Quantity Measurements. Choosing the Correct Procedure.

Quantity Measurement is Important

Quantity is a pretty easy concept to grasp.  But, it isn’t always easy to measure.  Quantity is basically an amount of something.  But different substances are easier to measure than others.  For example, if you have a cup full of marbles, you may be able to pour them out and count them individually.  What if you have a cup full of rice?  How many grains of rice do you have?  There are ways of measuring quantity other than just counting.  The two most common ways are by using a volume measurement, or a weight measurement.

If you go to the grocery store most of the packaged food is going to be measured by either weight, or volume.  Some of the more common weight measurements on packages for sale in the US would be ounces and pounds.  Some of the common volume measurements would be cups, pint, quarts and gallons.  So, what type of measurement do you use when trying to determine quantity?  It really depends on the physical attributes of the substance you’re measuring.

Quantity, How Much Is In The Jar?

When you are measuring a non-liquid substance, you will normally use weight at a measurement tool to determine quantity.  The reason you don’t use volume with a group of solid substances is because you can’t account for the tiny space in between the individual units.  For example, if you fill one cup with water, and one cup with ice cubes, you’ll notice that the ice cubes have space in between them, while the water completely fills the entire container. 

Measuring quantity of solid vs. liquid.

 When using weight as a measurement for quantity, you will typically weigh a sample of the substance individually, then measure the entire group.  If you take the weight of the entire group and divide it by the weight of the individual sample piece, you can approximate how many total pieces there are. 

Typically, when measuring the quantity of a liquid, you’re going to use volume.  Because a liquid will completely fill the container, you can fairly accurately determine the quantity of the liquid by the volume filled in the container.

For online calculators for volume or weight go to CalcuNATION.com.

Online Calculators for Weight Measurements

Online Calculators for Volume Measurements

Online Calculators for Volume and Area Measurements

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Math Education Should be Exciting for Students

Math Education is Difficult

Math education is a very challenging curriculum for teachers.  In general, many students have a tendency to avoid math.  Whether they think it is a tedious exercise, or fail to see the usefulness of mathematics in the real world, this stigma creates a barrier that math teachers have to cross to successfully reach students and influence them on how important math education really is.

Math Education to Me

I know that when I was younger, math was a very dry, boring subject to me.  Other subjects offered some level of entertainment.  Reading and grammar had stories, geography taught about exciting places in the world and history had exciting characters.  Math pretty much had numbers and long, drawn out formulas to memorize.  Even now, it doesn’t seem too exciting.  Math education didn’t become important to me until I learned how to use it in the applications of science. 

Making Math Exciting

For the most part, students aren’t shown the actual uses of math at an early age.  Most young students are only taught the fundamentals of math.  I even think that can be tedious and boring.  I think that if students are not only educated on the fundamentals of math, but are immersed in the real world applications of math in a fun way, there would be more of an interest in math education at an early age.

In science and physics, I was able to apply math to understand how simple machines were designed.  This started to pique my interest in math and how it is applied in the real world.  Fast forward 20 years and that is now what I do for my “real life” job.  I use math every day to apply drive systems.  My day includes simple math like trying to calculate the hypotenuse of a triangle, or more applied math like torque for the track drive on a bulldozer, or calculating the mechanical horsepower of a drive system.  I get to work on some pretty large and impressive machines.Math education is important for machine design.

My hat goes off to math teachers everywhere for trying to break down that math stigma barrier. 

For more information on math education and online calculators, go to CalcuNATION.com.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Electricians Use a Lot of Math. Shocking, I know.

Electricians may not be primarily known for their math skills.  You might be more likely to think about a guy running wires or cables through walls, taking apart outlets with screwdrivers, or walking around with their hair sticking straight up from a recent jolt.  But, in the real world, electricians are always using math to diagnose and create successful, useful and safe electrical connections and circuits.

math for electriciansEven if you aren’t aware of what electricians do, I’m sure you are aware of the potential dangers of electricity.  Using the correct equations to select wire size, or gauge, can be crucial to prevent dangerous conditions in a house.  How many times do you see a house fire on the news and the reason for the fire was determined to be faulty wiring?  Now, you might recognize the importance of correct wiring. 

