Ordering Fractions

In teaching maths, I find one of the best ways that students learn is through hands-on activities. 

"Concrete - Pictorial - Abstract" Approach to Maths 

Read this book by David Sousa to learn more about this approach. Essentially, the approach takes a unit of math and argues that students learn best by starting with working with concrete materials, moving to then using the strategy with a pictorial representation and finally moving to abstract problem.

This website has a wonderful example of this approach: http://www.loganschools.org/mathframework/CPA.pdf

The example is working with a worded problem relating to money.

Concrete: Students use play money to solve the problem.

Pictorial: Drawing out the problem with images of the money.

Abstract: Using the number operations to solve the problem.

So when I was teaching "ordering fractions with like denominators" to my class, I began with the concrete (using fraction pieces) and then moved to the pictorial (using flash cards). I combined concrete and pictorial by giving students a fraction flash card and having them arrange themselves to create a number line of fractions with the same denominator. Students were not allowed to speak to each other when arranging themselves so it ensured that the students all used their own knowledge to understand ordering of fractions. Having students move around to represent fractions is an excellent way of keeping students engaged and showing clear representations of fractions. It also allows students to stretch and have a change of pace from sitting down for an activity.

 For more information on the Concrete-Pictorial-Abstract approach, please read the following:
http://www.loganschools.org/mathframework/CPA.pdf
http://www.k8accesscenter.org/training_resources/CRA_Instructional_Approach.asp
http://fcit.usf.edu/mathvids/strategies/cra.html