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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.

By sorting non-standard as well as garden-variety geometric shapes, children see enough contrast to recognize what features make particular shapes special. Other fun activities connect elementary school geometry with early algebraic ideas and build a robust interconnected mathematics. See classroom video and take home activities for your students.

Participants will engage in and take home classroom-tested elementary school activities that bring out deep mathematical ideas. This presentation also shows teachers the power of extreme examples and near-miss non-examples, and how sorting and classifying activities can help children literally sort out their mathematical ideas. One style of activity, in which the teacher remains silent, rivets students’ attention as they must watch for clues and listen to each others’ conjectures.

Classifying is natural, part of how we construct categories and learn language; mathematics adds the refinement of articulating and then reasoning about attributes and relationships among them, creating matching rules (e.g., functions) and building yet new categories from the results. We will show, with video and activities, how children do this.