Additional Math Pages & Resources

Monday, February 28, 2011

Let's SEE what's on the label

I've done nearly 400 blog postings in the last 2 years, demonstrating how elementary school math can be used in real life. We've examined several kinds of labels and what they communicate. For example, Fuel Economy and Food labels. Today we will look at the kind of numbers used on labels you might find on windows and skylights.

Here's a typical Energy-Star label. Energy-Star is a government program encouraging efficient windows in residential low-rise dwellings. The window ratings are completely different in commercial and high-rise buildings.

When we say window, we're talking about an object placed into an opening in a wall (window) or ceiling (skylight).

An object made of glass (or other similar transparent substance) framed with plastic, wood or metal and often capable of opening or closing to let light and air in/out of the room.

There are a number of unique units of measure used with windows:

U-Factor: A lower number is better

U-factor measures how well a window prevents heat from escaping from inside the house. The rate of heat loss is indicated by the U-factor (or U-value) of a window assembly. U-Factor ratings generally fall between 0.20 and 1.20. The lower the number, the greater a window's resistance to heat flow and the better its insulation. In cold climates, a low U-Factor is better. To get a tax credit, windows must rate .30 or lower.

Solar Heat Gain Coefficient: A lower or higher number might be better

Solar Heat Gain Coefficient (SHGC) measures how well a product blocks heat from direct sunlight. The SHGC is the percentage of solar radiation entering via the window (both transmitted and absorbed). SHGC is a number between 0 and 1 - a lower number transmits less heat into the house. In warm climates, less heat is better. In cold climates, more heat is better. To get a tax credit, windows must rate .30 or lower.

Visible Transmittance: A higher number is better

Visible Transmittance (VT) indicates how much light comes through a window. VT is a number between 0 and 1 - the higher the VT, the more light is transmitted through the glass. In most cases, windows are installed to provide light, so a higher number is better.

Air Leakage: A lower number is better

Air Leakage (AL) means the volume of air, in cubic feet, that can leak through a square foot of window area (cfm/sq ft). Heat loss and gain occur by these leaks around the window assembly. The lower the AL, the less air will pass through the window assembly when it is closed. An ideal window is rated .30 or lower. This rating is optional.

Condensation Resistance: A higher number is better

Condensation Resistance (CR) measures the ability of a window to resist the formation of condensation on the interior surface of the glass. The higher the CR number, the better the window is at resisting condensation formation. This rating is a number between 0 and 100, and provides a way to compare the likelihood of moisture condensing on the glass. This rating is optional.

Noise Reduction / Sound Attenuation

Reducing  noise entering a home through windows can be as important as reducing the heat that comes in or goes out. Sound Transmission Class (STC) is one way to represent sound transmission. This frequently-used rating is based on reducing sound frequencies found indoors, such as voices or appliances. Outdoor-Indoor Transmission Class (OITC) is another scale that measures stronger, lower frequency sounds (traffic, trains, aircraft). OITC ratings are usually lower than STC ratings because these sounds are harder to block. The higher the number, the more noise is blocked. This rating does not appear on energy labels.

For more information on how your location may require different types of windows, check here. We didn't need to worry about energy ratings on our windows, as they were selected to block airplane noise, and not primarily for climate reasons - we're already in the perfect climate!

Friday, February 25, 2011

Let there be light!

Welcome to Excel Math's blog on using elementary math when you grow up.
    A very long time ago, in Internet terms, I did a few blogs on changing the windows at my house. If you wish to refresh your memory, here are some links.  Measuring 101 and An Inch Here and Inch There. And here are pictures:

    Version 1:

    Version 2:

    Version 3:

    Yesterday we finished replacing the kitchen window for the second time, with the new, improved Version 3 that solved some technical difficulties experienced with Version 2. It's slightly larger than the one we took out, and still smaller than the original window.

    My wife wondered if the difference in size would be "significant" to us. A perfect question for her Excel Math expert. Here's how we figure it out. The following drawings are done to scale using the actual dimensions I measured off the windows:

    Version 1:
    Version 2:
    Version 3:

    I calculated the square inches of the entire window, then subtracted the space occupied by the pillars. Each pillar was quite thin on Version 1 (1 inch x 36) with the original steel window framing, but quite fat (3x31 or 3x33) on Versions 2 and 3 with aluminum framing.

    Because the newest windows have thinner frames around the perimeter, there's more glass area in Version 3. The gain is 227 square inches, or about 1.6 square feet. Is that significant?

    Take a look at the small window below. It's 17.5 x 13.0 inches in size, or 227.5 square inches. That's how much extra glass area we gained in the Version 3 kitchen window.

    Now that we can see there is more glass, does that mean more light comes in? Maybe. It depends on the Visible Transmittance (VT) factor of the window.

    VT is an optical property that indicates the amount of visible light coming through the window; it is expressed as a number between 0 and 1. The higher the VT, the more light is transmitted. That sounds like a chance to use some more math. Next time.

    Thursday, February 24, 2011

    Counting Down

    In most cases, when you hear the word count referring to math, you think of adding 1 repeatedly to a number. As in, 1, 2, 3, 4 and so on, up you go up to the destination of 10 or 100. This skill is part of a group of concepts we call Number Sense.

