Calculators in school?

A few years (decades?) ago there was a discussion over whether students should be allowed to use calculators in class. There was no question as to primary students not starting with pencil and paper - or fingers and toes.

We like to look at the back-to-school ads even though neither we nor anyone we shop for is going to school. And of course, I’m always interested in what passes for the slide rule(1) I grew up with. So when this categorization caught my eye, I had to look into it.

Following the page to K-5, I found something that looks like the illustration (right, pink). This has functions I barely recognize and wouldn’t know what to do with a third of them.

If that is appropriate for 2nd graders, I decided to look at what they considered a College calculator. In addition to what you’d expect, 2/3 down the page there was something called “Elementary.” (left, blue)

I also found something just about anyone could use displayed as a “college” calculator: 

Finally, all by itself on a line, the last thing on the list is, approximately, what I might expect as a beginner’s calculator. A 10-pack plus teacher’s guide for $75.















Notes:

I only looked at these two categories. No telling what middle- and high-schoolers are expected to use.

Most of the K-5 calculators were described as “scientific.” College folks are encouraged to move up to “graphing” calculators. No where did I notice the specialty calculators of the 1970s such as “engineering,” “accounting,” or “statistical.” (although in my statistics class in 2002, it was taught on the still-in-production graphing calculator most high-schoolers had used for a decade. I was fumbling to keep up with the freshmen.)

(1)    http://numbersforeveryone.blogspot.com/2017/09/rip-slipstick.html

RIP Slipstick

  (note 1)

Yeah, that's me.

I cried when my last (cheap plastic) circular slide rule dissolved in my pocket about the turn of the century and I couldn't replace it.

A slide rule - and especially, a circular slide rule - is a great device for comparing ratios. I used it when grocery shopping to compare unit pricing between varied sizes. Put the units (ie: ounces) on one scale opposite the price on the other. Then look at the units for the different size and see their comparative price. I could say "that size is the best value" faster than even today with a custom app on my pocket device. People point out that the store prints the unit price right next to the price. But that doesn't take into account special discounts or coupons. The advantage of the circular slide rule for ratios is that when one number goes off the scale you don't have to push the slipstick (the movable piece in the middle of a linear slide rule [the type you see above]) to get to the rest of the scale - it just wraps around.

All a slide rule does is add or subtract two numbers (imagine putting 2 yard sticks end-to-end). Depending on how large and finely calibrated it is, you may only be able to accurately read 2 or 3 digits if all you want to do is add real numbers. Its real power comes when you change the scale to one where the numbers are not equally spaced from 1 to 10. The basic logarithmic scale allows you to multiply (or divide) by adding powers of 10. Other basic scales compute squares and cubes or their roots and trigonometric functions. Specialty slide rules can help calculate anything from an airplane's crosswind correction to astronomical events. In an earlier life my industry regularly used a slide rule to calculate the enlargement or reduction of pictures to fit a printed layout. It was designed to be accessible to people who had barely any facility with numbers.


I still have some good linear slide rules including my father's precision (for the time) rule (boxwood?) from the 1950s. I also have the aluminum Pickett that I won for some obscure "best something student" award at high school graduation and got me through freshman and sophomore chemistry and physics. (search "slide rule image" for some idea of the varieties and detail) (note 2)

Long after calculators were a $3 commodity I was taking a friend to lunch and he asked if I still had a slide rule somewhere in storage. He tutored at a disadvantaged elementary school and wanted to show the kids what it was like in "prehistoric times." I reached in the glove compartment and handed it to him. I carried it to calculate my gas mileage - my first (about age 10) and last (late 1990s) regular use of a slide rule. (note 3)

When I took an advanced physics class (in 1973) that required adding and subtracting 8 decimal places, I bought a digital calculator. It cost $100, was big as a dictionary, and had to be plugged into the wall; but it could do four functions on up to 12 digits. First my classmates laughed at me for carrying that thing to class and moving to a seat by an outlet. Then they started sitting around me and borrowing it during class. (note 4)

Notes:

 (1) Thanks to Bill Amend for my Sunday morning chuckle. All rights reserved to the holder. Click image for complete original.

 (2) I was about to pull out my collection and camera - but the internet has everything. All rights reserved to the holder.

 (3) When I started driving long trips alone with no radio or music player, I would calculate my mileage in my head. Nothing like doing long division to multiple decimal places in your head to build your concentration. (Do they even teach long division nowadays?) Find my spreadsheet at https://3500calories.info/links_blogger/MPG.xls.

 (4) About 2002 I took a statistics class. While the course was taught with the graphing calculator most traditional students had used since high school; I wanted to get my results off a computer because that was the method I'd have to support at work. I brought my computer into class and performed all the exercises twice - on the calculator and on the computer. 

What's a job worth?

The local amusement park is building a new roller coaster. To show their gratitude, the city and county government gave them some $900,000 as a thank-you gift for creating 270 new jobs to go with the attraction.

What's the value of those jobs? Let's go through a thought experiment - no pencils allowed.

