Math is Everywhere! Take a Look at a Clock!

As I was walking this morning in my neighborhood, my mind was filled with thoughts that geometric shapes are everywhere!  Do you agree?  Gazing at sidewalks, homes, street signs, and security lights, I saw shapes of rectangles, trapezoids, triangles, octagons, and even circles and spheres!   Try it sometime, you'll be amazed how many hundreds of shapes you see each and every day!

For today, let's take a look at the clock.  Other than public buildings, such as schools and medical offices, do you have a clock in your home?  Our society has quickly replaced wristwatches with digital forms of knowing the time on cell phones, tablets, computers, and other electronic devices.  Most of them are not displayed in the shape of a circle, but are digital.  Perhaps some of you reading this right now never learned the time of day by reading a clock, but have been exposed to only digital displays of time.

There are some easy lessons to learn from the clock.  What traditional shape is a clock?  It is a circle, isn't it?  If you are not familiar, there are numbers from 1 through 12 on the clock, and we use it to measure all 24 hours in the day.  The hands on the clock spin around quickly, quietly, and smoothly.  From the 12 to the 1, the hour hand indicates that 1 hour has just passed.  From the 12 to the 3, the hour hand has moved 3 hours.  From the 12 to the 9, the hour hand has moved 9 hours.  Each day, there are 2 times that it is 1 o'clock, 1:00am and 1:00pm.  There are also 2 times each and every day it is 6 o'clock, and 7 o'clock, and 8 o'clock,...etc. 

The natural movement of the hands on a clock to the right is called clockwise.  If the hands were to move in the opposite direction, it is called counter-clockwise.  When you assemble furniture, or repair your car, it is common for the instructions to guide you to turn the tool clockwise or perhaps counter-clockwise.

For the purpose of our lesson, we have assumed that our clock is a circle.  How many degrees are in a circle?  That's right!  There are 360 degrees in a circle.  Since there are 360 degrees in the entire circle, and there are 12 hours in the circle, how many degrees are in each hour?  We divide 360 degrees by 12, and the answer is 30 degrees.  We know that for each hour that passes, there are 30 degrees that have passed also, each day, every day, all day long.

Since we know there are 30 degrees in each hour, we can also determine how many degrees there are in either direction from one hour to another on the clock.  Yes, we can do it both clockwise and counter-clockwise! 

Let's try a few examples:
1.) How many degrees does the clock travel clockwise from 1 o'clock to 4 o'clock?
Solution:
* There are 3 hours from 1 o'clock to 4 o'clock.
* We know there are 30 degrees each hour.
* Simply calculate the product of 3 x 30 = 90 degrees.
That is correct!  There are 90 degrees from 1 o'clock to 4 o'clock.

2.) How many degrees are there from 5 o'clock to 1 o'clock going counter-clockwise?
Solution:
* There are 4 hours from 5 o'clock to 1 o'clock.
* Remember there are 30 degrees per hour.
* Calculate the product of 4 x 30 = 120 degrees.
You are correct, once again!  There are 120 degrees from 5 o'clock to 1 o'clock.

3.) Let's do #2 again, but this time we need to calculate the number of degrees from 5 o'clock to 1 o'clock traveling clockwise.
Solution:
* There are 8 hours from 5 o'clock to 1 o'clock.
* Use the 30 degrees per hour measurement once again.
* Multiply 8 x 30 = 240 degrees.
That's right!  You are quickly mastering your knowledge of the degrees in clock!

Try a few of these on your own!  They are fun and very practical!  Don't forget to share this great information with a family member or friend! 

Mental Multiplying--You Can Do This!

Are you like most people when you hear the words 'Mental Math' you immediately rebel and ask yourself, "Why mess with that?"  Or perhaps you might be thinking it is far too difficult and there is no advantage for me, right?

You could be at the market, and want to know very quickly how many units of something you can buy with the cash you have.  Maybe you are an attorney, and you need to do some quick Math while defending your client.  Whatever the situation, the quicker you can think on your toes, the greater the advantage you definitely have.

Let's take a look at the basics of multiplying a couple numbers in your head, and without using the calculator on your cell phone, or paper and pencil.

Evaluate 4(96)
Using the Distributive Property, think of a couple different ways to add or subtract two numbers to yield 96.
Solution 1:
4(100 - 4)
4(100) - 4(4)
400 - 16
384

Solution 2:
4(90 + 6)
4(90) + 4(6)
360 + 24
384

Which solution did you prefer?  Did you notice that both solutions gained the same answer?  It is important to proceed with your solution using numbers that are easy to multiply in your head, so we are referring to numbers that are being multiplied by a multiple of 10, and possibly multiples of 100 or 1000, in addition to performing simple calculations from numbers that are a part of the basic multiplication tables that most of us memorized in elementary or middle school.

Try it, and with a little practice, you will be an expert very quickly!  Don't forget to teach this great tip to a family member or friend!  If you take a few minutes to explain it to someone, you will increase your own skills and gain much confidence!

Happy Multiplying!