Please pick either "quotient" or "ratio" in fractions and provide real math class examples (What kind of activities? how do you teach? Using what materials, visuals, etc?) on the following topics:
1) comparing and ordering
2) relative size of fractions
3) improper and mixed fractions
4) equivalent fractions
5) renaming/simplifying of fractions
6) operating on fractions (add, subtract, multiply, divide)
When I have taught fractions in the past the key has always been to use visuals.
1)When teaching how to put fractions in order, or to compare them, the first step is make the fractions comparable. To do this, you must make the denominator of the fractions the same. Then the student can concentrate on simply putting the top numbers (numerators) in sequential order.
To show this, I would choose a concrete object such as counters. I would have a "fraction mat," a white piece of paper with blank fractions (just the fraction dividing bar shown ready for manipulatives). I would place the correct number of counters on top and bottom to show the numerator and denominator. Then I would show the students how if the fractions had the same number of counters on the bottom they would be in the same "family" and you could put them together.
-This "family" method begins when we first introduce fractions. The numerator is introduced as the first name and the denominator is the last name, or the family name of the fraction.
We make the fractions comparable by reducing the fraction (dividing by both the top number and bottom number by the same number to create a small fraction)
2) When discussing the relative size of fractions, it is important to remember "the larger the denominator, the smaller the fraction. A visual is also very important for this. Showing the same object multiple times, each time shaded in to represent a different fraction, will give students a visual explanation of what they are working with. This will also help them understand why 3/4+3/4 must equal more than one whole. A good example of this visual can be seen at: https://webmail.nn.k12.va.us/owa/ although I would use a more defining shape ...
This solution provides several strategies, techniques, and activities for teaching fractions. Ideas for visuals, web resources, and teaching materials are included.