    A variation on this process is called counting down. My hunch is that it's actually performed more often than counting up. It works just the same way, only you start with 10, 9, 8, 7 and so on down to zero, then you shout "Start the Movie" or  BLAST-OFF!  or   READY OR NOT, HERE I COME!

    For me counting down will always be associated with the launch of rockets at Cape Canaveral in Florida.

    There is specific language that evolved just for these rocket launch attempts. Go here to see NASA explanation of a countdown.  It begins with the term T-minus which stands for Launch Time minus so many hours or minutes.

    The announcer would say T-minus 2 minutes and counting ... and so on down to about 20 seconds, then go continuously down to zero (with a lot of noise going on in the background). Then whoosh!

    If you have the right job at NASA, you can get paid for counting down. It's a useful skill learned in elementary math class. Of course, even if you never grow up, you can keep playing with rockets.

    Wednesday, February 23, 2011

    How Long Will It Be Until? Part II

    Today in the Excel Math "what can I do with this stuff when I grow up?" blog, we will spend a bit more time on calendars and remembering when to pay your taxes. If you are a memory-challenged reader - I too admit to forgetting to pay my estimated taxes. Once.

    If you pay taxes to another country, please forgive me for focusing this blog on the US tax calendar. Having lived and paid in the UK where they are also zealous about this, I'm pretty sure every country wants its citizens to pay on time. That's why they sent you to school when you were young, so you can learn this stuff and be a good taxpayer when you grow up.

    First, US Federal Holidays for 2011
    • Jan 17  Martin Luther King, Jr. Birthday
    • Feb 21  President Washington's Birthday
    • Apr 15   District of Columbia Emancipation Day
    • May 30  Memorial Day
    • July  4   Independence Day
    • Sep 5    Labor Day
    • Oct 10   Columbus Day
    • Nov 11   Veterans' Day
    • Nov 24  Thanksgiving Day
    • Dec 26  Christmas Day
    Next, Saturday, Sunday, or legal holidays 

    If a tax due date falls on a Saturday, Sunday, or legal holiday (the list above plus state holidays), it is delayed until the next business day. The tax calendars include federal legal holidays, but you need to adjust for your own statewide legal holidays.

    Finally, the important dates

    The following list shows THE LAST DAY you can submit your information (and/or money) to the IRS without a penalty:

    • Jan 10 If you received more than $20 in tips in Dec 2010 you must declare them (same date every month)
    • Jan 14 First day it is normally possible to file your 2010 tax return (it was moved to Feb 14 this year due to tax law changes made in Dec)
    • Jan 15 Pay your estimated taxes for Q4 2010 if you are self-employed or a small business
    • Jan 31 Employers mail 2010 tax forms (W2, 1099) to people you paid last year
    • Feb 16 Fill out a W4 for 2011
    • Feb 16 Banks and brokers mail 2010 1099B and 1099S forms to people who paid/earned interest
    • Feb 28  Farmers and fishermen to file and pay their Q4 taxes
    • Mar 15 Corporations file tax returns
    • Apr 18 Individuals file their 2010 tax returns  (we get a few extra days this year, why?)
    • Apr 18 Pay estimated taxes for Q1 if you are self-employed, a small business, estate or trust
    • Apr 18 File schedule H for your Housekeeper
    • May 16 Non-profit organizations file 990 returns
    • Jun 15 Pay estimated taxes for Q2 if you are self-employed, a small business, estate or trust
    • Jun 15 Individuals who live overseas file their 2010 tax returns
    • Jun 30 Reports of overseas bank accounts worth $10k+ must reach the Treasury Department
    • Sep 15 Pay estimated taxes for Q2 if you are self-employed, a small business, estate or trust
    • Oct 3  Establish a Simple-IRA for 2011
    • Oct 17 File a late-extension 2010 tax return electronically

    NOTE 1: This is just my interpretation of the main dates and it is not definitive. I will not pay your penalties for you if you forget or if I got it wrong.

    NOTE 2: You can do most of these things electronically. But do not wait until the last minute to figure it out. There is no grace period for inability to file due to power shortages, going off-line accidentally, etc.

    NOTE 3: You are considered to have paid on time if your mail is postmarked by the US Postal Service before midnight on the due date. It doesn't actually have to arrive in the hands of the tax man. If you ship your tax forms by Fedex or UPS, there are some special conditions. 

    NOTE 4: There are a few exceptions to these date rules (see June 30th).

    If you need the real deal, click here to go to the IRS site and get the calendar for 2011.

    Tuesday, February 22, 2011

    How Long Has It Been? Part I

    Time is a word we use to describe our movements through time. Wait. That won't work as a definition. What is time anyway? A definition of time might include: 

    • a non-spatial continuum in which events occur in apparently irreversible succession from the past through the present to the future
    • a system of sequential relationships between events
    • a means by which we sense and record changes in our environment and in the universe
    • a way to describe separation among events taking place in the same location
    • a measured duration of activities 
    • a fourth dimension
    There are other ways to define time but these are adequate for our purposes today. If you have more "time" then you can go read these other Excel Math blogs on time: CalendarsDaylight savings.   Elapsed Time.   Avoid Being LateThanksgiving MathOnce in a blue moon.

    Math class is when our schools teach reading, measuring and recording time (watches and clocks and calendars), while History is where you learn about events that happen and their long-term meaning.

