FIT THE WORLD'S PRODUCTION OF GOLD IN YOUR CLASSROOM

Visit this link for rich applications of math:
http://money.howstuffworks.com/question213.htm

The particular article in the link addresses dimensional analysis and fundamental science in relation to math. MOST IMPORTANTLY IT MAY ENGAGE EVEN THE LESS MOTIVATED!

Try it with your prealgebra students as an application of unit conversions, exponents, scientific notation and basic geometry concepts.

Students will need to convert mass (kg) to volume (liters) using the specific gravity of gold, then to cm^3. This will allow them to see how the world's estimated annual production of gold will approximately fill up a cube 14 ft on an edge or, equivalently, a rectangular room 14 ft by 28 ft with 7 ft high ceilings.

By requiring students to research the data and conversion constants, you can integrate the web into the assignment.

A scientific calculator is an appropriate tool here, however, require students to WRITE all steps. It is very easy to lose track of the process when we do a series of 5 or more calculations. The result will appear to be incorrect but the student will be hard pressed to find the error.  It's human nature to press CLEAR and keep pressing more buttons until it works, then forget the exact sequence of keystrokes! 
RECORD EACH STEP ON PAPER WITH APPROPRIATE UNITS. BE A RESEARCHER!

Let me know if you try it and how it works out.

Sent from my Verizon Wireless 4GLTE Phone

GEOM CHALLENGE 2-7-12

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided into 35 quizzes with answers at back. Suitable for SAT I, Math I/II Subject Tests, Math Contests and Daily/Weekly Problems of the Day. Includes multiple choice, cases I/II/III type and constructed response items.
Price is $9.95. Secured pdf will be emailed when purchase is verified. DON'T FORGET TO SEND ME AN EMAIL (dmarain "at gmail dot com") FIRST SO THAT I CAN SEND THE ATTACHMENT!
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DON'T FORGET TO VISIT ME ON TWITTER AT twitter.com/dmarain

TODAY'S TWITTER PROBLEM - A CLASSIC GEOMETRY CHALLENGE
A regular octagon is formed by cutting congruent isosceles right triangles from the corners of
a square of side 1. What is the length of a side of the octagon?

[Ans: ≈ 0.414; also give "exact" answer!]

If interested in purchasing my new Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided into 35 quizzes with answers at back. Suitable for SAT/Math Contest practice or Problems of the Day/Week.

Price is $9.99 and secured pdf will be emailed when purchase is verified. DON'T FORGET TO SEND ME AN EMAIL FIRST SO THAT I CAN SEND THE ATTACHMENT!

"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur SchoDONTpenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Explain the SUPER pattern: 2-9-12-15-21

First, congrats to the NY/NJ Giants on another extraordinary accomplishment!
Kudos to both teams and Eli-te and Tom B in particular.

My opinion, but it drives me nuts when I hear that the Miracle Catch 4 years ago was just luck. It wasn't luck that enabled David Tyree to jump higher than Rodney Harrison. It wasn't luck which enabled him to hold onto the ball despite every attempt by the defender to rip the ball from his hand or his helmet. Not to mention Eli's "refuse to lose" attitude. The throw by Eli and catch by Mario Manningham last night was the result of endless practice, skill, and a will that was stronger than the opposition's. Why was Manningham able to make the HIGH PRESSURE play but Welker was not? I say it was DRILL,SKILL,WILL -- necessary ingredients for success in life!

Alright, you haven't read a blog post from me in eons so I cannot disappoint...
I do hope y'all have been following me on twitter.com/dmarain. I've tweeted numerous challenges for your students. Hope you've enjoyed them...

MATH CHALLENGE GRADES 3-8

LIST THE WAYS A FOOTBALL TEAM CAN SCORE 21 PTS. DO THE SAME FOR 17 PTS.
Repondez s'il vous plait! (supply your own accents!)


By the way, one of my daughter's friends had boxes of 9-0 and 9-3 in either order. She won $75 for the 1st quarter and $150 for quarter 2! My buddy had 0-8 in either order for the final score. If the Giants kick the field goal making it 18-17 and the Patriots kick a field goal, making the final score 20-18, he would have won $2500! He's a big Giants fan but talk about mixed emotions!


"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

A 4-yr old breathes life into MathNotations!

Ok, so I have neglected MathNotations for over a year and have chosen to express my thoughts in 140 character spurts. I've lost my faithful readership and abandoned the Carnivals.