A wire transmits electricity in a similar way to a hose transmitting water.  If you try to push too much water through the hose under too much pressure, the hose might rupture.  A similar thing can happen to a wire.  If you try to put too much voltage and current through a wire, it will get hot and possible short out.  This is why many house fires are caused by wiring.  A wire shorts out and causes a spark.

Three of the basic properties electricians use in math formulas are voltage, current and resistance.  Voltage is like pressure in a hose, it is the force of the electricity.  Current is like the volume of water travelling through the hose, the flow.  This electrical flow is measured in amps.  Resistance is pretty much what it sounds like.  It is the resistance to flow in the wire.  Named for a wise guy a long time ago, resistance is measured in Ohm’s.

Electricians use many equations when diagnosing a circuit.  Sometimes they use Ohm’s law, sometimes they calculate the power of a circuit by deducing the watts.  And sometimes they are just trying to decide the correct gauge of wire to use.  Either way, they are always using math, and these are just the very basics to give you a taste of what they do.

For more on the math electricians use, try some of these online calculators:

Electrical Calculators

Electric Horsepower Calculator

Electric Resistance Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

 

Area of Irregular Shapes Are a Regular Pain

Area is one of the most basic fundamentals of geometry.  When we first start to study geometry and shapes, we learn about perimeters, circumferences, areas and volumes.  Of course, when we start to learn something, we start with the basics.  In geometry, the basics are the simple shapes that we learn to recognize as children.  Squares, circles, triangles, rectangles, and the various other shapes are fairly simple to understand.  But, in the real world how often to we need to find the area of an exact circle, or a perfect square?  In reality, it is more useful to know how to calculate the area of an irregular shape. 

Irregular shapes are much more common than regular shapes.  And, finding the area of regular shapes with accuracy is an important ability to have.  The first example that I can think of is the layout of a home, or even a property.  Real estate agents need to know how to calculate the floor space in a house, and the size of a parcel of land.  It’s rare that either of these take the form of a perfect shape like a square, but with some practice and patience, you can use the formulas for simple shapes to determine the area of an irregular shape.

irregular shapeLook at this picture.  You probably don’t recognize the shape.  That’s because it is irregular.  We’ll call it a problemogram.  If you look closely, you can start to discern some of the properties of simple shapes. 

By breaking this large shape down into smaller shapes, we can calculate the areas of the seperate shapes and then add them to find the total of the larger shape.  If you look at the illustration below, it will show some of the measurements of this larger shape.

measured shape areaBy breaking this shape into a circle, rectangle, and triangle, we can calculate the independent areas of these shapes to determine the total of the original shape.  Be careful about the circle.  If you notice, half of the area of the circle overlaps with the rectangle and won’t be needed for the calculation.

So, we need to:  1. Calculate the area of the circle.  2. Calculate the area of the rectangle.  3. Calculate the area of the triangle.  4. Add all of the areas together and subtract half of the circle area that overlaps the rectangle.

By doing all of this, I get the following answers:  Area of circle is 12.5664 square units.  For the rectangle, I get 21 square units.  And the for the triangle I calculate 4.5 square units.  Add all of these together and you have about 38.07 square units.  Don’t forget to subtract the overlapping half-circle and you will have an answer of about 31.8 square units for the total area of the irregular shape.

What other irregular shapes would this be useful for in real life? 

Here are some online calculators that may be useful.

Hypotenuse Calculator (Pythagorean Theorem)

Geometry Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Rates Are Great For Comparing Performance

Rates are all around us.  We use rates to determine our vehicle speed, track our work performance, rank our favorite sports teams, and even keep tabs on our personal cash flow.  Once you know what a rate is, and how to recognize rates, you can effectively use rates to compare performance within a system.