    Today I want to think about the progression of time and how we keep track of things that have happened and may eventually happen. While we are cruising along in time, how do we maintain awareness of where we are in the stream, where we are going, and where we have been?

    We use a mental ability called our memory, a skill that enables us to retain, recall and relive events.

    We might use an anniversary. When a special date comes around each year, we think back to the day (and year) we were born, married, enlisted, graduated or retired. At the end of a person's life we have memorial services to refresh our memories about significant things they did or said.

    Many people use calendars (in paper or electronic form) to keep track of the passage of days and weeks, the events we have planned in the future, and the activities of the past. Here's a calendar for the month of January that my wife has saved from a decade ago.

    In Excel Math we teach kids about units of time, using a calendar, and calculating the day of the week or month "... so many days or weeks in the future (or past)." Why bother with this?

    Here are some examples of how you use time as a grown-up person:

    1. You have make an appointment to take your driving test on a business day at least 6 weeks before your birthday. Your birthday is the 21st of June 2011. What is the last day you can make this appointment?

    2. If you owe income tax, it may be deferred for a period not to exceed 180 days after you are discharged from military service. If you pay the income tax in full by the end of the deferral period, you will not be charged interest or a penalty for that period, if you remembered to notify the IRS before your service impacted your ability to pay.

    If you do not notify the IRS in advance, you will owe interest on any tax not paid by April 15, even if you should qualify for the 2-month extension because you were out of the country. The interest runs until you pay the tax; even if you had a good reason for not paying on time, you will still owe interest.

    A late filing penalty may also be charged. The penalty is 5% of the amount due for each month (or part of a month) your return is late. The maximum penalty is 25%. If your tax return is more than 60 days late, the minimum penalty is $135 or the tax amount, whichever is smaller. You might not owe the penalty if you have a reasonable explanation for filing late. 

    The Federal Government and the IRS do not consider "I didn't remember the date"  or "I couldn't figure out how many months I was gone" as reasonable explanations! If you have suddenly remembered that this example is going to apply to you this year, here's the form. Just change the date to tax year 2010.

    Friday, February 18, 2011

    When is one not one? Part V

    I'm very nearly finished with the subject of collective words in English and how they are related to math. We do not explicitly teach these words, as they fall into the language arts area in schools, but we do point out to kids when they need to know that a word has an effect on math.

    So let's get to the last of this series on how we use this number sense when we grow up.

    A few English words are neither singular nor plural, but instead imply two and TWO only. They are called dual words. For example:
    • both of us 
    • twice
    • either/or
    • neither/nor
    • former/latter
    • twin
    • tandem (a bicycle built for two - this one is mine!)

    However, you can find troublesome exceptions to this duality 

    Either normally implies  

      - one or the other but not both (Either Darcie or I will leave work first today.)

    But without any warning, it may also mean

     - both (We have parking places on either end of the building.)

    We can use other words that increase the count beyond duality. Here are some examples:
    • thrice, an archaic word meaning three times
    • triple, meaning three
    • triad, meaning a group of three
    • trinity, meaning three (and often implying three in one)
    • triplet, meaning three children born at the same time (or a bicycle for three)

    Can we get beyond three? Indeed we can. Quad, Quint, etc. You get the idea. And if you'd love to have one of these fancy multi-seat bikes, you can contact Santana Cycles.

    There are a few special words in English that imply:

    - lots of participants doing something

    or even though it is not stated explicitly, they might mean:

    - a few doing something many times over

    For example:
    • stampede, drive or round-up of cattle or other livestock
    • herd instinct is a closely-related concept
    • migration of birds and butterflies
    • exodus or diaspora or pilgrimage mean many people going, but with different nuances
    • rush as in a group of folks trying to get into a sorority, or to find gold first
    • massacre as in The Chicago St. Valentine's Day Massacre in 1929, etc.
    • epidemic or pandemic  is used of a fast-moving disease
    • bandwagon effect when lots of people jump quickly onto the same subject
    • snowballing implies the same thing, and finally a more current term:
    • going viral as in My blog is going viral (albeit very slowly).

    Thursday, February 17, 2011

    When is one not one? Part IV

    This blog is about elementary school math. We talk about how math is taught to kids (via our Excel Math curriculum), and how people use math when they grow up. This week we've been looking at the peculiar way the English language complicates our understanding of numbers.

    Specifically - the concepts of singularity and plurality.

    Today I'd like to introduce another concept in the subject of collective nouns - terms of venery. You may never have heard this technical term, but you know what I am talking about. It means words used to describe groups of animals.

    Here are some examples:
    • a colony of ants
    • a troup of apes
    • a hive (swarm) of bees
    • a flock of birds
    • a herd of cattle
    • a pod (school) of dolphin
    • a swarm of flies
    • a school (shoal) of fish
    • a cloud of gnats
    • a pride of lions
    • a nest of vipers
    • a pack of wolves
    • a can of worms
    The same sorts of singular terms can be used for plurality of plants:
    • a hill of beans
    • a bunch (cluster) of grapes
    • a bouquet of flowers (when picked)
    • a patch of flowers (when growing)
    • a grove of trees (thicket, stand)
    • a sheaf of wheat (sheaves)

    The list I've provided just scratches the surface. If you like this sort of thing, you can research the subject and find dozens more obscure terms generated by folks just for the sake of making a list of terms of venery.

