Why is 'x' Usually the Unknown in Algebra?

Ted Talk

Again, it's time for some math information you might have missed in school. (Don't worry, I missed a great deal as well.)  Today's question is: Why is the letter "x" the symbol usually used for an unknown?

Even though the letter "x" is commonly used in mathematics, its use often appears in non-numerical areas within different industries such as The X Files or Project X. Terry Moore clears up this mathematical mystery in a TED Talk presentation at Long Beach, California.  In a short and funny four minute talk, he gives an unexpected answer to "why." Just click under the illustration to find out the reason!

Magically Squaring Numbers

My college math students lack confidence (I classify them as mathphobics.); so, I like to show them math "tricks" which they can use to impress their peers.  I encourage them to know their squares through 25. (Yes, I know they can use a calculator, but the mind is so much quicker!)  When we get to solving equations using the Pythagorean Theorem, I introduce this trick. Please note: For the trick to work, it must be a two digit number that ends in 5.
Suppose we have 35².  (This means will be making a square.)

• First, look at the number in the hundred’s place. In this case, it is the “3”. 
•  Next think of the number that comes directly after 3. That would be “4”. 
•  Now, in your head, multiply 3 × 4. The answer is 12. 
• Finally, multiply 5 × 5 which is 25. 
•  Place 12 in front of 25 to get the answer. Thirty-five squared is 1,255.
• 3 × 4 = 12      5 × 5 = 25       
• The answer is 1,225.

This means that we can build a square that is 35 by 35, and it will contain 1,225 squares or have an area of 1225 squares.

Now let's try 65². 

• One more than 6 is 7; so, 6 x 7 is 42. 
• Place 42 in front of 25 (5 x 5) and so 65 squared is 4,225.
• 6 × 7 = 42      5 × 5 = 25      
• The answer is 4,225.

How about finding the square root? We begin by looking at the numbers in the thousands and hundreds place. In the answer of 1,225, we would use the 12. Think of the factors of 12 that are consecutive numbers. In this case, they would be 3 and 4. Use the smaller of the two which, in this case, is 3. Now place a five after it. You now know the square root of 1,225 is 35.

Thirty-five represents the length of one of the sides of a square that contains 1,225 squares.

Now, try some numbers on your own. When you get comfortable with the "trick", try it with your students. They will find out that math can be magical!

The Best Laid Plans. . .Writing Lesson Plans

Lesson plans have always been an Achilles heel for me.  I have taught for so-o-o long, that how to teach the lesson as well as knowing the content is not an issue.  I always have a Plan B, C, and D ready - just in case.  I now teach on the college level where no one checks my plans; however, I still write an outline for the day so I know that I have covered the important points. 

My first job, when I retired from our local school system, was teaching math at a private school.  Mind you, I had been teaching math for over twenty years; yet, the administrator wanted me to do detailed plans which had to be turned in every Friday. I grudgingly did them, but would add little comments in the comment section. That space became my way of quietly venting; so, I would write such things as:  "So many lesson plans; so little time. Writing detailed plans is not time well spent.  To plan or to grade, that is the question.  I am aging quickly; so, I need to make succinct plans."

My supervisor finally relented and allowed me to do an outline form of plans. However, he visited often to observe my teaching, which I didn't mind.  At least he knew what was happening in my classroom.  I have learned from teaching and observing student teachers that anyone can come up with dynamite plans, but the question is: "Do the plans match what the teacher is doing in the classroom?"  Remember Madelyn Hunter?  Oh, how my student teachers hated her lesson plan design, but they did learn how to make a good plan. To this day, I still do many of the items such as a focus activity and a lesson reflection at the end.


My Husband's Lesson Plans for a Week in October

As many of you know, my husband is a middle school science teacher. He is the "Sci" part of my name. Anyway, he is in his 43rd year of teaching, and he still does lesson plans - not the detailed ones we did our first couple of years of teaching, but plans he does have. He divides one of his white boards into sections using colored electrical tape as seen in the illustration on the left.  He then writes what each class is doing for the week in a designated square. In this way, the principal, parents, and students know the content that will be covered. Even the substitute (he is rarely sick) has a general idea of the day's activities. If plans change, he simply erases and makes the necessary corrections.

So what kind of plans are you required to do?  Maybe there are no requirements for you, but do you still write plans?  Are they in outline form or just brief notes to yourself?  I am interested in knowing what you do; so, please participate in the this conversation by leaving a comment.



Only $3.00

By the way, do you need a lesson plan that is easy to use, and yet is acceptable to turn into your supervisor or principal?   Check out my three lesson plan templates. One is a generic lesson plan; whereas, the other two are specifically designed for mathematics (elementary or secondary) and reading.  Checklists are featured on all three plans; hence, there is little writing for you to do. These lists include Bloom’s Taxonomy, multiple intelligences, lesson types, objectives, and cooperative learning structures. Just click under the resource cover.

Common Classroom Irritations

Have you ever noticed that the same old problems keep resurfacing year after year in your classroom? Isn’t it funny how the little things sometime put us over the edge? I can always deal with that “special” child, but the continuous line at my desk about drives me crazy. Here are two different classroom irritations which I find to be the most annoying plus some possible solutions to think about before school starts.

A. Getting a Drink; Using the Restroom

1)  Set the number of times each student may go per the week.

2)  Have a restroom pass so only one student is out of the classroom at a time.

3)  Count when the children are getting a drink at the drinking fountain such as 1-2-3.  This way everyone is given the same amount to time.
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4)  Keep a bottle of hand sanitizer by the door so children may use it before lunch to clean their hands. (Unfortunately, not all children wash their hands after using the restroom.)

B. The Pencil Sharpener

1)   Have a box of pre-sharpened pencils that all the children may use.

2)   Make a designated time when students may sharpen pencils. If you have an electric pencil sharpener, unplug it during the off limits time.

3)   Designate an individual to be the “pencil sharpener.” This can be a daily job in your classroom. This person performs the task of sharpening pencils before school, after school, or during any other designated time.

4)   Have two cups of pencils near the pencil sharpener, one for dull pencils and one for sharpened pencils. When a child’s pencil is dull, s/he places it in the dull cup and takes one from the sharp cup.

$2.00

Do you want additional ideas on how to solve common classroom irritations plus more ideas for the ones mentioned above? Check out the complete resource that fully discusses:

           1)  Children Who Are Always at Your Desk
           2)  The Pencil Sharpener
           3)  Getting a Drink; Using the Restroom
           4)  Tattling
           5)  Stress – Especially at Test Time
           6)  Teasing
           7)  Unmotivated Students

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