Remember these are amusement park jobs. They pay seasonal workers a little over minimum wage.

1) Be generous -- average pay $10/hour. But it's an average of 30 hours a week for 12 weeks. That's $3,600 for the season. (30*10=300*12 -- round number math)

2) Median income in this area is about $48,000 so it takes 13+ jobs to make a full-time equivalent. (3,600*10=36,000, 3*3,600=10,800, 36,000+10,800=46,800)

3) That's closer to 20 new full-time equivalent jobs. (2*13=26*10=260)

Now you have to know some specifics about the employment market in the region. Most of the employment in this county is professional white collar. The amusement park straddles the state line and is a short commute from two adjacent former blue collar counties. In this area typically less than half the blue collar staff comes from this county.

Is it still a good deal to pay $900,000 for effectively 10 new median jobs?

Can your politicians handle these concepts?


. < >This work by Bill Barnes is licensed under a Creative Commons BY-NC-SA 3.0 US License. Permissions beyond the scope of this license may be available at http://zaitech.com/satellite/contacts.htm.
(c) 2008 Bill Barnes - Disclaimer - Home Page - Blogs Home

More on gas prices

Do you drive around for low gas prices? If a station offers a nickel-a-gallon discount for cash, do you pull out your Jacksons? Do you drive the first vehicle in the driveway?

With the price of gas passing $4.00 a gallon, you should rethink all these activities. It's a matter of percentages.

(For these calculations, we will assume the average car gets 25 MPG in a 15 gallon fillup and pays about $4.00 / gallon. As the price goes up, your mileage goes down, or you pump less gas at a stop, the logic gets stronger.)

If you get off your customary route to pay $3.99 rather than $4.05, you're saving 6c per gallon. With that fillup, you've saved $.90. That will buy you less than 1/4 gallon more or about 5.5 miles. That may be more than around the block, but it won't justify going to the next interstate exit and back.

The same numbers apply to savings for cash. Of course, if your credit card gives you a 1% or 3% rebate, not many stations will give that much discount. 3% of $4 is 12c. This assumes you pay off your credit card without interest. If you pay the bank 3 or 4 months' interest at 9% APR (a good rate; some people pay two to three times that), you've more than lost your 3% rebate.

Which car do you drive? If you have one car that gets 22 MPG and another at 27 MPG, should you make an effort to drive the more efficient one? If you have a 10 mile one-way commute, you'll save about $.67 per day. That may not sound like much; but come Friday, it's another beer at happy hour. Obviously a bigger spread means more money. Here we're talking about a 22% difference; 5 MPG is a bigger percentage if you're starting with less but only 13% between 42 and 37 MPG cars.

Download the spreadsheet for your own calculations.

(c) 2004-2008 Bill Barnes w/ public domain components. Free distribution with permanent acknowledgment.
More like this: http://3500a.blogspot.com/

Can the government lower gas prices?

Tax moratorium. Open the Strategic Petroleum Reserve. Encourage new refinery construction. Fast-track domestic drilling permits.

As gas approaches $5 per gallon it seems everyone in and out of politics is pushing their favorite scheme for Washington to push prices down. They're all likely ineffective in the current free-market economy. Short of an explicit cap on retail prices - something that is never seen in this country - any administrative action to reduce wholesale costs will have minimal effect at the retail end.

Beside the policy debate, cutting taxes or releasing federally owned crude (presumably at a price well below market or cost) would have a minimal effect on the price at the pump. Even if the entire value of the stimulus ended up in the consumer's pocket, it would not return us to even 6-months-ago prices. The federal tax is 18c/gallon. Giving away 5% of US consumption from the SPR would deplete the reserve in less than two years and cut prices by only 25c/gallon. Whether either of these discounts makes it to the nozzle is problematical in a free market.

In my opinion, the other two schemes to attempt to influence the market face ethical challenges over economics. They require that current Americans run even more roughshod over the rest of the world and the future than we already are.

Some pundits claim that US refineries are running flat out and couldn’t produce more product if the input were available. Capitalism says anything can be done, if you’re willing to pay the price. Instead advocates want a defacto subsidy to expansion, either monetary or by relaxing pollution and safety requirements for an industry that already has plenty of problems in those areas.

And yes, relaxed regulations could allow more oil to be pumped on US territory. One writer stated that he knew energy companies can work safely and drill the outer continental shelf without any risk of direct environmental damage. I agree, but that is not the point. On the one hand, we fret about human-induced climate change; but on the other laments that we need to produce more oil to reduce the price so we can burn more oil … . If we are serious about passing a livable world on to future generations, we shouldn’t be trying to use a few more gallons today.

Economics should provide an eventual resolution to the question of gas prices – albeit one that may not be to the liking of current complainers. All commodities should reach an equilibrium price based on supply and demand. As prices go up, producers will find or redirect more supply. Also as prices go up, consumers will reduce their demand forcing suppliers to cut the price to justify their infrastructure. Eventually everything will balance out.

