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.
Monday, October 31, 2011
Sunday, October 30, 2011
Very Difficult Treasure Hunt
Labels:
Puzzles
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.
Yes, it will take you a while.
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
Labels:
UVM-Basic Algebra,
UVM-Combinations
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.
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
Labels:
UVM-Combinations,
UVM-Geometry
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.
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
Labels:
UVM-Geometry,
UVM-Series
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.
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
Labels:
UVM-Geometry
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.
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
Two Puzzles for Seniors: 2004 #04 and 38
Labels:
Puzzles,
UVM-Exponents,
UVM-Number Theory
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.
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
Labels:
UVM-Fractions,
UVM-Geometry
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.
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.
Labels:
Data,
Statistics
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.
What does that mean Regis? The Death rate tripled. Holy Batman, mackerel. They're quoting Government documents and it sounds so official.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”).
The number is SO BIG.
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.
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
Labels:
UVM-Fractions,
UVM-Geometry
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.
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
Labels:
UVM-Fractions,
UVM-Functions
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.
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
Labels:
UVM-Functions,
UVM-Geometry,
UVM-Pre-Calculus
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.
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
Labels:
UVM-Algebra,
UVM-Functions,
UVM-Radicals
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.
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
Labels:
UVM-Combinations,
UVM-Geometry
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.
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
Two Puzzles for Seniors: 2002 #17 and 25
Labels:
UVM-Combinations,
UVM-Logarithms
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.
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
Two Puzzles for Seniors: 2002 #16 and 26
Labels:
UVM-Geometry,
UVM-Trigonometry
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.
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
Labels:
9 Kinds of Stupid,
College Prep,
Law
![]() |
| Broke in a broken system. |
"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
Labels:
UVM-Algebra,
UVM-Geometry
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.
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
Labels:
I Don't DO English,
I Don't DO Math,
Just a rant
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.
"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
Labels:
UVM-Algebra
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.
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.
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