    Today's ridiculous complication: A gaggle is what you call a group of geese in the water, but a skein is what you call them when they are flying.

    Here's a slight diversion in our search for singular and plural complexity - a collective form called nosism (or the Royal We). It's when you refer to yourself in the second person. Rather than saying "I am not happy" you would say "We are not pleased."

    A variation of this is the Patronizing We, expressed by servers at a restaurant who include themselves in your group by asking "Are we ready to order yet?" or by doctors who ask "How are we feeling today?"

    Finally, I will finish off with an example of the Editorial We:

    Are we having fun with singularity and plurality yet?

    Wednesday, February 16, 2011

    When is one not one? Part III

    The last two days we have investigated words that mean more than one item, even if the word itself has a singular form (pair, dozen). These wacky words undermine our perfectly logical concepts of plurality (more than one) and singularity (one).

    Our assumption or expectation, in English is that the average noun is singular. It's the norm for a word to mean one. A bird is one bird. A bee is one bee. We change that base word to express plurality.
    • we add an s:   bird and bee -> birds and bees
    • we add an es:  potato -> potatoes
    • or we learn the exceptions by stumbling over them: zero -> zeros
    • we take away a y and add ies:  cherry -> cherries
    • or we leave the y and add an s:  monkey -> monkeys
    • we add an n or en or ren : ox -> oxen; child -> children
    • or we learn the exceptions by stumbling over them: hoof -> hooves
    Some words keep their same form - for example, a sheep, one sheep, two sheep, three sheep.

    English is an irregular language with many rule-breaking exceptions, so you constantly run across examples like cactus (plural is cacti), forum (plural is fora) or lotus (is the plural loti or lotuses?)

    Other languages have their own rules.

    In English (Spanish, Portuguese, Italian, etc.) we refer to one as singular, but zero and whole numbers greater than one are plural.

    He has zero or no cars, he has one car, he has two cars.

    While, in French and some other languages, zero is singular, not plural.

    Can you see the complexity of teaching number sense and plurality to a group of English-as-second-language students from different countries?

    I talked to a Frenchman once who had spent a year in a ESL class in Los Angeles when he was young. He didn't learn much English or math, but he said he's still fluent in street-Spanish ...

    Not only do ESL students have to learn the language, but they have to learn our crazy rules regarding plurality, which affect how we talk about numbers and hence how we do math.

    Remember the exception yesterday? A forest fire plus a brush fire are two separate fires. But if they come together we then have just one fire again.

    Here are some exceptions for today:

    Did you know opera is the plural form of opus? And although you can see graffiti around on buildings, you'll probably never see a graffito?

    Photo taken by Small Luxury World

    Tuesday, February 15, 2011

    When is one not one? Part II

    Yesterday's blog started a series of posts on the idea that some singular words imply more than one object. Like pair or dozen.

    Today I'm going into dangerous territory - the intersection of the English language and math - to talk about other kinds of collective words. Note that these examples are specific to English. Other languages have the same sorts of issues but the examples will vary.

    Have you heard of count nouns and mass nouns?

    A count noun can be modified by a number (or number word) and the result makes sense.
    • For example, plates on a table. I can have some plates, one plate, ten plates, etc. I need only the noun and the number.
    A mass noun cannot be directly modified by a number (or number word). If you try, the result makes no sense. With a mass noun, you must decide on a unit of measure (a measure word) and put a number word in front of your chosen unit, then put both in front of the mass noun.
    • For example, silverware on a table. I can have some forks, one knife, ten spoons, etc. But I only have a mass of some silverware, not three silverware or three silverwares.
    • Another example: water in a pool. I can have some water, but not three waters or seven waters. Using a unit of measure, I can have three gallons of water, or four buckets of water.
    Measure words are shown in the preceding examples - gallons and buckets. In addition to formal units (gallons) there are informal measure words that do not represent a metric or standard unit, such as bucket, drop, crumb, grain, etc. Measure words are combined with numbers and mass nouns to describe how much of the "mass" you are interested in.

    Another word (concept) - cumulativity - can be used to describe how words work when things are added together.
    • For example, a plate plus a plate equals two plates. Plates becomes plural.
    • Some water plus some water equals more water, not two waters. Waters does not become plural.
    • However, a brush fire plus a forest fire equals two fires, but if they join together, we have a fire again. English is the language full of exceptions. And fire can be singular and plural as needed.
    Now we'll look at two Latin phrases, singulare tantum (only singular) and plurale tantum  (only plural). These words have unique forms:
    • For example, dirt, wealth, etc. come only in singular form. You may not say dirts or wealths.
    • For example, scissors, trousers, etc. only come in plural form. You may not say scissor or pajama.
    Notice that we could add the measure word "pair" to the plurale tantum word scissors to get one pair of scissors or five pairs of scissors.

    I'm going to continue on this theme again tomorrow. This pair of blogs will become a trio? triplet? triad?

    Monday, February 14, 2011

    When is one not one? Part I

    One is not quite one, when it is a pair, or a dozen, or any other kind of singular word that refers to a multiple number of items.

    Since we are talking about math and how to use it in real life, it's important to understand the difference between singular and plural in language as well as numbers. Let's see what we can list as items that come in groups.