The key to all rates is time.  Rates are used to track a measurement per given unit of time.  As an example, the speed or your car is calculated in miles per hour, or kilometers per hour.  This rate is set as a length of distance per unit of time.  Other speed rates may be feet per second, feet per minute, kilometers per minute, meters per second, etc.  It really depends on what speed rate would best describe the performance.  After all, it would be much more complex if we measured the speed rates of vehicles in feet per hour. 

In the investment world a key phase is “rate of return” or “return on investment (ROI)”.  This rate is used to compare how quickly you either gain money, or lose money on an investment.

Right now I’m in a hotel.  If you pass by many hotels or motels as you travel, you might notice that they advertise rates.  The rate is how much it costs to stay at the hotel and is usually an amount of money per night, or per week.

There are other rates than just measuring distance per time unit (speed) and money per time unit.  Other rates can be volumes per time unit (flow), beats per second (heart rate), frames per second  (photography/videography),  weight per time unit, etc.  As stated before, rates are basically any measurement relative to a unit of time.

So the next time you are in the car, watching sports, reading the newspaper, or watching TV, see how many different rates and rating systems you can identify.

For more on rates and other online calculators, try some of the links below.

Speed Conversion Calculators

Flow Conversion Calculators

Length Conversion Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Efficiency, It Gets in the Way of Good Math.

Efficiency is often overlooked as a factor in math.  We use math as a tool for our daily lives, but rarely does a mathematical equation work perfectly when applied in real life.  There are so many variables that can play a factor in any application of mathematics that affect the outcome.  Efficiency is one of the most common variables that affect math in applications.  It is especially common when math is applied to a mechanical system.

The core purpose of a mechanical system is to transfer, convert or apply power in a useful way.  The laws of energy state that energy is never created or destroyed.  Energy is merely transferred.  Unfortunately, every time you transfer, convert, or apply energy, there will be efficiency issues. 

In mechanical systems friction and the resulting heat are a major issue that causes efficiency issues.  Can you think of a motor, whether in your car, or in an appliance, that does not get warm as it runs?  Every surface within a system that comes in contact and moves against another surface will have friction.  This friction converts some of the input energy of motion into heat energy.  Think about the heat that is created when you rub your hands together.  Every metal surface that makes contact with another metal surface creates heat from friction in a similar way.

So, efficiency is a factor in many systems.  If you take a car, you can see where energy is transferred from one system, to the next, and where the efficiency losses affect the system.  Start with the fuel, the potential energy in the fuel is converted to mechanical motion in the cylinder.  But, this process isn’t perfect, some of the fuel will end up not burnt and exit through the exhaust.  Even the piston that moves down creates friction with the cylinder wall and the crankshaft.  As power is transferred to the transmission, all of the gears and bearings rub and wear against each other, creating more friction and heat.  As power moves out of the transmission and into the final gear drive to the wheels, energy is lost to more friction to the gear sets in the final drive.  Even the tires will create heat from the friction between the tire and road.

There are many ways that we fight this friction by properly maintaining the systems of our vehicles.  Fresh oil, proper tire inflation, and regular tune-ups help each system transfer power more efficiently. 

So, when applying math to real world applications, it is always important to be aware of the energy losses and efficiency issues that could be a factor. 

For more information on some of the calculations used in gear drive systems and other mechanical calculators, follow the links below.

Menu of Machinery and Engineering Calculators

Gear Reducer Output Calculator

Gear Increaser Output Calculator

Chain and Sprocket Output Calculator

Belt Drive Output Calculator

Mechanical Horsepower Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Carpenters, Using Math to Build and Construct.

Carpenters would have a hard time building anything without math.  Without the knowledge and application of math skills houses may end up looking like something from a fun park.  Constructing a solid piece of furniture, a level counter top, or a comfortable room with plumb walls requires many different math skills.  A good carpenter will have a strong understanding of general mathematics, measurements and geometry.

