What's wrong with these special-price offers?

I got a subscription renewal letter in the mail Saturday, and it seemed appropriate to mention it in this what can I do with my elementary school math? blog.

Here are the prices for a newspaper purchased at a newstand:

• 7 days a week for $8.00 ($1.14 per issue)
• 4 days a week for $5.00 ($1.25 per issue)
• 1 day a week for $2.00 ($2.00 per issue)

Here are the initial-term special prices for a newspaper subscription delivered to my home for 13 weeks:

• 7 days a week for $3.65 ($.52 per issue) 54% savings vs newstand
  
• 4 days a week for $2.50 ($.625 per issue) 50% savings vs newstand
  
• 1 day a week for $2.43 ($2.43 per issue) 21.5% penalty vs newstand

A weekly subscription costs less than half as much if delivered to the house, while a single Sunday paper costs $.43 cents more if delivered to my house than to the newstand! 

And here are the terms for an unlimited-term subscription initiated on the paper's website:

• 7 days a week x 4 weeks for $13.89 ($.50 per issue) 4% savings vs mail offer
• 4 days a week x 4 weeks for $10.00 ($.625 per issue) Same as mail offer
• 3 days a week for 4 weeks for $9.00 ($.75 per issue) A completely new deal
• 1 day a week for 4 weeks for $8.97 ($2.24 per issue) 8% savings vs mail offer

Presumably these are regular prices? Or is newstand pricing full price? Who can say?

In the fine print at the bottom of my mail-order offer, I learn these facts:

• the offer will continue past the initial term at the published full-price rate
• prices include sales tax
• the initial term is 13 weeks
• the subscription offer price applies to the first 6 months (26 weeks)

Do you see a problem here?

1. The initial term is 13 weeks.
2. The introductory rate lasts for 26 weeks.
3. The full price applies after the initial term is over.

I have two words for this. Math Class. Someone should have been paying attention in Math Class.

Which term is it? Do I get 13 or 26 weeks? Which price is best? Regular, mail-in-offer, or something else? How could I possibly be an informed buyer with inaccurate, incomplete or misleading offers? What's special about the special introductory price offered in the mailing?

Nothing. It's cheaper to sign up on the Internet.  But I do see one more option.

I can get the eEdition, a service they refer to as A Life-Like Newspaper and an exact replica of the newspaper (presumably soy ink would still stain my hands and elbows?).

The replica is offered either on the Internet or via an Apple App for only $1.98 per week for 7 days-a-week delivery. That works out to $.28 per issue.

The last price I paid for daily delivery (before ending my 30 years of subscribing) was $55 for 6 months, or $110 a year. My average price paid was $.30 per issue.

I ended my subscription because I am an editor. I started working for newspapers in 1967. I can't tolerate the decline in editorial standards - or rather, I can no longer bear to pay for products full of grammatical errors.

As evidence, here is some content cut and pasted from the local newspaper's eEdition page:

• When you open a new issue of the eEdition each day the paper will download itself on to your device in the backround. This will allow you to read at anytime and anywhere you wish
• On the right side of the screen you will notice 6 icons, here is what they do: 
• Help (Question Mark Icon) - This will give you instructions on finger tools for the Ipad screen
• $ (Dollar Icon) - This will take you back to the Newsmemory App. To get back to the paper from here simply click Done in the upper left hand corner.

Note: Please submit Newspaper Delivery, Online Subscriber Services Access, eEdition support and all other Newspaper Account requests via the Electronic Forms Page by clicking on the contact web page link.

Grand Complication Math, Part V

This is the final installment of my Grand Complication Math series, where we have been looking at complicated problems that are solved by creatively applying elementary math in a variety of ways. This is not Rocket Science.

