Comparing Fractions

Common Core Georgia Performance Standard MCC.4.NF.2

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

When given any two fractions and asked to compare, it is sometimes difficult to determine which fraction is greater than another fraction. This is especially the case when the two fractions don't share a common denominator. For the purposes of this post, I am going to assume the students that I am working with are familiar with the concept of a common denominator and how to find one.

However, given two fractions without common denominators, how can we compare the two?

Visual Model Method

One way to compare two fractions would be to draw a picture and then make a comparison based upon your drawing. This method is not always the best route to take when working with paper and pencil. However, a computer program that gives you exact measurements can show this method with great ease. To work with this method, follow this link to an activity and work the problems listed in the google document.

Common Denominator Method

The second way to compare two fractions is to find a common denominator and then compare the numerators. A common denominator can alway be found by multiplying the denominators of both fractions. For example, to compare 1/2 and 3/8, we can give the two fractions the common denominator 2 x 8 = 24 in order to compare them. In order to represent 1/2 in units of twenty-fourths, you must multiply the numerator and denominator by 12. Thus, showing that 1/2 is equivalent to 12/24. Then, you must represent 3/8 in units of twenty-fourths. To do so, you must multiply the numerator and denominator by 3. Thus, showing that 3/8 is equivalent to 9/24. Since 9 units of 1/24 is smaller than 12 units of 1/24, then one can assume that 12/24 is greater than 9/24 (12/24 > 9/24). Follow this link to an activity containing a further explanation and problems to solve using this method.

Benchmark Method

The final way to compare fractions is to compare each fraction to a particular "benchmark" fraction. Some examples of good benchmark fractions are 1/4, 1/3, 1/2, and 1. In order to use this method, it is perhaps best to use the given fractions as units of length so that you can say that the fraction that is the closest distance to the benchmark (without surpassing the benchmark) is the greater of the two. Follow this link to view a video and work with this method.

So there you have it...three different ways to compare fractions. If you're a student who'd like more practice or an instructor who's looking for more supplemental activities for your kids, the following games should suit your needs:

Balloon Pop Fractions

Tug Team

Fractions Dolphin Racing

WELCOME!

Throughout this semester, this blog will serve as a means to share my thoughts, ideas, and potential techniques in regards to the lessons covered in my MATH 7020 class at the University of Georgia. Specifically, this blog will focus on various ways to "flip the classroom" concerning specific lessons covered by my professor (Dr. Sybilla Beckmann-Kazez). 

As a self-proclaimed computer-whiz, I am particularly interested in placing a heavy emphasis on technology as a tool to "flip" the aforementioned lessons. It is my hope that these posts will serve as a lesson plan of sorts and show how, exactly, I would go about "flipping a classroom" that covers the same material that Dr. Beckmann's course covers.

Prior to showing you how I would flip the classroom, I should discuss what "flipping the classroom" really means.

As shown in the MADDrawProductions video above, "flipping the classroom" is a technique in which teacher's can have their students cover the required curriculum without sacrificing the individualization and one-to-one time 

with their students. The traditional teaching model has teachers spending the class period standing in front of the class lecturing and having the students perform assignments outside of class. The "flipped" model does what it's name suggests and turns that model on it's head. Instead of surrendering the vital time with the teacher in order to hear the lecture, the students are assigned to watch, read, and investigate the content material outside of class. This allows precious class time to be spent actually working on assignments in which a teacher may be of assistance. 

Another important characteristic of the "flipped" model is that it allows children to learn the material at a pace that is beneficial to them. For students who struggle with the material, the ability to have more one-to-one time with the teacher in class may allow them to finally grasp it. On the opposite end of the spectrum, a student who may find an assignment relatively easy and boring may benefit from this model by moving ahead to more difficult tasks or serve as a peer tutor to another classmate.

Although I am a big proponent of the "flipped" classroom model, there are some foreseeable shortcomings that a teacher may face. Some of these shortcomings include:

• An increased work-load on teachers in the "pre-planning" phase of their year
• Requires a high degree of trust between students and teachers
• May become interrupted by the need to teach for standardized testing
• Relies on an availability of technology for the students wether it be at home, in class, or public access to a computer lab

Despite these shortcomings and those not listed, I am adamant that this model best suits how I would approach teaching as a profession.


Here's a cool infographic taken from Knewton's website pertaining to the "flipped" classroom model:

Created by Knewton and Column Five Media