One of the reasons why fractions are often considered difficult to teach and learn is that they are often introduced with more complexity than makes sense. For example, 1/2 is treated as a different "kind" of number from 2 1/2 (one called a "fraction" and the other called a "mixed number") and working with them is taught separately. By contrast, we would never think of treating 0.5 and 2.5 as different "kinds" of numbers.
Think Math! introduces fractions as numbers on the number line, and introduces order of fractions by comparing them to 0, 1, and then 1/2, developing all the ideas of equivalent fractions and the arithmetic of fractions naturally and directly connected with the arithmetic of whole numbers. The result is much easier for students to grasp and master quickly.
This PowerPoint presents the essential mathematical ideas, the Think Math! approach, and the reasons Think Math! takes this approach. Explanatory notes accompany the slides.
Download now! (Revised 25 Jan 2013.)