Each day I have given you a photo of a Grand Complication watch - a mechanical device with many features all fitted into one case. Today I am offering a Patek Philippe watch said to be the most complex in the world:

FEATURES
A unique double-dialed, astronomical and astrological gold pocket watch, with the ability to indicate:

• sidereal time
• second time zone
• time of sunrise and sunset in Geneva
• equation of time
• perpetual calendar
• century leap year correction
• century, decade and year indication
• four-year leap year indication
• season, equinox, solstice and Zodiac indication
• star chart
• phases and age of the moon
• date of Easter indication
• split-seconds chronograph with hour and minute indicators
• Westminster chime on four gongs
• “Grande and Petite Sonnerie” chimes
• alarm
• winding indicators for the time-keeping and striking mainsprings
• three-way setting indicator
• winding crown position indicator
• thermometer with scale in ℃
• tourbillon regulator

Now let's use some of our math abilities to describe this Caliber 89 Patek watch [click on the images to enlarge them]:

DIMENSIONS

• Total weight 1100 g (2.42 lbs)
• Case weight 500 g (1.1 lbs) of 18k gold
• Movement weight 600 g (1.32 lbs) of nickel silver
• Movement diameter 71 mm
• Movement thickness 28 mm
• Case diameter 88 mm 
• Case thickness 36.5 mm without crystals
• Case thickness 41 mm with crystals

 COMPONENTS

• Complications 33
• Jeweled bearings 126  
• Screws 332
• Gear wheels 184
• Springs 68
• External knobs, slides and levers 12
• Domed sapphire crystals 2

DIALS

• Dials of silver-plated gold 2
• Indicating gold hands 7
• indicating blued steel hands 16
• Indicating windows 6
• Applied gold numerals 11
• Colors of ink on dial 4

 EXTERNAL DETAILS

• Time to design and construct  - 9 years
• Production run - this is #1 of 4
• Ownership - the watch is in the hands of its 3rd owner since 1989
• Auction sale price in Nov 2009 - 5,120,000 Swiss franc 

Grand Complication Math, Part IV

This week I've been posting about Grand Complication Math problems - complex problems solved with lots of creatively-applied chunks of regular math.

I created this term based on Grand Complication Watches, which combine multiple functions in one small mechanism that you can wear on your wrist. Here's an Ulysse Nardin watch called the Ghengis Khan, with Westminster Chimes, minute repeater, tourbillon, and automatons (animated figures who fight when the chimes are activated).

What is our Grand Complication Problem today? Balancing a checking account.

That doesn't seem so hard, does it? Simple arithmetic. You subtract the outgoing checks from your balance, add the deposits as they occur, and voilá, it's done.

Right? Wrong. Those were the good old days.

Nowadays, if you use an electronic bill-paying service (essentially electronic personal checks):

• You might have some bills set up to be paid automatically when they come due. You can set up these payments (standing orders) for your house loan, credit card, mobile phone bill, utility bill and so on.
• Don't forget that your newspaper, magazine subscriptions, airline credit card, Amazon Prime, eBay or Skype bill might at any time be taking money from (direct debit) your account for past or future services.

NOTE: Standing orders are payments sent out by the payer (you) while direct debits are pulled from your account by the payee (them).

• You probably have Direct Deposits for paychecks, and automatic transfers to/from other bank accounts. 
• Don't forget any monthly fees your bank might be charging you on a regular basis, and any one-time fees for bouncing a check, using overdraft protection, wiring funds or using ATM machines.
• Remember transfers to/from Paypal or other outside bill payment services. 
• Remember charges for downloading music or Apps from the iTunes store, or renting movies on-demand.

These are all intangible, invisible, electronic services. You can also use a debit card at an ATM machine, a Point of Sale (POS) terminal, gas pump, cash register, etc. You can load money onto a cash card for another person to use.

• You might experience more exotic debits and credits, such as wire transfers (essentially electronic cashier's checks). These bank-to-bank exchanges are identified by routing codes (Fedwire, BIC, IBAN, SWIFT, etc) and can take some time to process. They invariably involve fees applied on each end and/or in the middle.

NOTE: Wire transfers result in unpredictable amounts arriving in your account. You ask a friend to wire $1000. She sends $1000 plus pays a wire fee of $25. You get $982.17 due to handling fees applied by banks along the way, then are charged $10 to receive the money! Your deposit is $972.17, not $1000. Her debit is $1025, not $1000. The banks get $52.83.

• You may run into Regulation D, which limits you to 6 electronic transfers a month from savings or Money Market accounts (pre-authorized, automatic, or bill-pay transfers, including ACH; overdraft protection; transfers to other accounts or payable to a third party by messenger, telephone, fax, or home banking). Requests arriving after the limit is reached will not be allowed and will incur penalties. The "counting" occurs when your request is received, not when you make it, so some transfers may surprise you by falling into the wrong month. You can avoid limits if you bank in person, mail your  request or use an ATM but ATMs are not real time transfers, and may take 2 days to process.