If you’ve ever been involved with carpenters, or carpentry in general, you may have heard the phrase “measure twice, cut once”.  This is a key phrase in carpentry.  Being accurate in measurements helps to eliminate making mistakes when cutting lumber.  This helps to eliminate wasted time and money associated with these mistakes.  Fractions are a constant math function in a carpenter’s life.  Also, being able to add, subtract, multiply and divide is critical to know what your measurements should be as well as accurately estimating costs.  Many carpenters will have sharp math skills and don’t be surprised if they can quickly calculate these general math functions in their head.

In addition to accurate math skills for measurements.  Carpenters need to be able to convert measurements.  Not everything is measured with one length or weight unit.  Being able to convert between measurement units is key.  Converting between inches, feet, yards, pounds, ounces, and even metric units is important. 

To be sure that walls are straight, cabinets are level, and furniture is built solid, carpenters use geometry.  Being able to calculate area, volume, side lengths, circumference and hypotenuse lengths, are key math skills needed for a carpenter.  Knowing the equations for these basic geometry functions are important to building solid structures.

The next time you look at a piece of furniture, a cabinet, or a house, think about some of the math used to build that structure and how important it is to your daily life.

For more on some of the math calculations a carpenter uses, try the online calculators at CalcuNATION.

Measurements and Conversions Calculators

Length Conversion Calculators

Geometry Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Water Conservation. Are You Flushing Your Money Down the Toilet?

Water conservation is a hot topic these days.  One of the most wasteful places that we use water is the bathroom.  I’ve posted thoughts and calculations on wasting water in the bath and shower, but I’ve never discussed one of the other fixtures that uses a lot of water.  The toilet. 

“Flushing your money down the toilet.” is a fairly common phrase for wasting money.  In some ways, it is literally true.  I don’t condone anyone making it a habit to not flush the toilet, even though some people do.  Even if that habit is meant to save money and promote water conservation, it’s still kind of gross.  However, we can look at just how much water is used when you hit the handle and how much money that costs per flush.

To figure this out, we first need to find out how much water is actually used to flush a toilet.  Many toilets have a different amount of water that is used per flush.  This rating is usually tagged somewhere on the fixture.  Some new toilets are designed with water conservation in mind.  These units will have fewer gallons per flush ratings than older models.  The toilet in my house uses 1.6 gallons per flush. 

Now, we need to know how much the costs are for not only water service to your house, but sewer service also.  My most recent water bill charges a price of $20.00 for up to 2,500 gallons of water per month.  Every 1000 gallons of water over that is an additional $4.72.  The sewer costs are also set at $20.00 for up to 2,500 gallons of water and $4.72 for every additional 2,500 gallons.

As long as my total water and sewer usage is under 2,500 gallons per month, my combined cost of water and sewer together is $.016 per gallon.

So, if my toilet flushes at a rate of 1.6 gallons per flush, and my cost per gallon is $.016, then multiply the two numbers to come up with $.0256 per flush.  Just under 3 cents to flush the toilet. 

So the next time someone tells you that you’re throwing your money down the toilet, you can tell them how much it truly costs to flush that money away and lecture them on the importance of water conservation.

I know it’s dirty math, but someone has to do it.

For more on how to calculate volumes, flow and pressure, try some of the online calculators at CalcuNATION.

Volume Conversion Calculators

Flow Measurement Calculators

US Gallon Volume Conversion Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

 

Bald Versus Non-Bald. The Challenges of the Dome.

Being bald is more than a hair style, or in some cases, a non-hair style.  It turns into a way of life.  If you are fortunate enough to embrace your own baldness, you can find the positive aspects of being bald.  One of the most common references to baldness is that being bald is “low maintenance”.  For those that aren’t lucky enough to be bald, it’s not as “low maintenance” as you might think.  It may save some money at the barber shop, but there are other hassles and expenses that need to be recognized.