    A pair of things that we wear:
    • glasses
    • headphones 
    • earrings
    • shorts
    • trousers
    • pajamas
    • socks
    • slippers
    • shoes
    • mittens
    A pair of things that we use:
    • scissors
    • tweezers
    • pliers
    • garden shears 
    • chopsticks
    • knitting needles
    Other pairs
    • lips
    • wings
    • skates
    • skiis 
    • dice
    Things that come in a dozen:
    • eggs
    • donuts
    • golf balls
    • months
    • flowers
    FLOWERS! OH NO, it's Valentine's Day. I've got to get busy ....

    Friday, February 11, 2011

    Dividing things, Part II

    Division is an interesting math operation in that it can be displayed in many different ways.

    Here are 4 of the most common ways to use numeric symbols to represent 369.963 divided by 3.  (Because I chose these numbers carefully, I will eventually get a pleasing quotient of 123.321 with no remainder.)

    Of course, as shown below in the paragraph, you can also depict this operation in text:

    Three hundred sixty-nine point nine six three divided by three.


    One third of three hundred sixty-nine and nine-hundred sixty-three thousandths.

    You can depict the same thing graphically. Here is a rectangle 369.963 units wide, and beneath it are three smaller pieces, each of which is 123.321 wide. In this case, I was able to create them on my drawing system, so I know each of the units is an even third of the original. Does it help you imagine the task at hand?

    Or to make it interesting, we might create a picture that incorporates this division problem into a story:

    "Mike cut a 369.963 gram block of cheese into 3 pieces. How heavy was each piece of cheese?"

    We could portray the same thing using tangible items - that is, blocks, or sticks, or things like that. Things you can touch and manipulate, not just see on the screen or page.

    Alternatively we could use different media. I could announce to you verbally what the assignment is. Although it seems similar, the spoken word is not the same as the written word, especially if you can't read well. Or if you are deaf, or blind.

    All of these methods of representation allow the user to interact with the values 3 and 369.963 in order to do the division, or repeated subtraction. They take an abstraction or an actual event, and portray it in a useful way.

    Some representations are easier to create than others. The numbers are easy enough to type, but putting them into a division box takes more work. Generating the division symbol with a pair of dots above and below a hyphen (  ÷  ) is also a bit of effort on most computers because it does not appear on the keyboard.

    Use the form that suits you best. We try to vary our presentation in Excel Math, so kids of all types have many chances to succeed at learning to divide.

    Thursday, February 10, 2011

    Dividing things equally, Part I

    We have a saying in English "you can't add apples and oranges". In other languages it might be apples and pears, or yams and potatoes, but the point remains the same. Two dissimilar objects cannot be treated equally. (Read more)

    Which brings me to the subject of today's blog. Dividing stuff equally. I have treated the subject of division before. And dividing equally before. Twice, in fact. So why treat it again? Because it comes up so frequently in life, and in death.

    There's almost always something left behind when someone dies, and the deceased often says "share equally among my 4 children." Which turns into a nuisance when you have
    • an apartment building
    • a car
    • 4 pieces of jewelry
    • 3 gold coins
    • 2 apples
    • an orange
    • a cat
    How do we divide those items evenly?

    In math we can't easily some units or fractions. So we convert them.

    If I want to divide .8751 by 3, and 11/16 by 3, I learn it is easiest to do so in decimal numbers. Why?

    8751 ÷ 3
    I can do the first one in my head - 3 goes into 8 just 2 times, leaving 2; then 3 goes into 27 exactly 9 times; then 3 goes into 5 just 1  time, leaving 2; then 3 goes into 21 exactly 7 times so the answer is .2917

    11/16 ÷ 3
    Akk! This is harder. 3 goes into 11 just 3 times, leaving 2; then 3 goes into 16 only 5 times, leaving 1. What now?

    Let's convert this into a decimal number instead. I know 16 goes into 100 exactly 6.25 times. Multiply 11 by 6.25 and you get 62.5 + 6.25 which is (move the decimal 2 places) now .6875.

    We can divide .6875 by 3 which goes into 6 exactly 2 times; 3 goes into 8 just 2 times, leaving 2; 3 goes into 27 exactly 9 times; leaving 3 to go into 5 only once with a remainder of 2 (out of 3). So the answer is .229166666 ... alas, it never comes out even.

    This is similar to the level of difficulty in dividing 1 bracelet between 3 women that want it, not for its monetary value, but for its connection to their mother. It will never come out even.

    We usually liquidate items from an estate, turning things into cash that can be divided evenly.

    But that's not a solution for items with intangible or sentimental value. It's not a new problem, either, as this account from the reign of King Solomon indicates:

    One day two women came to King Solomon. One of them said: 

    "Your Majesty, this woman and I live in the same house. Not long ago my baby was born at home, and three days later her baby was born. Nobody else was there.

    One night while we were all asleep, her baby died. While I was still asleep, she got up and took my son, put him in her bed, then put her dead baby next to me.

    In the morning when I got up to feed my son, I saw that he was dead. But when I looked at him in the light, I knew he wasn't my son."

    "No!" the other woman shouted. "He was your son. My baby is alive!"

    "The dead baby is yours," the first woman yelled. "Mine is alive!"

    They argued back and forth in front of Solomon, until finally he said, "Both of you say this baby is yours. Someone bring me a sword." 

