Unlocking Fractions for the Confused and Bewildered - A New Approach to Teaching Fractions

I wish I understood this!

I teach remedial math on the college level, and I find that numerous students are left behind in the mathematical dust if only one strategy is used or introduced when learning fractions. Finding the lowest common denominator, changing denominators, not changing denominators, finding a reciprocal, and reducing to lowest terms are complex issues and often very difficult for many of my students.

I classify my students as mathphobics whose mathematical anxiety is hard to hide. One of my classes entitled, Fractions, Decimals and Percents, is geared for these undergraduates who have never grasped fractions. This article encompasses how I use a different method to teach adding fractions so these students can be successful. Specifically, let's look at adding fractions using the Cross Over Method.

Below is a typical fraction addition problem.  After writing the problem on the board, rewrite it with the common denominator of 6.

Procedure:

1) Ask the students if they see any way to multiply and make a 3 using only the numbers in this problem.

2) Now ask if there is a way to multiply and make 2 using just the numbers in the problem.

3) Finally, ask them to find a way to multiply the numbers in the problem to make 6 the denominator.

4) Instruct the students to cross their arms. This is the cross of cross over and means we do this by cross multiplying in the problem.

5) Multiply the 3 and 1, then write the answer in the numerator.  *Note: Always start with the right denominator or subtraction will not work.

6) Next multiply the 2 and 1 and write the answer in the numerator. Don’t forget to write the + sign. *Note: One line is drawn under both numbers. This is to prevent the students from adding the denominators (a very common mistake).

7) Now have the students uncross their arms and point to the right using their right hand. This is the over part of cross over. It means to multiply the two denominators and write the product as the new denominator.

8) Add the numerators only to find the correct answer.

9) Reduce to lowest terms when necessary.

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It is important that students know the divisibility rules for 2, 3, 5, 6, 9 and 10. In this way, they can readily reduce any problem. In addition, it is extremely important that the students physically do the motions while they learn. This not only targets the kinesthetic learner but also gives the students something physical that makes the process easier to remember. The pictures or illustrations for each technique also benefit the visual/spatial learner. Of course, the auditory student listens and learns as you teach each method. 

I have found these unconventional techniques are very effective for most of my students.  If you find this strategy something you might want to use in your classroom, a resource on how to add, subtract, multiply, and divide fractions is available by clicking the link under the resource cover. A video lesson is included to help you.

Geometry Humor Can Make Mathematicians Smile

I 've been using Pinterest for as long as I can remember, and I love it. Not only do I post many resources and teaching ideas there, but I learn so-o-o much. For example, I learned how to pack one suitcase with enough stuff for a week. (My husband is thrilled with this one.) I also learned that when you fry bacon, to make a small cup out of aluminum foil; pour the bacon grease into it; let the grease harden; then close up the aluminum cup and toss it into the trash. That is one I use all of the time!

On my Pinterest account I have a board entitled Humor - We Need It! I post many math cartoons or humorous sayings there. My favorite subject to teach my college remedial math students is geometry, and I have plenty of corny jokes that I intersperse into my lessons. Here's one.

What did the little acorn say when it grew up? Gee- I'm - A - Tree! (Geometry)

Or about this one?

What did the Pirate say when his parrot flew away? Polly-Gone (Polygon)

Here are some other geometry funnies from Pinterest.

Try placing a riddle or cartoon in the middle of a test.  I often do, and I know exactly where the students are by their laughs.  It helps them to relax and maybe get rid of those mathphobic tendencies.  I hope these math cartoons brought a smile to your face.  Have a great week of teaching!

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You might also like Geometry Parodies, a four page handout that includes 20 unusual definitions of geometry terms. Each definition is a play on words or a parody. Twenty-six geometric terms that are possible answers are listed in a word bank, but not all of the words are used in the matching exercise. An answer key is included.

Does A Circle Have Sides?

Believe it or not, this was a question asked by a primary teacher.  I guess I shouldn't be surprised, but in retrospect, I was stunned. Therefore, I decided this topic would make a great blog post.

The answer is not as easy as it may seem. A circle could have one curved side depending on the definition of "side!"  It could have two sides - inside and outside; however this is mathematically irrelevant. Could a circle have infinite sides? Yes, if each side were very tiny. Finally, a circle could have no sides if a side is defined as a straight line. So which definition should a teacher use?

By definition a circle is a perfectly round 2-dimensional shape that has all of its points the same distance from the center. If asked then how many sides does it have, the question itself simply does not apply if "sides" has the same meaning as in a rectangle or square.

I believe the word "side" should be restricted to polygons (two dimensional shapes). A good but straight forward definition of a polygon is a many sided shape.  A side is formed when two lines meet at a polygon vertex. Using this definition then allows us to say:

1) A circle is not a polygon.

2) A circle has no sides.

One way a primary teacher can help students learn some of the correct terminology of a circle is to use concrete ways.  For instance,  the perimeter of a circle is called the circumference.  It is the line that forms the outside edge of a circle or any closed curve. If you have a circle rug in your classroom, ask the students is to come and sit on the circumference of the circle. If you use this often, they will know, but better yet understand circumference.

For older students, you might want to try drawing a circle by putting a pin in a board. Then put a loop of string around the pin, and insert a pencil into the loop. Keeping the string stretched, the students can draw a circle!

And just because I knew you wanted to know, when we divide the circumference by the diameter we get 3.141592654... which is the number π (Pi)!  How cool is that?

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If you are studying circles in your classroom, you might like this resource. It is a set of two circle crossword puzzles that feature 18 terms associated with circles. The words showcased in both puzzles are arc, area, chord, circle, circumference, degrees, diameter, equidistant, perimeter, pi, radii, radius, secant, semicircle, tangent and two. The purpose of these puzzles is to have students practice, review, recognize and use correct geometric vocabulary in a fun, non-threatening way.