If you’re reading this and you have a full head of hair, then good for you.  For the average joe with a mop on his head, we can make a few assumptions.  For your daily maintenance, you probably spend some time washing your hair, and combing your hair.  Your expenses for keeping your flowing locks in check probably amount to the cost of some hair products like shampoo and maybe some hair gel.  Of course we can’t forget the costs of going to the barber maybe once every two weeks?  So, in a given month, a well follicled male would probably spend around $20-$40 on hair products, depending on how fancy he is.  And, at the barber shop, we’ll assume for the sake of this example, he might spend $30 per month.  That comes out to about $50-$70 per month to maintain the lifestyle of the rich and hairy.

Now let’s look at your average good looking bald guy.  He doesn’t have the expenses of going to the barber shop, or having to purchase shampoo or hair gel.  However, there are other expenses.

If our hair challenged friend uses a razor on his head daily to keep that shiny top looking good, he has extra costs on shaving cream and razor blades.  And, razor blades aren’t cheap either.  At least not good ones.  If you do use bad razor blades, you risk cuts on your noggin.  This is where the added cost of band-aids comes in.  If your baldness is something you’re not ashamed of, then you will be out in public with your chrome dome.  I don’t know many people that aren’t aware of the dangers of sunburns, but I can assure you that the top of your head is sensitive and not a great place to be peeling.  Now, we’re adding the cost of sunscreen….good sunscreen…applied a lot. 

So, from personal experience, I can assure you that there are some monthly costs associated with maintaining a bald dome.  It also takes some time every day to make sure you aren’t looking scruffy…in spots.

In summation, I don’t really see much of a difference in cost or time when it comes to maintaining a nice head of hair, or a nice head of nothing.

This post was written to help support CalcuNATION.  Here are some examples of health related calculators.

Nutrition and Health Calculators

Caloric Needs Calculator

Caloric Energy Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Old MacDonald Uses Math on His Farm. E-I-E-I-O. Part 2

Old MacDonald uses math on his farm to be the best farmer he can be.  Being a farmer, he takes on multiple roles in his business that are usually split up between many employees in other businesses.  He takes on the responsibilities of accountant, executive management, workforce, and maintenance.  In part 1, we looked at some of the simple ways that he has to look at finances when running a farm as a business.  Old MacDonald has to be constantly vigilant to keep costs down and his revenue stream up.  One way that he keeps costs down is to do his own maintenance and mechanic work whenever he can.

Many of the machines on a farm play critical roles.  Without tractors, combines, trucks and implements, Old “Mac” wouldn’t be able to perform the day-to-day functions necessary to produce a profit.  It’s very important that the equipment functions properly when needed.  And many times, especially when weather is involved, he may need the equipment to perform flawlessly in a short window of time.  A great example would be trying to harvest when a storm is brewing. 

Because of the importance of his machinery, Old “Mac” constantly maintains and repairs his own equipment.  This ensures him that everything is ready when it’s needed and it helps keep his costs down from having someone else work on it.  Because of this, he has a general knowledge of mechanics and hydraulics. 

Many of the machinery on the farm uses hydraulics.  Most of his machines have pumps, motors and cylinders.  It helps Old “Mac” to know how the items function.  Being able to “backyard engineer” some of the equipment saves time and money. 

It would be handy if Old MacDonald was familiar with the math of cylinder force, speed, and hydraulic horsepower.  I’d bet he would give some engineers a run for their money on machine design.

Of course, there are the costs of duct tape and baling twine that have to be accounted for.

For more information on mechanical and hydraulic math, try some of the online calculators at CalcuNATION.

Machinery and Engineering Calculators Menu

Hydraulic Calculators Menu

Cylinder Force Calculator

Cylinder Extension Speed Calculator

Cylinder Retraction Speed Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)