But the living embodiment of "Kids Say The Darndest Things" will always bring me back. The precious gems uttered by my then 2-yr old grandson still garnered more hits than any Math Ed diatribe or challenge problem, so it's only fitting he would bring me back now that he just turned 4.

Here then are 3 recent anecdotes...

1. He's the only 4-yr old in a summer beginning reading class at our local community college, the other students being 5 and 6. The teacher was reviewing letter recognition and sight words. Each child was asked to come to the board and point to a letter in a word, say, the 'T' in CAT. Things went well until she got to my grandson. "Ok, _____, go to the board and point to the 'B' in BIRD." My grandson, who was sitting with his feet up on the desk, replied with "No thank you. It's the one on the left".

2. My daughter noticed my grandson was spending a lot of time at a party with a certain young lady. On the ride home my daughter teasingly asked my grandson if _______ was his "girlfriend". "No", he emphatically replied, "She's not my girlfriend, she's just a friend!"

3. At the pediodontist the other day, my grandson was doing very well and then the hygienist asked my grandson which of three flavors he would like for his teeth cleaning. My grandson replied, "All three!" She explained they don't do that, he had to pick just one and he came back with, "How many teeth are in my mouth!" She relented and used all 3 flavors. Afterwards she asked which was his favorite and he came back with, "I don't know. They all tasted the same."

Again I suggested to my daughter that she get an unlisted phone number and turn off her cell phone when he starts kindergarten!










"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Update 6-6-11

Now that I am a full-time tweeter, I realize that I've lost most of my followers in the blogophere but I will post every now and then.

1) Twitter enables me to publish my "puzzles" 2-3 times daily. That's probably the best domain for brief math challenges. In the end, it's still all about content. If you're on just to promote yourself, people will see through that quickly, but they will come back if you offer something interesting and substantive.

2) Anyone miss the musings of my now 4-yr old grandson? Well,when he was 3, he was in his preschool class hanging out with his 2 buddies. One started to make loud silly boy noises and the teacher reprimanded him. A moment later my grandson did the same. The teacher approached him and asked why he would do that right after his friend was told to stop. He replied without hesitation, "That wasn't me, it was just an echo of ___." This is why I told my daughter to get an unlisted number immediately!

3) Actually his about-to-be 8-yr old brother is unique in his own right. His interests in and knowledge of science, astronomy in particular, astound me. He is already an expert on galaxies and nebulae. What do you think he wanted for his birthday other than a telescope? An authentic lab coat! Of course, we obliged.

4) It would be remiss of me not to mention my 2 granddaughters. Not only beautiful and very smart, they are filled with love and joy. What a blessing!

5)Looking for some controversy here? Miss my provocative comments about the current state of math education in the US? Sorry, I'm a very boring person. All I want is a blend of procedural mastery (practice!) with conceptual understanding. Although there are numerous ways to help ALL students understand, there are established practices and principles of effective math instruction which cannot be ignored. Using multiple representations, linking to prior learning, motivating with real-world examples and guiding with questions are some of these essential components. These will never go out of style.

6) Although I am a strong proponent of a standardized curriculum, I fully recognize that this leads inexorably to teacher eval based on test scores. This politicizing of education and imposing a strict business model on an essentially human endeavor will have far-reaching negative consequences.





"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Math Teachers Are "UNION" People!

The title is a pun but the need for a "more perfect union" is integral to our Constitution! I don't think our Founding Fathers would support any attempt to dissolve our unions. For this reason I advocate the immediate recall and/or impeachment of all governors and Congresspeople who are attacking the fabric of our nation by a concerted and conspiratorial assault on teacher unions.

Remember, if unions were not effective there would not be such a movement to destroy them. It's all about power and dollars...






"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

List the NINE 2-digit PRIMES which...

Here are the last two math challenges I just tweeted for middle schoolers and beyond. You may want to use this as a fifteen minute activity to improve reading, review basic terms and concepts, develop reasoning and writing in math. There was an error on the 2nd question as it originally appeared on Twitter. I then corrected it.

List the nine 2-digit primes which produce prime numbers when their digits are reversed.




List the SIX 3-digit primes which produce primes when their digits are written in ALL possible orders. 137 fails b/c 371 is not prime.

For both questions students should work in teams of 2-4.

For the first question, students should not be allowed to use a calculator!

For the second one, have them experiment with a calculator for a few minutes. If a student thinks they found one, their teammates must verify it! After 3 minutes ask: "Have you noticed that the numbers you're looking for cannot contain certain digits like 2. What digits and why? Discuss it and one member of the team must record the team's findings and provide a written explanation!

