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Joe Champion and Ann Wheeler

A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.

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Robin S. O'Dell

Using a rule as a seesaw helps students steady their understanding of the mean.

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Pamela Edwards Johnson, Melissa Campet, Kelsey Gaber, and Emma Zuidema

Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.

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Trena L. Wilkerson, Tommy Bryan, and Jane Curry

Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.

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Katie L. Anderson

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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Terry L. Kurz and Jorge Garcia

An alternative method for teaching prime decomposition explores using tools rather than factor trees.

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Aimee J. Ellington and Joy W. Whitenack

A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.