    Solomon ordered, "Cut the baby in half! That way each of you can have part of him."

    "Please don't kill my son," the first woman pleaded. "Your Majesty, I love him, but give him to her. Just don't kill him." 

    The other woman shouted, "Go ahead and cut him in half. Then neither of us will have a baby."

    Solomon said, "Don't kill the baby." Then he pointed to the first woman, "She is his real mother. Give the baby to her."

    Everyone in Israel was amazed when they heard how Solomon had made his decision. They realized that God had given him wisdom to judge fairly.

    Wednesday, February 9, 2011

    Numbers, numbers everywhere

    This blog is usually about math. Not today. Today it's going to be different. We'll think like kids - use our imaginations.

    Today we pretend. Pretend we are tired of learning math. Pretend we know nothing about math or numbers and that we don't need to know. Pretend that later in life, it won't matter one bit.

    We'll think short-term, as kids do:

    Who cares? I don't need no stinking numbers when I grow up!

    You're right. Go play. 

    Who needs numbers when they grow up? 

    A-OK with us. You can work in our warehouse, packing boxes. 

    Right on. Don't need no math for that job. No worries. Give me some tape and I'm set.

     Wait - I don't know how much to put on this shelf.

    Which bolt was that you wanted?

     What is all that stuff written on the whiteboard?

    Will the forklift tip over if I lift up those pallets? I dunno ...

    Are they paying me enough or am I getting cheated?

    What about my overtime? Do I get more money if I work Saturday?

    Say, when's that holiday about the Presidents coming along?

    Guess I'll just have to stay here until the bagels get brown ... or catch fire!

    I wonder if this thing still works? How far back do I stand?

     Can't figure this out either  [Don't worry, no one can figure out the microwave]

     So what's this thing for? Looks like a telephone without a handle.

    I want to watch the game - can someone turn this thing on? Anyone know what channel?

    Hi there. It's reality calling you.

    Too bad. It's too late. Tough luck.
    No Numbers, No Math - No Work, No Play.

    Let's stop pretending. You know you want a math education. Call us. 

    Toll Free  866 866 7026 

    PS - that means that call is on us - you don't have to pay. 

    Excel Math

    Tuesday, February 8, 2011

    Math, Music and Wires

    I confess that I did not like math in high school. In 11th grade I went to my counselor and asked for Auto Shop instead. She talked me into a compromise - Electronics Shop.

    There in Mr. Valison's class I caught the tail end of vacuum tubes and the bleeding edge of solid state electronics. This was the best career-preparation move I ever made, as for the last 40 years I've put that electronics knowledge to good use (and discovered math is essential).

    Today I present some wires. My wife says it's a mess, but this is after I spent a morning cleaning and straightening and bundling the wires, cables, fiber-optic pipes, and so on.

    It's a typical household setup nowadays, with TV on top, a pull-out shelf filled with DVDs, a coaxial cable coming in from the antenna, a single DVD player, a Blu-Ray player, a 5-disc changer, an amplifier/control unit, Apple TV, cable modem, AT&T mobile phone hotspot transmitter, and a WiFi wireless router. Not to mention all the power connections, HDMI links and a Mac Mini with keyboard and mouse. [Click the photo to see more detail]

    All the sound has to get to the speakers somehow, so I have wires running to the speakers in this room, and to my junction panel in the hall closet. I installed this panel 20 years ago when I bought this house, thinking it would be nice to keep the wires hidden. The sound comes in at the top, splits into right and left channels, then is routed through fuses and impedance-matching resistors to a junction block capable of serving 5 rooms. At the moment we are using 4 sets of speakers plus those in the TV room. [Click the photo to see more detail]
    What does this have to do with elementary math as we teach in Excel Math? I'll list a few places where you need math in your home sound system:
    1. figuring out the monthly cost of all the services to which you are subscribing (cable, satellite, Netflix, Apple Store, etc etc)
    2. adding up the cost of all the hardware that you are buying 
    3. calculating resistance and impedance when you install so many speakers
    4. deciphering the frequencies that TV stations transmit so you can choose an antenna
    5. determining how much space you need to hold all the CDs, DVDs and videocassettes your family owns
    6. determining the disk storage you will need to hold all the digital files your family owns or will be buying
    7. calculating the length of the wiring to install the speakers around your room or house
    8. deciding which remote controls you need, and how to program them with the right numbers to cut down on the total pile of remotes on the shelf
    9. trying to figure out which addresses your network components are using (and violating), such as, etc.
    10. looking up part-time jobs on the web so you can earn extra cash to pay for all this junk
      If you didn't have training in this field, then you can use your math skills to figure out how much to pay one of the 20,000 Geek Squad technicians to come in and fix up your systems.

      Or you could just read a book, hopefully on math. Here's one.
      (And not on a Kindle or iPad, because that takes you back to Step 1, above.)

      Monday, February 7, 2011

      Math on Television

      I spent a couple hours on the floor this weekend, re-routing wires around the back of my television set and sound system. In the process of doing this, I rediscovered a few secrets about TV screen sizes.

      (Go here to refresh your mind on measuring screens)

      Our old TV was a Sony WEGA 32" tube-type model. Here's an old photo of it, in its cabinet. The screen is 32 inches diagonally. It has a 4:3 ratio of width to height. What are the screen's dimensions?