After 3-4 more minutes, have them refer to a table of primes online (or print it and hand out a copy to each team). If they don't find it within the 15 min time limit, have them finish it for extra credit for the next day.

Here is one of the numbers: 113. Good luck!


"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

"You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught." --from South Pacific

Odds and Evens Week of 1-31-11

• Tom Friedman writing in the Opinion Pages of 1-30-11 NYT about Singapore politics, economy and education:

... 

If Singapore has one thing to teach America, it is about taking governing seriously, relentlessly asking: What world are we living in and how do we adapt to thrive. "We're like someone living in a hut without any insulation," explained Tan Kong Yam, an economist. "We feel every change in the wind or the temperature and have to adapt. You Americans are still living in a brick house with central heating and don't have to be so responsive." And we have not been.

Singapore probably has the freest market in the world; it doesn't believe in import tariffs, minimum wages or unemployment insurance. But it believes regulators need to make sure markets work properly - because they can't on their own - and it subsidizes homeownership and education to give everyone a foundation to become self-reliant. Singapore copied the German model that strives to put everyone who graduates from high school on a track for higher education, but only about 40 percent go to universities. Others are tracked to polytechnics or vocational institutes, so the vast majority graduate with the skills to get a job, whether it be as a plumber or a scientist.

...

It is a sophisticated mix of radical free-market and nanny state that requires sophisticated policy makers to implement, which is why politics here is not treated as sports or entertainment. Top bureaucrats and cabinet ministers have their pay linked to top private sector wages, so most make well over $1 million a year, and their bonuses are tied to the country's annual G.D.P. growth rate. It means the government can attract high-quality professionals and corruption is low.

America never would or should copy Singapore's less-than-free politics. But Singapore has something to teach us about "attitude" - about taking governing seriously and thinking strategically. We used to do that and must again because our little brick house with central heating is not going to be resistant to the storms much longer. 

MathNotations' Reaction:

• ..."teach us about 'attitude'..."  I'll second that.  As I have often mentioned regarding Singapore'a attitude toward education:  In Singapore and other rapidly developing nations, education is seen as an investment.  In the USA, it is seen as an expense.  Talk about attitude...

• We can no longer afford to excuse the educational performance of our students in math and science in international comparisons with the hackneyed and questionable argument:

We have to educate all the kids, their population is uniform with little diversity. 

                 

Here's my incredibly simplistic and naive approach to "e-quality" education:

STOP the experimental research! Take each underperforming student and extend the school day using retired or current teachers, pay them and make sure that child does not leave until he/she can do their homework on their own and demonstrate understanding. Supplement and enhance individual instruction with the best learning software out there (*adaptive* software is the most exciting for me). 

Any volunteers? 

• Singapore appears to be attracting the best and brightest into politics - our most recent congressional election attracted some stellar individuals and then some others...

• For me it's all about our nation's values. If we don't deem the education and welfare of our youngest citizens to be our highest priority, then where exactly is our future?

Bravo, Tom, for a compelling piece. Much food for thought...

• Have you been keeping up with the many Twitter Math Problems and Challenges for the past 6 months?  I generally don't post answers so you need to tweet a response, send me a Direct message or retweet it for others to see. Follow me at @dmarain.
  
  
• Remember my tribute problem to Martin Gardner? Jan writes, "Has seriously no-one suggested the 120-25 variant? :)" Ah, simplicity! Or is it Occam's Razor (when you have two competing theories that make exactly the same predictions, the simpler one is the better).
  
  
• I recently asked a version of the following on Twitter:
  
  What special qualities separated your best math teacher from everyone else?
  
  On Twitter, I wanted a response consisting of just ONE quality. Here, I'm looking for the top 3-5. Ok, so I open the floor once again to this oft-repeated query. To focus on math teaching, I would ask you to reference only those unique skills/talents which are inherent to mathematics. I may not get any response to this, but I do believe this list will be of some use for someone.  It would be particularly useful to hear from students and parents as well as from professional educators
  
  
• This little challenge for your Algebra I students is a bit long for Twitter. Let me know the outcome if you use it in class:
  
  Start value = googol (1 followed by 100 zeros)
  Multiply Start value by 5.
  Add 5 to the result.
  Square the result.
  Divide result by 1 more than googol.
  Divide result by 5.
  Divide result by 5 again.
  Subtract googol from result.
  Final result = _______?
  
  This is not meant to be a challenge for your mathletes!

"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

 "You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught." --from South Pacific