2. The concept of "how", accompanies the concept of "why. The "how" something works is teaching the mechanical pieces of the lesson. This is often boring to the child and not very well received, but if combined with an insightful "why" lesson you will have a far simpler task ahead of you. Each child will process the information differently, so you may need to alternate the focus of lessons by using one period going over the how and another going over the why and supplementing with practice sheets.
3. Clarifying the term "Equivalent" and Finding A Common Demoninator: Perhaps the most crucial part of teaching equivalence in fractions is teaching the children how to find a common denominator. The term itself is intimidating, but the task is not impossible. The best way to teach children how to find a common denominator is to use manipulatives. The fact that Students' have misconstrued the equal sign is a topic that has been researched for more than thirty years (Weaver, 1971,1973).
It might be beneficial to start off with discussing with the class what the term "equivalent" means to them. At least by doing so we can gage where our students are from a terminology standpoint. This would be beneficial if applied the terms numerator and denominator as well. Because we are dealing with rather large terms it helps to have visual aids. This is where the use of manipulatives comes in handy. Manipulatives are an essential teaching tool which allow children to learn visually.
B. The Concept of Finding Equivalent Fractions Using Manipulatives.
The problem with textbooks and workbooks is that often the children are distracted by the instructions and fail to use the visual aid. Children move from addition and subtraction (concepts that they have likely been using well before their formal education began on the topic) and are suddenly thrust into an area which is completely foreign. Cursory review of math text and exercise books reveals a great deal of "words" which I think are intimidating. Yes there are pretty pictures with bunnies, pies, balls and whatnot. Yet children still fail to become engaged. Why not turn the lesson into a visual demonstration that you and the children can enjoy Moreover, by watching the children actively participate, we as teachers are able to assess their true comprehension. This is the advantage of using manipulatives. Additionally, it is a wonderful way to insure complete class participation.
C. Steps I would teach students in finding Equivalent fractions.
I have found that children of all ages are very interested in detective work. There is a sense of power and self confidence that comes with solving a mystery. Television is replete with various shows that show crime scene investigations along with the science behind it. Moreover, both girls and boys seem to have an equal interest in the field. I would suggest to my students that we are CSI detectives. I would suggest that the first thing that we might want to do is to ID (identify) our fraction. Included with that identification would be all of the alias our fraction might use to evade our