Is that enough? Have I finished my list? No.

• Beginning in July 2011, banks will be able to pay interest on checking accounts (not yet allowed in the USA) so we might have some more complications ahead of us.

Have I convinced you yet that balancing a checking account is a Grand Complication Problem?

Many people just continually check their balances to avoid overdrafts, and never verify all the transactions.

Grand Complications, Part III

We are half-way through a Grand Complication Math problem - a situation that uses relatively simple math but involves many different calculations. I made up this term in recognition of the Grand Complication watches that some of my friends collect.

 A Vacheron Constantin Grand Complication

Yesterday we started to solve the Grand Complication Math problems related to moving. We calculated the volume of household goods, came up with a total, then selected a rental truck with a greater capacity than our volume of goods.

One additional factor in moving is related to using up all the cubic space in the truck. Unless you have lots of pillows and things you can toss up above, or you are an expert packer, it's not always possible to stack items. Therefore, much cubic volume in the truck is wasted.

We should also confirm we don't have items too long, or too wide or too high for the truck. That's not likely unless we are loading a playground set or some other strange items.

Now we just have to be sure we don't put too much weight in the truck.

NOTE: I went with a friend to collect soft drinks donated for a charity event. The forklift driver looked dubious when we showed up in a Ford F100 pickup. We thought the pallets of sodas would fit. He lifted the first pallet into the truck, and lowered the forks. The front wheels of our truck came up off the ground! Oops. The truck was rated to carry 1200 pounds of cargo - and we had tried to carry twice that! (120 cases/pallet x 20 lbs/case = 2400)

How do we calculate the weight of furniture? Luckily we don't have to weigh things as we are loading. We can use a rule of thumb developed by professional movers. They estimate density at 6 or 7 pounds per cubic foot for household goods. If you have lots of books, your load could weigh more. If you have lots of pillows, you're going to have a light load.

To finish up with our Grand Complication Math problem, let's estimate that the Romeros have 600 cubic feet of household goods. Their truckload will weigh about 4200 lbs.

The 14-foot moving truck from U-Haul holds 700 cubic feet and can carry 6000 lbs. That should be large enough to carry the Romero family's things.

Have my friends overloaded their Citroen station wagon with camping equipment?

PS Imagine that Mrs Romero is an elementary math teacher and she has a 35-student classroom set of Excel Math Lesson Sheets to put in the truck. How much will they weigh? Are they more or less dense than household goods?

Here is the answer:

• Each curriculum set weighs 90 lbs
• The set is split between 3 boxes
• Each box is 14 x 9 x 9 inches or 1134 cubic inches
• A cubic foot is 12 x 12 x 12 inches or 1728 cubic inches
• Each box is 1134 ÷ 1728 = .66 or 2/3 of a cubic foot
• The curriculum weighs 30 lbs per 2/3 cubic foot or 45 lbs per cubic foot
• That's 7 times as heavy as household goods!

Go here to see our pallets of books

Grand Complications, Part II

This blog talks about using elementary math. Yesterday I coined the term Grand Complication Math (which is often tediously called higher-order thinking skills).

I use this term because I am a watch collector, and we call a watch with multiple complex functions a Grand Complication. Here's one from Jaeger-LeCoultre. It's called the Hybris Mechanica Grande Sonnerie, and it makes music as well as containing a perpetual calendar and many other functions.

In our Excel Math curriculum, we help kids prepare for adult life by giving them opportunities to solve grand complex problems. Here's an example that will be familiar to anyone who's had to move house. It comes from our Fifth Grade curriculum.

The Romero family is moving. The children, Julio and Marisa, threw away lots of stuff, but they have plenty left to move. Mr. Romero asked Julio to look at all the furniture and decide what geometric shape each piece resembled, so he could calculate the size of the moving truck they would need to rent. Here are some of the pieces.

The drawing above shows how the geometric shapes could be used to estimate the size of the load. The table below shows the answers to the first question asked in this Grand Complication problem:

 

Having accomplished the first task, Julio then had to compare the size of their load to the capacity of the trucks for rent. Since the price of the truck is based on its capacity, plus the difficulty of maneuvering a large vehicle, Mr. Romero didn't want to get one too large.