      I forgot to measure it before I gave the TV away, but given this information, we can figure it out. That's what math is for, right?

      Our latest TV (which we got from a friend) is a 40" Sony Bravia. That means 40 inches diagonally. It has a 16:9 ratio of width to height. It's much wider so I had to cut the top of my TV stand.

      What are the screen's dimensions? I could measure the TV when I get home today, but that's no fun. Let's calculate its size too.

      You learned in elementary school (using Excel Math, I hope!) that the length of the diagonal c (the hypotenuse) of a triangle is related to the other two sides of the triangle. The formula that describes their relationship is called the Pythagorean Theorem and in layman's terms is stated this way:

      a2 + b2 = c2.

      We need this formula for our calculations. Here's my work on calculating the dimensions of the first Sony TV:

      It is 32 inches diagonally and it has an a/b ratio of 4:3. Diagonal c = 32 and c2 is 1024.

      I now need to find numbers for a and b where two things are true at the same time:

       a2 + b2 = 1024 and simultaneously 3a = 4b

      If you look at my work on the whiteboard, you will see I came up with a = 25.6 and b = 19.2

      I did this by trial and error - I just chose some dimensions and calculated until I found the right answers. Now on to the new set. We use the same process.

      It is 40 inches in diagonally, and has an a/b ratio of 16:9. Diagonal c = 32 and c2 is 1600.

      I now need to find numbers for a and b where two things are true at the same time.

      a2 + b2 = 1600 and at the same time 9a = 16b

      If you look at my work on the whiteboard, you will see I came up with a = 34.85 and b = 19.6

      Let me explain in more detail. I did this by trial and error - I just chose some dimensions and calculated until I found the right answers. You can do it too, there's no fancy math here:

      1. choose a number a , say 35 and multiply it by itself (square it) a= 35 x 35 = 1225
      2. check to make sure that's smaller than c2 or 1600. It is.
      3. multiply a by 9 to get 315, then divide 315 by 16 to get b = 19.7 (this is to ensure the dimensions match the 16:9 ratio of our set)
      4. multiply 19.7 x 19.7 (square it) to learn that b2 =388
      5. add 388 and 1225  and get 1613 - is this sum equal to 1600 or c2 ? No, it's too large.
      6. start over with a smaller a, such as 34.9 and see what happens.

      The numbers in red on each screen represent the square inches of screen area or a x b.

      You can see the new TV is larger than the old one. But how much larger? How would you calculate the difference?

      You might do it this way 40 inches divided by 32 inches = 1.25 times larger diagonally.

      You might do it this way 683 divided by 492 = about 1.4 times larger in surface area.

      Same TV sets, same math, almost-but-not-quite-the-same question = different answers.

      (I'm home. I measured. The calculations were correct!)

      Friday, February 4, 2011

      Hair today, gone tomorrow Part III

      We seem to cover the strangest things in this blog, while attempting to show how math is used in everyday life. This series on hair has come around to the question of what is a haircut? and Who can give you a haircut?
      It would seem (to a man) that a haircut is when a barber cuts some of your hairs shorter, using a sharp tool. But most people want more than just cutting. We really want to look better, and cutting hair is only one part of an attractive appearance.
      The term barber faded. Hair stylist came to mean a much cooler person who doesn't just cut hair. What is a hair stylist then?  This is best answered by referring to legal definitions. When the lawyers and the government get involved, it becomes complicated! Here's what California has to say on the subject, at its Barber/Cosmetologist website
      • A barber can prep, style, cut, color and shave hair, and can apply cosmetic preparations, antiseptics, powders or lotions to the scalp, face or neck. Barbers are the only ones who can shave a consumer or display a striped pole outside their shop.
      • A cosmetologist can prep, style, cut, color, bleach or straighten body hair, including tinting eyelashes; may give facials and remove hair by waxing or tweezing. The license allows them to provide any services of an esthetician or manicurist (see below)
        • Estheticians can perform facials and remove body hair by tweezing or waxing. They may apply makeup, false eyelashes, and do face or neck massages. They can bleach skin using chemical exfoliation.
        • Manicurists can give manicures and pedicures and apply gel, acrylic or silk false nails. They are limited to working on hand and foot areas only. Ingrown toenails must be treated by a doctor.
      • Electrologists may use a needle or probe to remove hair from a person using electric current. They are the only licensees that can use needles. 
      • Wigologists are people trained in wig and hairpiece fitting, styling, coloring and repair.
      • Physicians (and nurses working with them) can do laser hair removal or aesethetic cosmetic (plastic) surgery.
      Services provided in the following areas do not require certification from the state as barbers or cosmetologists, although they might need other training or licensing:
      • Hairbraiders create elaborate braids and cornrows in naturally curly hair. Braiding is specifically exempted from cosmetology licensing in California and some other states. 
      • Massage Therapists who treat muscles beyond the face and neck.
      • Practitioners who apply permanent makeup, cosmetics or tattoos.
      • Operators of tanning salons.
      Having said all that, here is some information from the Bureau of Labor Statistics. If you want to consider hair styling as an occupation in the next decade, we're going to need almost a quarter-million more than we have today.

      in 000s
      in 000s
      New Jobs
      in 000s
      New Jobs
      in %
      % Self
      in 000s
      Barbers5460 6 11.6 80.6 14.0 $24,050
      Cosmetologists 631758 127 20.1 43.5 220 $23,140
      Teachers 750860 110 14.7 20.8 226 $31,100
      Mathematicians 33.6 0.7 22.5 0.0 1.5 $95,150

      However, if you want to earn lots of money, you could take up math. Notice there aren't many mathematicians, and none of them are self-employed. Although they make a lot of money, they certainly don't make anyone else look better. Except perhaps by comparison.

