra rules.
Difficulty: Boring ... but that's solely my personal feelings.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 08, answer 34.

Saturday, October 29, 2011

Two Puzzles for Seniors: 2004 #07 and 35

Wordiness.
Difficulty: Too simple? Maybe.

Difficulty: Interesting. Don't count ties.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 07, answer 35.

Friday, October 28, 2011

Two Puzzles for Seniors: 2004 #06 and 36

How well do yours remember their geometry rules?
Difficulty: Similar triangles.  Simple.
Difficulty: It's the obligatory infinite series, but what's the ratio? That's what will trip them up.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 06, answer 36.

Thursday, October 27, 2011

Two Puzzles for Seniors: 2004 #05 and 37

Time for circles and triangles.
Difficulty: "I never thought it would be THAT."
Difficulty: You can hear it now ... "Why did they just ask for the sum of the areas of the triangles?"

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 05, answer 37.

Wednesday, October 26, 2011

#AnyQs -- Roof tiles

Two Puzzles for Seniors: 2004 #04 and 38

How well do yours remember exponents?
Difficulty: Simple, maybe.
Difficulty: Number theory. Tough little bastard until the AHA! moment.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 04, answer 38.

Tuesday, October 25, 2011

Two Puzzles for Seniors: 2004 #03 and 39

Every year, they manage to work the date into question.  Here's this year's:
Difficulty: Pretty Simple.

Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 03, answer 39.

Monday, October 24, 2011

Samples must be numerically significant or else conclusions are worthless.


Parents Against Tired Truckers is losing it's religion over the results of a new study on an experiment up here in Vermont. Just as in education, small sample sizes and incomplete data are being misunderstood and misrepresented to further a viewpoint that may do more harm than good. PATT has it's heart in the right place, but it's brains are sorely lacking.

Vermont asked the Feds to study whether allowing 100,000 lb rigs on major highways would be more dangerous than having them travel the back roads.

The study results came out. PATT shouted

The Trucking Industry Is Wrong on the Maine and Vermont 100,000 lb. Truck Pilot Program – DEAD Wrong 

Wow. That must be some study. "Dead wrong" isn't mincing words.

" .. the Truck Safety Coalition (TSC) released startling information revealed in response to a Freedom of Information Act (FOIA) request sent to the Vermont Agency of Transportation (VTrans)."
Impressive. "Startling", you say? Took a FOIA request, huh? I must read further. "Catastrohic results" "People needlessly died." Damn.
The number is SO BIG.
Documents show that during the 100,000 lb. truck pilot project in 2010, Vermont’s commercial motor vehicle fatal crash rate tripled from .49 fatal crashes per 100 million miles traveled in 2009 to 1.44 fatal crashes (“Vermont Truck Interstate Pilot Study- Report to Congress (State of Vermont Version for Review) – Summary Report (Draft)” prepared for FHWA by Cambridge Systematics, Inc, hereinafter “Vermont Report”).
What does that mean Regis? The Death rate tripled.  Holy Batman, mackerel.  They're quoting Government documents and it sounds so official.

Well, actually, it doesn't mean much at all. You see, Vermont had one death involving trucks on its roads in 2009 and three in 2010. Yeah, the death rate "tripled" but you need to have a bigger sample size before you can claim that trucks are making things more dangerous.

You also need to look at the reality of those crashes. In the one crash, two trucks and a car were involved in an accident that was blamed on icy roads and bad conditions. One of the truck drivers and the car's driver were killed. In the other accident, the car (probably drunk) crossed the 50-foot median and hit the truck head-on. Again, hardly the fault of the truck driver.

As in education, there's always some fool trumpeting results based on small sample sizes and assuming the study will scale up. Remember when Bill Gates spent nearly a billion dollars to create the Small Schools Initiative? The smaller schools that did better than the large public schools were showcased until the next year when the same school would do worse, at which point the deformers would shout about some other school which HAD done well that year. Variation of the small groups, not the inevitable superiority of the charter school, small-school, voucher school, Catholic School, whatever.

To give you another example, consider Daisuke Matsusaka (RedSox). He had four starts. Two were terrible and then two were decent. Can we say that trend is positive? Yes, but I'm not giving him a contract based on that.

Still another comes from here:
Last week I tossed a coin a hundred times. 49 heads. Then I changed into a red t-shirt and tossed the same coin another hundred times. 51 heads. From this, I conclude that wearing a red shirt gives a 4.1% increase in conversion in throwing heads.

Pretty foolish.  Besides, everyone knows that wearing a red shirt is tantamount to a death sentence anyway, so I'm not sure what can be made from this "study" either.

Two Puzzles for Seniors: 2004 #02 and 40

A nice fraction and a seemingly simply area question. Nice!
Difficulty: Simple.
Difficulty: Easy after the AHA! moments. 

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 02, answer 40.

Sunday, October 23, 2011

Two Puzzles for Seniors: 2004 #01 and 41

Start of a new series. A nice fraction and a holy craptastic function thing. Wow!
Difficulty: Simple.
Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 01, answer 41.

