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.


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.

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.
Even 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.

Look 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.

By 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)