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Triangle Center Technology

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

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GPS: From Folding to Dynamic Geometry Environments

In this month's Growing Problem Solvers, we focused on supporting students' understanding of congruence and similarity through rigid motions and transformations. Initial understandings of congruence and similarity begin in first grade as students work with shapes in different perspectives and orientations and reflect on similarities and differences.

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Problems to Ponder

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that span grades PK-12, arranged in order of grade band. Links to the problem answers are available in this department.

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Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.

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Fractions are Numbers, Too!

Student understanding of fractions as numbers, a foundational element of fraction sense and a critical prerequisite of work with operations, is explored through real-world connections.

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Quick Reads: The Different Representations of Rational Numbers

a good idea in a small package

Students' preferences when working with particular representations are explored.

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Gain insight into students' understanding of the concept of fraction as operator as well as their reliance on rote procedures to convert fractions to decimals.

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Systematic Interventions for Teaching Ratios

Consider this research-based intervention approach to ratio using concrete, semiconcrete, and abstract representations to help students who struggle with this concept.

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Orange You Glad I DID Say “Fraction Division”?

Students explore multiplicative comparisons and the meaning of remainders using their own concrete representations, including orange wedges.

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Solutions: Chewing (on) Gum

This department showcases students' in-depth thinking and work on previously published problems. The December 2012/January 2013 hands-on exploration of the history of chewing gum appeals to a wide range of learners. It was a perfect followup to a multiplication unit that a third-grade class in Pennsylvania had just studied.