      Thursday, February 3, 2011

      Hair today, gone tomorrow Part II

      Today I will focus on math related to the hair on our heads.

      No doubt you have heard the phrase "as thin as a human hair". How thin is that?

      It depends on your ethnic origin. Hair thickness ranges from .04 to .25 mm - on average it's about one-tenth of a millimeter or .1 mm. [Click for a larger image]
      Thicker hair emerges from large hair follicles - thickest tend to be red/orange and dark or black hair. Finer hair comes out of smaller follicles and tends to be lighter or blonde. We don't know for sure if this is genetic.

      Of course we've been talking about a hair from the top of your head. If you haven't already noticed, ear hairs, nose hairs, moustache and beard hairs can be much thicker.

      Our hair follicles have a self-regulation function that determines how long their hairs should be. Eventually hairs stop growing, fall out, and a new hair emerges. But not always. Sometimes it keeps growing.

      Here's a young lady named Xia Aifeng, in China. Her hair is 2.75 m (9 ft) long. You can search for her on YouTube and watch her washing, combing and throwing her hair around.

      As we get older, the regulation system may stop working on a few of your follicles too. That's why some older people have long ear and nose hairs. How long? I checked at the Guinness World Records site:
      • Toshie Kawakami in Japan has one eyebrow hair 17.8 cm (7.0 in) long
      • Anthony Victor in India has ear hairs 18.1 cm (7.1 in) long
      • Richard Condo in the USA has chest hairs 22.8 cm (9.0 in) long!
      If this seems gross, just wait. It could happen to you!

      Notice that so far we are only talking technical details about our existing hair(s), with nothing said about removal, hair styling and coloring, or hair loss. Those are subjects full of math as well as emotional risk! Maybe something for another blog...

      If you are interested in more details about your hair, you might want to visit the Hairfactz site.

      As for me, I'm going to have lunch and go get my hair(s) cut.

      Wednesday, February 2, 2011

      Hair today, gone tomorrow Part I

      Let's apply math to the hairs that plague us. We have hair on our heads, hair on various other parts of our bodies, and hair on our furniture from our pets.

      I have read that the average person has about 5 million hairs on his or her body. Of those, perhaps 100,000 or so are on top of our heads. We are born with all the hair follicles (roots) that we will ever have. In fact, some babies are born hairy, with what are called lanugo hairs, but those quickly turn into vellus hairs or terminal hairs. Here's a very hairy baby related to one of our employees ...

      Hair grows all the time, and falls out when it has done its duty. Although all of us (people) shed hair, it isn't that big a deal unless it ends up clogging the drain in the shower.

      When we go bald we don't really stop growing hairs, the terminal hairs from those particular follicles just become ever so much finer and nearly invisible - they become vellus hairs. Most people have more-or-less visible terminal hair in various places, but invisible vellus hair elsewhere. Our skin is not completely hidden, thus we don't call our hairs fur, or a coat.

      Why am I writing about hair and fur and coats? A convergence of hair-related activities, I guess. It's time for me to get my hair cut, AND I got a nifty advertising email from Dyson about a dog vacuuming attachment. This might turn into a best-selling item for them, as many dogs shed hair all over the place.  So today we will talk about pet hair/fur.

      I only had one question for Dyson - Does it work on cats? Sadly, No. They say this new item is not good for cats. I can say from experience that vacuums and my cats don't get along. Although Tiger III looks cute here, that doesn't mean he won't bite me if I come near him with the vacuum!

      Cats and dogs, along with many other mammals have what we call fur - dense hair all over their bodies. This fur may also be referred to as their coat. Cats have various types of hair, such as whiskers, guard hairs, down (undercoat), vellus (fine hairs), awn hairs, etc. You can see all those types of hair in the picture of Tiger's face.

      The color of cat fur is determined by its genetic makeup. My cat's hair color is called red tabby. Did you notice how close his hair color is to the golden retriever in the Dyson ad? Here he is (above Tiger is on the left) with his friend Boomer from across the street (below Tiger is on the right). They look amazingly alike in size and coloration but came from different litters in different cities, so we are sure they are not related.

      Here's one of our previous cats having a nap. We called him Tiger II. Yes he's enormous in this photo but he was 21 years old then, so his weight didn't seem to shorten his lifespan any.

      I don't have pictures of Tiger I but he was also the same color. As for why we have had 3 cats of exactly the same coloration for a total (so far) of 32 years I can't say. We did have a completely black cat too, named Panther. Here she is giving me the "I can't be bothered with you" look.

      Cat fur coloration is a complex topic and there's plenty of math in it! Sadly I have used up all my time showing you pictures of my pets, so you have to go elsewhere to learn more about the names for colors and to learn about the genetics behind coloration. And here's a site with an interactive tool so you can see what possible colors might come out of a litter (assuming you know the father and mother).

      Tomorrow we'll cover more hair math.