Friday, October 21, 2011

Two Puzzles for Seniors: 2002 #20, 21, and 22

Greatest Integer Function and Radicals in one problem? Be still my beating heart. A problem where intuition works best? Awesome. Similar triangles masquerading as a tough problem. Wow!
Difficulty: moderately difficult for students who don't see how the GIF is applied here. Of course, the resulting radicals are complicated, too.
Difficulty: Simple answer is the correct one.  Proving it is an interesting discussion.
Difficulty: Again, pretty simple if they're paying attention.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 20, answer 21 and answer 22.

Thursday, October 20, 2011

Two Puzzles for Seniors: 2002 #19 and 23

Functions and Prime Factors! Yay! Radicals! Yay! What's the mathematical idea here?
Difficulty: Medium. The trick for me was prime factors ... and remembering the 1.
Difficulty: Medium. Just go for it.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 19 and answer 23.

Wednesday, October 19, 2011

Two Puzzles for Seniors: 2002 #18 and 24

Permutations with a twist. Let's go do the twist. And ARCLength!

 Difficulty: medium.

Difficulty: Are they paying attention?  It's a lead-pipe cinch that most will get the degrees of arc and forget to RTFQ.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 18 and answer 24.

Tuesday, October 18, 2011

Any Questions? License Plates

Yup. Nearly 100 years old.

Two Puzzles for Seniors: 2002 #17 and 25

Using every possible rule of Logarithms and a bit of combinatorial thinking:
Difficulty: Pretty Tough for students.
Difficulty: Much simpler than it appears. Brute force solution works best.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 17 and answer 25.

Monday, October 17, 2011

Any Questions?

Four one-gallon milk jugs in the red crate.
Nine half-gallon milk jugs in the gray crate.

Two Puzzles for Seniors: 2002 #16 and 26

Trig rules. Did'ya memorize the half-angle formulae or will you need to derive them?
Difficulty: Easy if memorized. Difficult, if not..
Difficulty: Pretty easy, if you draw the diagram correctly from the description.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 16 and answer 26.

Sunday, October 16, 2011

California - Tech vs Fine Arts

Broke in a broken system.
Joanne shares about California's new law.
"Music and art teachers are complaining about a new California law that expands graduation requirements: Students can take one career or technical education course in place of art, music or a foreign language, reports the San Jose Mercury News. Arts and foreign-language courses are twice as likely as vocational classes to be certified as college-prep courses, so students who choose career tech could be ineligible to go from high school directly to the University of California and California State University systems."
So here's my question ... if VoTech is what the kid wants to study, why are we so hell-bent on getting him into a college degree he'll waste his time on?

Take that woman in the picture.  She went $100,000 in debt to finance a women's studies and religious studies major at NYU and now is working as a photographer's assistant for $20 per hour. (It's obviously CitiBank's fault for giving her the loan. That's why they posed her there.)

Why?  Why should she incur that debt for such a meaningless degree?  Because she's stupid, self-centered and gullible -- she willingly took out loans without considering how she'd pay them back.

California provides a free college education to its residents (well, except for fees, but I digress.)  Why should California provide a free college education for someone like her who serves no practical benefit to the society which pays that bill?

There is nothing wrong with a life and a career without a degree. Millions of people accomplish it all the time.  They become fine upstanding members of the community and college grads look down their noses at them at their peril.

We must stop this "college for all" one-track mindset.
Some urban districts, such as Oakland Unified, San Jose Unified and East Side Union in San Jose, use UC’s college-prep curriculum as their graduation requirement.
Which is ridiculous.

Public schools should not be pretending that all kids belong in college nor should it require that all kids be ready to make that step before we're willing to let them go out and be successful.

Two Puzzles for Seniors: 2002 #15 and 27

Weird expressions and the Sum of an Infinite Series ... yum.
Difficulty: moderately difficult.  Students have trouble if you ask for the value of an expression rather than for a value of x. How does that second expression relate to the first?
Difficulty: Sum of a series. But what's the ratio?

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 15 and answer 27.

Saturday, October 15, 2011

Circle of Failure

The other day I was in a 504/IEP meeting and a kid was being considered for alternative programs.  The tech center guy was sitting across the table and was discussing the kid's options.

"Well, the Hospitality Program would be a good fit."
"She doesn't want to put in any effort. What would be her options after that?"
"Well, she could work with the elementary school kids.  She really likes kids."


What I wanted to say was "This girl has failed at every possible program we can think of. She is lazy, and spoiled, and even her mother can't bribe her to do well.  She hates math and barely tolerates English and Social Studies. She couldn't care less about academics of any kind.  ... Why would you put her with a bunch of impressionable elementary kids?  How can that possibly work out well?"

Fortunately, I didn't have to say that, but at some point you need to put the majority's needs ahead of the reclamation project.

Two Puzzles for Seniors: 2002 #14 and 28

Mixture problems don't seem to show up as often nowadays as they used to. I think we've changed the algebra curriculum to pave way for the 7th and 8th graders ... I'm thinking that these questions were deemed irrelevant or too difficult.
Difficulty: Intuition doesn't help here. Only algebra..
Difficulty:Fairly difficult. Where do I start?

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 14 and answer 28.