Writing Papers - Using a Graphic Organizer

I am currently teaching a Personal Development college class which is required for all new in-coming freshmen. In this class, we learn about learning styles, AVID strategies, how to take notes, how to read a textbook, etc. Their final project is a poster with an accompanying paper.  Here are the guidelines I give my students when it comes to writing the paper.

1) This paper should link and connect your ideas with any aspect of self, identity and personality concepts, mindset or learning styles we have discussed in class. In other words, use the class readings and discussions as a “lens” through which you view this person. Do this by using specific vocabulary used in class (e.g. conscious identity claims, growth or fixed mindset, grit, introvert or extrovert, learning style, soft and hard skills, etc.). 

2) Be sure to discuss how and what made this person successful. You might discuss their background, how and where they were raised, what challenges they overcame to succeed, how they reacted to failures and mistakes, what gave them the desire to succeed. 

3) This is not a facts paper about the person. This is about the character traits and attributes of the individual. Although facts can be included, most facts should be on the poster part of this project.

The first semester, the papers were just awful. I could use other words, but needless to say, they were painful to read. The next semester, I created A Graphic Organizer for Writing Papers. My students were amazed at how much easier writing a paper was. Many had never used a graphic organizer like this in English; so, this whole concept was new to them. (This was hard for me to believe, but I guess on the college level, such visuals are rarely used.) 

Only $2.75

This graphic organizer not only helped my students to arrange ideas thus communicating more effectively, but it also facilitated understanding of key concepts by allowing the students to visually identify key points and ideas more efficiently.

The blank graphic organizer found on Teachers Pay Teachers is divided into 11 sections, one for each paragraph. The students write the main idea followed by five details for each paragraph, not in sentence form but in a few words. Separate grids for the introduction and conclusion paragraphs are included. Even though there are 11 paragraphs, the organizer can be reduced to include as many paragraphs as you desire. My students were required to write a paper that was about two pages in length (500 words) when typed; so, this worked well in getting them to that point. Why not take a peek at the preview to see what you think? And if you choose to purchase the item, I would love your feedback.

I trust your students will find this graphic organizer easy to use as well as being a helpful aid in writing papers.

Algebraic Terms - Finding the Greatest Common Factor and Least Common Multiple Using a Venn Diagram

I tutor math at the college where I teach. Many of those students have been confused on how to find the greatest common factor for a set of algebraic terms. Having an elementary background, I introduce them to a factor tree which, believe it or not, many have never seen.

When just a rule is given by an instructor, often times, students get lost in the mathematical process. I have found that utilizing a visual can achieve an understanding of a concept better than just a rule. A Venn Diagram is such a visual and helps students to follow the process and understand the connection and relationship between each step of finding the GCF and LCM.

It's important to always begin with the definitions for the
words factor, greatest common factor and least common multiple. If a student doesn't know the vocabulary, they can't do the work! I continue by explaining and illustrating what a factor tree is (on your left) and how to construct and use a Venn Diagram as a graphic organizer.

Let's suppose we have the algebraic terms of 75xy and 45xyz. I have the students construct factor trees for each of the numbers as illustrated on the left.

Then all the common factors are placed in the intersection of the two circles. In this case, it would be the 5 and the xy. 

The students then put the remaining factors and variables in the correct big circle. Five and three would go in the left hand circle and the three 2’s and the z would be placed in the right hand circle.

The intersection is the GCF; so, the GCF for 75xy and 40xyz is 5xy.   To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle.

5 × 3 × GCF × 2 × 2 × 2 × z = 15 × 5xy × 8z = 240. The LCM is 600xyz. 

Free Item

This method is applicable and helpful in algebra when students are asked to find the LCM or GCF of a set of algebraic terms such as: 25xy, 40xyz. (LCM = 200xyz; GCF = 5xy) or when they must factor out the GCF from a polynomial such as 6x²y³ + 9xy². Using a Venn Diagram is also an effective and valuable tool when teaching how to reduce fractions. 

Are you interested in finding out more about this method?  Then download my newest free resource entitled: Algebraic Terms and Fractions - Finding the Greatest Common Factor and the Lowest Common Multiple Using a Venn Diagram. 

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!