If you object to what a seller is doing – whether it’s raising prices or building an ugly store in your neighborhood – the free market response is to stop giving that seller your money. You can force gas prices down by buying less – change your driving habits or change your vehicle to use less gas per mile.

RESOURCES:
SPR
Daily oil demand

Excel Auto-fill and Formatting demo

This spreadsheet has some interesting features on page BadgeLog. Because this spreadsheet uses many Excel features, I offer it as a download.

• The formula in N7 was fun. I create the logon ID from the first letter of the first name and the last name. BUT, I don't create this ID until I've entered the date to verify that I've actually created the account. The other blue column is also automatically filled.

• 4 columns (green) contain drop-downs created with the Data > Validation tool and data on the Lists page.

• I used Conditional Formatting to indicate the columns that are either auto filled or have drop-downs.

• There's a neat macro (which I didn't create from scratch) to automatically fill in the shading. After I delete lines or resort the spreadsheet, the macro clears existing formatting and recreates the shading. This one is hard-coded, but the original prompted for variables for many of the specs.

(c) 2004-2007 corp04@zaitech.com w/ public domain components. Free distribution with permanent acknowledgment.

Ratios

With the advent of HDTV, all the reviewers talk about the new 16:9 screen ratio as opposed to the old - square - 4:3 ratio.

I always thought widescreen TV and widescreen computers were the same thing. Until I was trying to design a PowerPoint(r) presentation to show on a TV. I set the page size to 16x9 and it didn't fill my computer quite right. Then I looked at the actual resolutions.

HDTV is nominally 1920 x 1080 (pixels). My computer monitor is 1440 x 900. I could quickly divide and see that HDTV is 1.78:1 while the computer is 1.6:1. But how do these ratios compare - in integers?

I'll save you the suspense. HDTV is, in fact, 16:9. The computer turned out to be 16:10 - a little squarer so that a presentation to fill the TV will leave a little top and bottom on the computer.

Google Docs and Excel(r) have an advanced* function called =GCD - "Greatest Common Denominator". We all learned about the Least Common Denominator in the 4th grade, but what is GCD? It's the largest integer that will evenly divide both sides of a fraction. If you divide both sides of a fraction by the GCD, you get what I was looking for: a simple integer ratio.

You can download the worksheet+ as a picture or live Google Doc that you can use as your own. Either way, column J contains the formula (without the ' ) to fill in under the raw data.

* GCD may not work in Excel until you load the Add-In. From the Tools menu, select Add-Ins... and check Analysis ToolPak. When you click OK, it may ask for your original Office CD to load the component.

Miles per Gallon

OK, maybe I'm compulsive about keeping trivial records. But with $3+/gal gas, everyone's starting to be interested in how they're doing day-to-day.

This workbook+ contains one simple formula =(F8-F7)/E8 [ (mileage this fillup)-(mileage last fillup)/(gals this fillup) ] in col G to calculate MPG at your last fillup. Since you may not be consistent in how full you get your tank, I also included 2-tank and 3-tank averages to smooth it out.

My Audit column recalculates the cost as the price per gallon times the gallons to catch typos. If it's off by more than a few cents (to allow for the hundredths of a gallon), one of the numbers is wrong. Sometimes I know the audit is going to be invalid if I didn't actually fill up once and a "single tank" represents multiple purchases at different prices (this is common if I know I'm travelling to a low-price area, but need another 2 gallons to get there).

For MPG tracking to be accurate, you have to be faithful. If you regularly buy gas without filling up, you have to combine individual purchases to create a "tank" that you know all the miles were burned on.* And, if you forget to write down the gallons just once, not only is that tank invalid, but so is all your cumulative data. Like I said, I'm compulsive.

I haven't yet figured the simple formula (I can do it with programming) for row 1 to get an accurate average of all the non-0 entries in a column. If I set the average past the current bottom of the worksheet, it counts all the empty rows. As it is now, my "lifetime" is only to where I was last time I wrote the formula.

* If you don't fill up ...
You can only calculate MPG if you know exactly how many gallons you burned for a given number of miles. If you can only afford $5 at a time; one day that $5 may bring you up to 7/8 full and the next you leave the pump just 1/3 full. That means you burned more gas than you bought, but you don't know how much. If you occasionally miss a fill up, just add all the partials to the next time you top off and call it one "tank". If you never fill up ... well, your lifetime average will be close (because being off by 4 gal when you're calculating MPG for 400 gal isn't significant).

(c) 2007 Bill BarnesMore like this: http://3500a.blogspot.com/
+ To use the published workbook:Click the link to open a web picture - not a working spreadsheet - of my workbook. Type the content from the Formulas page into a spreadsheet. The heading "Date" goes in cell B3. You only really need the five formulas on row 7 that start =(F7-F6)/E7. Then you can use your spreadsheet's autofill function to replicate them on the rest of your rows. Be sure not to type the " ' " before the "=".

Even easier; if you have a Google account, you can open a live spreadsheet in Google Docs. From there you can export it for your own use with the formulas intact.