However, as anyone of us can attest who has rented too small a truck, there's also a price to be paid for unloading it (when it's proven to be inadequate) and moving everything to a larger truck. Or making two trips.

Here are the truck dimensions. We multiply the length x width x height of the truck body to get total volume.

Our 5th grade students generally say that Mr. Romero could rent the smallest truck. But they haven't accounted for all the other items in a house! Here's a list of items I found on moving sites:

• BOOK CARTON = 1.5 CU FT
• LINEN CARTON = 3.0 CU FT
• LARGE CARTON = 4.5 CU FT
• EX.LARGE CARTON = 6.0 CU FT
• CLOTHING WARDROBE = 10-20 CU FT
• DISH PACK = 5.2 CU FT
• PICTURE CARTON = 3-5 CU FT

NOTE: Don't forget to subtract about 60 cu ft to allow for  the roll-up door!

So far this isn't rocket science.

1. Inventory the furniture, calculate the volume of each piece, get the sum of all the volumes and set aside. 
2. Inventory the trucks, calculate all the volumes, and compare those volumes to the sum you already have. 
3. Choose a truck.

What next?

As any truck driver knows, trucks have capacity limits for WEIGHT as well as CUBE (cubic volume). A truck full of feathers is always within limits, but a truck full of math books is not. The current federal limit is 80,000 lbs for an 18-wheeler tractor-trailer. Smaller trucks have lower limits. Our Excel Math delivery truck cannot be filled to the brim, or it would be squashed flat to the ground by the weight of our curriculum.

How do you calculate the weight load of the truck without having to fill it up, go to a scale, weigh the truck, and then off-load any excess?

Come back tomorrow for Part III of Grand Complication Math.

Grand Complications, Part I

In the world of mechanical watches, there's a term called Grand Complication. It means that the watch performs several difficult functions, such as chiming the time of day, showing the phase of the moon, and serving as a stopwatch. It has to be able to do all these things at once, proving that its maker was highly skilled in design and fabrication of tiny mechanisms.

Photo from SJX of the PuristS

Elementary mathematics (as taught in our Excel Math curriculum) may sometimes lead you into grand complication calculations. (the more common description is higher-order thinking skills). This kind of problem-solving requires us to analyze the situation, learn some new facts that we've never known before, and combine multiple techniques or skills.

Here's an example:

I'm having a pint of bitter in the UK. The glass seems larger than a pint glass in the USA. The price seems reasonable, but I'm not sure how it translate to the cost of a pint back home. How can I compare them? I want to know the equivalent cost per unit of beverage.

A fair amount of time elapsed before I solved this grandly-complicated issue. Here are the calculations:

UNITS OF VOLUME
A pint glass in the UK  and a pint glass in the USA - are they the same volume? Research tells me that a pint glass is:

• 20 fluid ounces (570 mL) in the UK [ a UK ounce = 28.41 ml ]
• 16 fluid ounces (473 mL) in the USA [ a US ounce =  29.57 ml ]

No, the glasses do not contain the same volume of liquid. The volume of the pints are different and the volume of the ounces are different. The best way to find an equivalent price is to compare equivalent volumes. Let's use a liter. We need a conversion factor we'll call V, so we can change each of the "pints" to a liter.

• How many UK pints to a liter?  1000 ÷ 570 ml = V so V = 1.75
• How many US pints to a liter?  1000 ÷ 473 ml = V so V = 2.11

CURRENCY
A pint glass cost £2.50 in the UK. How much is that in US dollars?

• the exchange rate today is 1.67 US dollars to 1 pound sterling
• therefore 1.67 x  £2.50 = $4.17 US dollars for a UK pint

A US pint glass of bitters in my local restaurant is $5.00 US

COST PER UNIT
 How much is the price, in US dollars, per liter of bitters?

•  UK $4.17 x 1.75 = $7.30
•  US $5.00 x 2.11 = $10.55

CONCLUSIONS
It's cheaper in England. This is a very complicated problem to solve, but only simple math computation skills were needed - I used multiplication, division, ratios, volume, price per unit and foreign exchange.

This is indeed a Grand Complication Math Problem.

In doing this research I noticed that my local place proudly offers bitters in a 20 oz. glass.

To which I reply, US or UK ounces?