Math Happens

Without using a calculator, order these numbers from largest to smallest:
√7, √3 + 1, (2√10)/3

Welcome Back all Paw Paw High School Students.  Begin another engaging year aboard the mathematics train of knowledge.  As engineer, youchart the course on the map of your own success.  Good Luck and Good Driving

During brunch this Sunday after church, we were having cinnamon rolls, generic brand, out of a tube baked to perfection.  There was one left, and two of the children decided to split it in half.  Of course, my children, instead of slicing it in half about the diameter, started to unwind the cinnamon roll from the outside toward its center.   The roll began with a 3in. diameter at its widest point and the strand being unwound is about ¼ inch in width.  Assuming the height of the strand (and entire roll) is constant, how far does the strand need to be unwound (and then cut) such that each child will have half the roll. Mmmmmmm.

P.s.  This is the last entry for the summer math problems.  Be sure to look for posts pertaining to the school year.

I sold my last bit of soybeans this week.  I had to estimate the number of bushels remaining when signing a contract and establishing a price.  My bins are rectangular prisms. Four bins measure 7 ft. by 12 ft. with 6ft. height of beans. Two bins measure 7 ft. by 10 ft. with 12ft. height of beans. One measures 7 ft. by 14 ft. with 10 ft. height of beans and the last measures 7ft. by 8 ft. with an 8 ft. height of beans.  Approximately, how many bushels did I have to contract?

There is a national debate going on about the debt ceiling limit and what to do about it.  In  2001 and 2008, the government sent each tax giving family a check to spend and thus hopefully stimulate the economy. The total received from both checks ranged from $600 to $2400.  What if we sent the government money in a similar fashion?  The current debt ceiling is $14.3 trillion.  How much would every man, women, and child have to give to pay off 50% of the debt ? Assuming a family of 4, what % of what a family would have to pay did they receive in stimulus checks?

The movie Captain America debuts on Friday.  This week’s problem is inspired by a former student who contacted me on how he used math to build a replica of the Capt. America shield.  The only dimension on the internet is that it is 30” in diameter.   The shield has an inner blue circle with a centered 5-point star.  Then there are three (R,W,R) concentric circles of equal width(click link on right for image).   To create his shield, he estimated the width of the concentric circles to be 3”.  The main difficulty is creating the inner star with the correct dimensions and placed properly.  Show how you would use math to create a perfect inner star.   (Hint: Trigonometry may be needed).

Our church is using a new liturgy setting this summer.  One of the canticles is in 2:2 time.  As you may know in 4:4 time each measure has 4 beats with a quarter note worth one beat; similarly, in 6:8 time, each measure has 6 beats with a quarter note worth two beats.

1. How many beats is a quarter note in 2:2 time?
2. Therefore, a quarter note in 2:2 time is analogous to what kind of note in 2:4 time?
3. What fraction of a beat is each of the following notes in 2:2 time:  dotted quarter note, half note, whole note, eighth note, and ONE note in a triplet of quarter notes?

Thank goodness I could do the math quickly and knew how to keep time in singing the canticle.

With gas over $3.50/gallon and my wife driving about 360 miles a week during the school year in a van averaging only 19 miles to the gallon, we decided to purchase a Ford Fiesta that averages 35 miles to the gallon.  Here is some of the information that went into that decision.

1. Approximately what will be my monthly savings on fuel at a gas price of $3.50?  Assume 4 weeks per month.
2. For every $.25 increase in gas prices, how much more will I save on a monthly basis?
3. Create an equation in slope intercept form to represent the amount of money saved in a month per penny increase/decrease,x, from $3.50. (Hint: for the price of $3.50, x = 0; why?)
4. Using this equation, what are my monthly savings if gas goes to $4.85 per gallon?
5. If I am spending an additional $55 a month on insurance, at what gas price, if any, will the cost of insurance negate my savings?

My family and I recently went biking at Starved Rock State Park.  We took a side trail to a picnic grove, hoping to find a nice spot to each lunch.  From the trail entrance, we (roughly) traveled 540 yards north, then 200 yards west, and we then biked another 810 yards north and 650 yards west, finally arriving at the picnic grove.  Most of the kids thought the bike ride was too long.  So if we had been able to create a straight trail from the trail entrance directly to the picnic grove, how many yards could we have cut out from our biking trip?

Chris Matthews, host of NBC hardball, while on the Bill Maher show made the following observation about republican presidential hopeful Micelle Bachman:  ” After the Republican debate, Michelle Bachman’s  recognition by voters may not change exponentially but should improve arithmetically.”  Using mathematical analysis, write the interpretation of his statement and find a substitute math word for “exponentially” that better correlates to “arithmetically” OR a substitute math word for “arithmetically” that better correlates to “exponentially”.